IRUVX-PP Experts Report. A. Lindblad, S. Svensson, K. Tiedtke

Transcription

1 This compendium serves both as a summary of the reports generated by the IRUVX experts on optics and photon diagnostics and as an introduction to Free Electron Lasers, their function, and some of the necessary technologies to make them work. A compendium on beam transport and beam diagnostic methods for Free Electron Lasers The ambition has been to encompass the subject of Free Electron Laser technology in an introductory manner (part I), which supports the rather deep excursion into photon diagnostic methods that follows (part II). The list of references is extensive and could be used for more in depth studies. IRUVX-PP Experts Report A. Lindblad, S. Svensson, K. Tiedtke Members of IRUVX-PP WP7 and WP3 Expert Groups Photon Beam Transport and Diagnostics and Metrology for FEL Optics: Rafael Abela, Günter Brenner, Anna Bianco, Marion Bowler, Roberto Cimino, Daniele Cocco, Henrik Enquist, Uwe Flechsig, Christopher Gerth, Anthony Gleeson, Fini Jastrow, Ulf Johansson, Libor Juha, Pavle Juranić, Barbara Keitel, Jörgen Larsson, Andreas Lindblad, Eric Louis, Bernd Löchel, Rolf Mitzner, Paul Morin, Robert Nietubyć, Luca Poletto, Paul Radcliffe, Amparo Rommeveaux, Mark Roper, Frank Siewert, Ryszard Sobierajski, Andrey Sorokin, Giovanni Sostero, Sibylle Spielmann-Jaeggi, Svante Svensson, Cristian Svetina, Muriel Thomasset, Kai Tiedtke, Peter van der Slot, Hubertus Wabnitz, Christian Weniger, Marco Zangrando. This work is supported by IRUVX-PP, an EU co-funded project under FP7 (Grant Agreement ). Partners of IRUVX-PP the preparatory phase of EuroFEL EuroFEL_Cover_final.indd :04

2 Imprint Publishing and contact: Deutsches Elektronen-Synchrotron DESY IRUVX-PP Project Coordinator Notkestr. 85, Hamburg, Germany Tel.: ISBN This compendium is neither for sale nor may be resold. Editors: Dr. Andreas Lindblad, Prof. Dr. Svante Svensson, Dr. Kai Tiedtke Copy deadline: March 2011 Cover layout: Monika Illenseer Printing: Konrad Triltsch GmbH, Ochsenfurt-Hohestadt Editorial note: The authors of the individual scientific contributions published in this compendium are fully responsible for the contents. Cover: FLASH experimental hall at DESY in Hamburg and diffraction image. (Photos: Heiner Mueller-Elsner / Agentur-Focus.de; DESY)

3 A compendium on beam transport and beam diagnostic methods for Free Electron Lasers IRUVX-PP Experts Report A. Lindblad, S. Svensson, K. Tiedtke Partners of IRUVX-PP the preparatory phase of EuroFEL

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5 This book was set with L A TEX using the memoir class

6 Foreword The development and use of X-ray free electron lasers have undergone a remarkable development during the last decade: the first lasing in the VUVat 100 nm wavelength was achieved in the year 2000; in Europe the soft X-ray free electron laser Flash started operations in 2005 followed by the hard X-ray facility Lcls in the USA; during the time of writing of this book the first seeded X-ray free electron laser has been commissioned, the Fermi@Elettra. During the following decade we will see upgrades to the currently operating facilities, as well as the emergence of new sources. Within the coming years there will be hard X-ray free electron laser operating on three continents: The European X-Fel, Lcls in North America and Scss in Japan. The progress in accelerator technology and in free electron laser science has resulted in emerging concepts for more compact and more efficient sources, which can make it feasible for national laboratories to build such facilities; In more or less advanced planning and design stages, this is under consideration in Sweden, Switzerland (SwissFEL), South Korea (PAL X-Fel) and other countries. Free electron lasers have unprecedented beam properties and are currently the most intense and well collimated man-made photon source in the UV to the hard X-ray range. A pulsed X-ray source like this allows for investigation of matter on the scales natural to the nano-world: femtoseconds and nanometers current development aims for X-rays on the natural atomic scales: attoseconds and Ångströms. As access to this type of source is becoming easier to gain the enthusiastic user community is ever expanding a significant step essential for lowering the threshold for scientists, often coming from the synchrotron or laser communities but not experts in the free electron laser field, to conduct experimental work utilizing the sources unique capabilities. As the field is relatively young (at least for the X-ray regime) the forthcoming decade(s) will see the field mature beyond pioneering experiments into a broad plethora of experimental applications with an equally broad and diverse user community from many different fields. Although obviously attractive with regards to photon beam quality, the construction, commissioning and operation of a free electron laser facility is technically very challenging. The accelerated electron beam needs to have very high quality from the very start, and throughout the accelerator and the magnet array of the undulator(s) requiring specific knowledge in, land development, beam dynamics and simulations, electron beam diagnostics, synchronization technology, undulator technology and laser seeding. The beam of X-rays with extremely high fluence needs to be transported to i

7 ii Foreword the user experiment with the resulting demands on X-ray optics with regard to surface characteristics, damage etc.in addition, each photonpulse needs to be diagnosed and its characteristics stored for later inclusion in data-analysis, for poly-color experiments (involving other laser pulses) information for pulse-synchronization needs to be available and so forth. In this phase, the funding programmes of the European Commission (EC) for the development of new research infrastructures helped interested European institutions enormously to join their forces for developing key technologies required for the design and construction of the next generation free electron laser sources in Europe: The European Fel design study project EUROFEL funded by the 6 th Framework Programme for a period of three years, , focused on components the electron accelerator and the free electron laser itself. This project was followed by Iruvx-PP, the preparatory project for a sustainable future European FEL consortium called EuroFEL. Iruvx-PP includes significant funding for further technical developments regarding both the electron and photon beams. This compendium is an amalgamation of the collaborative efforts of two of Iruvx- PP s workpackes, the third and seventh whose efforts were focused on X-ray photon beam optics and diagnostics. Contrasting the mainly political and structural objectives of Iruvx-PP, it provides an immediate practical result and delivers timely together with an introduction to free electron laser technology and science an urgently needed text which details the latest developments in the field in a manner also accessible for non-experts. Ithasnotbeenintendedtoprovideacomplete indepthaccountofthewhole fieldof free electron laser science but rather to provide: (i: a presentation of key technologies and concepts needed to understand the various requirements that are imposed on the electron and photon beams, which limitations different technology choices impose on the final output of the free electron laser; (ii, detail, sometimes expand and put into context the various internal reports generated in the workpackages. Taken together both ambitions have generated a nice recollection of the collaborative efforts of the members constituting the workpackages in an accessible form that hopefully will help future students and colleagues to get acquainted with the exciting field of free electron laser science. Josef Feldhaus, Hamburg, 25 th February, Scientific coordinator of the Iruvx-PP project

8 Preface Caveat Lector This book s humble beginning was as a summarizing report of the collective efforts within the 3 rd & 7 th workpackage of the Iruvx-PP programme. During the time of writing (the last twelve months of the programme) the members of the workpackages produced reports on their findings often containing reviews of the various fields where the undertakings took place. Each such report have been, more or less, basis for sections and indeed whole chapters in this book, notably in the second part. The reports titles and their authors are mentioned in the very beginning of the chapters where material from them have been used. A summarizing report may be interesting in itself, but to heighten the appeal to a broader audience and to future students and colleagues it was thought that when adding context to the reports (who by themselves deal mainly with X-ray optics and photon diagnostic methods) a good introductory textbook describing the various challenges pertaining to work and development of free electron lasers could be realized. Hence the first part of the book describes the physics and concepts that govern free electron lasers. The various components of a free electron laser are also described from the electron gun to the undulators, and some X-ray optics. The second part of the book focuses heavily on diagnostic methods that can be used to quantify the properties of the free electron laser photon beam. In the last chapters of part two the current running and planned facilities are described in the light of what we have learned in the first part of the book, planned and performed experiments are described as to give an orientation of what scientists are trying to achieve with the facilities. The bibliography of this book contains both references to books and articles that reflect the current state of the art, at least for part two of the book, at the time of writing (February 2011). No such list is ever complete and will soon become dated however through citations to those papers the reader will soon find where the field have developed. Without any doubt many of the references will remain key references for quite a foreseeable time. iii

9 iv Preface Acknowledgements I would like to extend my gratitude to my co-editors Prof. Df. Svante Svensson and Dr. Kai Tiedkte for giving me the opportunity to work with this book. I also thank them for the many nice discussions and the good criticism during the authoring process. Naturally I also like to thank the authors of the reports which constitute parts of this book without which I would literally have started with a blank page. Thanks to the many nice presentations on the workshops and free electron laser conference last year I have been kindly introduced to the fantastic subject of free electron laser science. Again, for the opportunity to work with it and writing a book about it I will be forever grateful. Andréas Lindblad, Uppsala, 28 th February, 2011.

10 Contents Foreword Preface Contents i iii v I Free electron lasers a primer 1 Introduction Historical exposé & scientific background Laboratory X-ray and UV/Vis photon sources X-ray tube and anode sources Synchrotron light sources Lasers High Harmonic Generation Lasers Free electron Lasers Development of X-ray free electron lasers Seeding schemes esase HGHG EEHG Harmonic afterburners Definitions used throughout the book Brilliance and Brightness Emittance Synchrotron radiation and its properties Radiation from a moving charge Maxwell s laws Charged particle at rest or moving with constant velocity The fields from a charge in arbitrary motion Frequency and coherence of synchrotron radiation v

11 vi Contents 2.2 Radiation from a bending magnet Undulator radiation The undulator equation Microbunching Interaction between the electron beam and the radiation field Exponential gain Scaled free electron laser equations Sase Coherence properties Free electron laser hardware A prototypical FEL amplifier Electron guns General requirements Thermionic emitters Photocathode emitters Normally conducting guns Superconducting guns Summary Radio-frequency driven accelerators The accelerating RF-field Energy gain in a radiofrequency driven accelerating cavity Warm technology: Copper Superconducting technology Undulators Undulator tolerances example X-ray optics Demands on optics precision at free electron lasers Focussing mirrors back-reflecting geometry example Damage Diffraction gratings Monochromators Beam attenuators Beam-splitting methods Introduction Beam-splitter specification Amplitude division beam splitters Partially transmitting materials Crystal diffraction beam splitters Gratings Grids Wavefront division beamsplitters Beamline apertures Knife-edge mirrors Knife-edge crystals Fresnel bi-mirror Slotted or perforated mirrors

12 Contents vii Structured arrays Time-based splitting Summary Techniques requiring the least development Techniques requiring more development II Beam diagnostics 6 Introduction Diagnostics categorization Subcategorizations Conclusion Spectral diagnostics: Intensity & Energy X-ray spectrometry Intensity/Beam energy Gas monitor detectors Calorimeters Solid state devices Photon-energy Ion time-of-flight Electron time-of-flight Beam cross-section diagnostics Introduction The ideal cross-section diagnostic Distribution of diagnostics along the beam Content of this chapter Definitions Direct imaging of the beam Imaging a replica of the beam Summary of imaging techniques Scanning techniques Scanning wire Scanning crossed wires Scanning slit Scanning pinhole Scanning knife-edge Summary of scanning techniques Ionization beamprofile detectors Imaging ion chambers Fluorescence detection in residual gas monitors Sampling techniques Spot size Techniques useable with unattenuated beams Photoionisation saturation of rare gases Techniques requiring attenuated beams Wire, knife-edge and slit scans

13 viii Contents Photographic film Gas-filled detectors Charge coupled device (CCD) Multichannel plate (MCP) Solid State Detectors Position and centroiding Sampling techniques Wavefront measurements THz/IR techniques Thermal detection Photonic detection New detectors IR and THz beam profiling Summary Pulse length, profile and jitter Introduction Cross-correlation techniques Electro-optic techniques Autocorrelation techniques Intensity autocorrelation Autocorrelation techniques for complete pulse characterization Frequency Resolved Optical Gating (FROG) Polarization-gate FROG (PG FROG) Self-diffraction FROG (SD FROG) Transient-grating FROG (TG FROG) Second-harmonic-generation FROG (SHG FROG) Third-harmonic-generation FROG (THG FROG) Spectral Phase Interferometry for Direct Electric-field Reconstruction Reflectivity modulation Streak cameras Summary Free electron laser experiments The holy grails of free electron laser experiments Molecular movies Single-molecule/nanostructure imaging Single-shot spectroscopy/imaging Time-resolved spectroscopies UV/Vis pump-x-ray probe spectroscopy Nexafs Imaging and Crystallography Non-linear X-ray science Photoionization Free Electron Laser facilities Operating facilities Flash Injector and accelerator

14 Contents ix Undulators sflash Flash-II Experimental stations: Scss X-fel Scss Injector & accelerator Undulators X-ray free electron laser/ Spring Injector & accelerator Undulators Injector & accelerator Undulators Experiments: Lcls Linac Coherent Light Source Injector and accelerator Undulators Lcls-II proposal Experiments: Facilities under construction The European Xfel Injector and accelerator Undulators Experiments: SwissFEL SwissFEL injector test facility the SwissFEL proposal Injector & accelerator Undulators Experiments Proposed facilities PAL-X-fel Accelerator Undulators Outlook & Conclusions Current trends More compact sources and alternative approaches Higher repetition rates Polarization control Coherence & Seeding Harder X-rays Conclusion Bibliography 201

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17 Part I Free electron lasers a primer

18 1. Introduction Written by: A. Lindblad 1.1 Historical exposé & scientific background Ever since the advent of electricity it has been possible for humankind to produce artificial light sources not emanating from chemical processes, i.e. different from candles, bon-fires, and the like. With the discovery of X-rays by Wilhelm Röntgen in for which he subsequently got the first Nobel prize in physics His discovery was made possible with the advent of vacuum tube discharge sources in the end of the 19 th century in a discharge tube (invented by William Crookes and others, Figure 1.1) electrons travel between two electrodes in a gas tube between which a high electric voltage have been applied, Röntgen discovered that, even though he covered the cathode, using cardboard, wood, books (and seemingly whatever came in handy) a phosphorous screen placed in the other end of his laboratory room still glowed. In part II of this book we will see how such screens are still in use to characterize X-ray sources 2. Figure 1.1: A Crookes tube from 1910 s. The interaction of X-ray photons with matter can generate many answers in the scientific inquiry spurred by the rapid development of quantum theory and thus our understanding of atoms and matter, combined with the development of X-ray lightsources with ever-increasing quality (Figure 1.3). As evident in the short list below both scientific topics ranging from biology, chemistry and physics and industrial research and development (notably the pharmaceutical industry) have greatly benefitted from the development of this area of science. X-ray imaging medical imaging, materials science, safety 1 Reported in Über eine neue Art von Strahlen ( eine neue Art von Strahlen) published the December 28, 1895, where Röntgen refers his discovery as X-rays (a notion which the modest Röntgen preferred, in many languages this type of radiation is still known as Röntgen-rays). An english translation can be found in Nature 53, (January 23, 1886). The discovery was deemed important enough to be translated and communicated within a month of the original publication. 2 For instance, Section 8.3, (see page 113) 3

19 4 1. Introduction X-ray diffraction crystallography, materials science X-ray absorption and emission spectroscopies materials science, long range order. X-ray photoelectron spectroscopies materials science, chemical bonds, spinresolved Of course the technological development of techniques for particle accelerators, sample handling, radiation detection, vacuum have both received and given synergetic effects in society at large. High energy photons or particles from radioactive sources 3 is an alternative as particle sources, though they lack tunability and the energy is often too high to be used for many of the important applications of X-rays. Applications of radioactive radiation have been found elsewhere, notably in radiation therapy, as gene-markers, the carbon-14 age-determination method etc. In Ernest Rutherford s laboratory (1909), Hans Geiger and Ernest Marsded used a beam of alpha particles generated from a radioactive decay of the element radium impinging on a gold foil to find out how charge was distributed within atoms. They intended to investigate the prevailing plum pudding model 4 where the positive charge was delocalized (the pudding) and the electrons submerged (as the plums). The gold foil was surrounded by a sheet of zinc sulfide which would fluoresce when hit by alpha particles. From the plum model it was expected that the alpha particles would not scatter at all, however it was observed that a significant fraction of the alphaparticles was backscattered by very small concentrated positive charged objects in the gold film this was taken as a strong indication of the existence of an atomic nucleus, a result which was not expected. In 1911 Rutherford explained the experiment in terms of scattering which resulted in the Rutherford planetary model of the atom. In Rutherford s laboratory significant developments followed this, especially the development of particle accelerators with the purpose of splitting the atom. A note on the development of some particle accelerator techniques and concepts emanating from Rutherford and his students, relevant for this book, can be found on page 52. For a lot of medical purposes (therapeutic and otherwise) radioactive materials are increasingly phased out to the benefit of particle accelerators where control of the particle energy is possible and thus the interaction length and dose can be controlled. Theories on the nature of light a small historical primer In the 17 th century investigations into the nature of light were pursued by means of the modern scientific method. Light was thought of as waves or particles both with their shortcomings. The discourse between the two, seemingly incommensurate, standpoints were ultimately resolved by the advent of quantum mechanics in the beginning of the 20 th century which argue that light (and matter) can behave both as waves and particles. 3 That is: photons, electrons or their antiparticles: positrons, or 4 He nuclei gamma, γ, beta, β ± and alpha, α radiation, respectively. The greek names for radiation were all coined by the english physicist Ernest Rutherford. For his work on radioactivity transmutation, the notion of half-life, and the differentiation between alpha and beta rays he received the Nobel prize in chemistry The plum pudding model of the atom was proposed by J. J. Thomson in 1904.

20 1.1. Historical exposé & scientific background 5 Robert Hooke and Christiaan Huygens both published theories (In the 1660s and late 1670s respectively) on light that built on light rays being waves. The main proposition was that light, being waves, would not be affected by gravity thus slowing down upon entering a denser medium. The wave theory though assumed the existence of a medium in which the waves could propagate through: the luminiferous æther 5. Isaac Newton described light as particles (corpuscles) to explain reflection of light (Opticks, 1704). Perhaps owing to his work on gravity, he postulated that the corpuscles were accelerated when they entered a denser medium, because of the larger gravitational influence on the particles from the medium, which helped explain refraction. Nowadays we know that this was a step in the wrong direction since the speed of light is slower in a denser medium than in a dilute medium. Investigations into the various properties of light such as refraction, reflection, polarization and diffraction undertaken in the beginning of the 19 th century tilted the balance in favor of the wave theory. However as both theories made different predictions on how the speed of light changed upon entering a denser medium the most convincing test to be made, i.e. measuring the actual speed of light had to wait until 1850 and Léon Focault for a precise enough experiment to be performed 6. His results favored the wave theory of light and thus put the particle theory of light out of the scientific limelight In the later part of the 19 th century James Clerk Maxwell formulated the governing equations of electromagnetism. His theory built on that electromagnetic waves travelled at a constant speed equal to the speed of light he published the notion that light was a form of electromagnetic wave in On the physical lines of force. A full theory, describing mathematically the behavior of electric and magnetic fields the celebrated Maxwell s equations 7 was published in 1873 by Maxwell in A treatise on electricity and magnetism 8. Heinrich Hertz confirmed Maxwell s theory by generating and detecting radiowaves in a laboratory setting and proving that radiowaves 5 The existence of the æther medium was cast into strong doubt by the famous Michelson- Morley experiment (this is the Michelson with the interferometer setup). They reasoned along the following lines: when the earth revolves around the sun it should produce a substantial wind in the æther medium thus, the speed of light would be slightly different depending on the experiment (at the earth surface) was facing the wind (foul wind) or facing from the wind (fair wind). The changes in speed of light, both daily and seasonal, was expected to be very small hence the need for an interferometer which would split up a beam and propagate the beams along long arms and recombine them, which would produce a interference pattern if the beams did not propagate in the same manner, i.e. a beam propagating parallel to the æther wind would propagate slower than one propagating perpendicular. Michelson and Morley combined their efforts in 1887 and their experiments cast doubt on, but did not disprove, the existence of the æther medium; their most important contribution remains the interferometer that bears their names. 6 The Fizeau-Focault apparatus consisted of a light source and a two mirrors spaced 35 kilometers apart. The mirror closet to the lightsource was rotating at a constant angular rate. The elapsed time for the light to pass the distance l between the mirrors is 2l/c (c being the speed of light). During the flight of the light the moving mirror will have rotated away from its original position. The angle at which the returning light is observed is then α = dα 2h dt c. A drawing of the original experiment can be found at: (From his collected works Volume Two - Recueil des travaux scientifiques de Léon Foucault, 1878). 7 Stated in detail below (see page 23). 8 The basic equations was in fact published already in 1865 in a paper entitled A dynamical theory of the electromagnetic field[1].

21 6 1. Introduction exhibited the same properties as light waves, e.g. reflection, refraction, interference and diffraction. Electromagnetic radiation can ionize atoms. This was discovered by Heinrich Hertz in 1886 in the course of the inquires described above. The apparatus Hertz used was a high voltage induction coil to create a discharge between two pieces of brass and a piece of copper wire with a brass sphere on one end and on the other a sharp point directed towards the sphere. The basic idea is that the charges in the discharge oscillate back and forth thus emitting electromagnetic radiation; if the emitted light would create another spark between the tip of the wire and the brass sphere light would then be proven to be electromagnetic waves. The photoelectric effect During 1886, Hertz carried out a series of experiments with his apparatus showing that electromagnetic waves were reflected through prisms, that it was polarized etc., just the same properties as light waves. The only snag was that it sometimes was very hard to see the tiny spark created at the wire tip 9, to improve this Hertz enclosed the wire in a dark casing which reduced the intensity of the spark. He soon found out that if the part of the casing shielding the discharge was removed the intensity was not reduced and that glass, but not quartz, reduced the intensity quartz being transparent to ultra-violet light. By using a quartz prism to disperse the electromagnetic waves it was also found that the greatest intensity of the detected spark was obtained in parts of the dispersed light which were above the visible range. Hertz reported his observations in Annalen der Physik 10 but offered noexplanations of thephenomena 11 herather concluded that this phenomenon was probably of no practical use whatsoever as we will see below this was a rather pessimistic conclusion. In 1899, J.J. Thompson observed that negative particles were emitted when a metal surface was exposed to ultra-violet light. Later, in 1902, P. von Lenard observed that the emitted particles kinetic energy 12 did E kin f 0 frequency f Figure 1.2: A minimum frequency of the photons are required to ionize a material. depend on the color (frequency) of the light and not on the intensity of the light. In one of his annus mirabilis (1905) papers Einstein gave a mathematical description of the photoelectric effect[3]. The ionization was described to be caused by the absorption of a light quantum and that different materials had different onset frequencies f 0 for electron emission was explained by that the size of the energy packet needed to be large enough to overcome the first ionization potential of the material. 9 As one remedy it was suggested that a suitably prepared frog s leg would serve equally well as a detector. 10 In, Über einen Einfluss des ultravioletten Lichtes auf die electrische Entladung[2]. 11 The spark in the detector was enhanced by charges knocked out from the material in the detector by photons from the ultra-violet parts of the spectrum emitted from the discharge. 12 More exactly he measured the stopping potential of the emitted electrons. He performed the experiment by shining light on the positively charged plate of a parallel plate capacitor and observing the potential that causes the induced current to become zero.

22 1.2. Laboratory X-ray and UV/Vis photon sources 7 For this work he was awarded the Nobel prize of physics 1921 for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect. The use of quantized energy-levels was used in 1900 by Max Planck to explain the distribution of radiation from a black body. To avoid the ultra-violet catastrophe of classical electrodynamics, i.e. that the radiation energy distribution tends to infinity for short wavelengths, he assumed that the energy of the emitting oscillators was quantized. By stating that light consists of discrete energy packets, Einstein could formulate an equation that explained the photoelectric effect: ε kin = ω φ where the kinetic energy of the photoelectron is related to the frequency of the light and the work needed to escape the material. is Planck s constant (divided by 2π) and ω = 2πf is the angular frequency of the light. The slope of the line in Figure 1.2 is thus Planck s constant. In section 3.2, we will see how the photoelectric effect is utilized as one way to provide a high quality source of electrons to be used in accelerators. The effect also forms the basis for electron spectroscopy which is an important experimental field as well as a diagnostic possibility for free electron laser light sources (as elaborated upon in Section 7.3). 1.2 Laboratory X-ray and UV/Vis photon sources Peak Brilliance of X ray sources X-FEL Average brilliance of X ray sources Peak brilliance [Phot./(s mrad 2 mm 2 0.1% bandw.)] rd gen. synchrotrons 2nd gen. synchrotrons 1st gen. synchrotrons X-ray tubes Average brilliance [Phot./(s mrad 2 mm 2 0.1% bandw.)] X-FEL 3rd gen. synchrotrons 2nd gen. synchrotrons 1st gen. synchrotrons X-ray tubes Time Time Figure 1.3: Development of the brilliance of man-made X-ray sources. The brilliance is a measurement of beam quality that measures how directional and pointy a source in combination by how strongly it emits light within a certain bandwidth, (see page 19).

23 8 1. Introduction V anode V - + Water out Water in X-rays Figure 1.5: A schematic of an improved Crooks tube Figure 1.1. The development of X-ray sources with respect intensity and source quality have, as shown in Figure 1.3 developed superexponentially 13 since the end of the 19 th century. A technological development like this is logical, when one considers the accumulated knowledge of relevant physics and related areas 14. When the X-ray tubes reached their optimum potential, that is when the effort in terms of time and money did not yield enough payback to develop the technology further accelerator based synchrotron light sources took over as the developing technology. Currently both synchrotron storage rings and free electron laser develop in parallel since they satisfies different demands from the user community ω [kev] Figure 1.4: Generic spectrum of X-rays from a tube X-ray tube and anode sources source. The X-ray tubes used by Wilhelm Röntgen and others in the years leading up to and the first years into the 1900 s was limited in intensity (and brightness) largely by the power that the anode could dissipate without melting. In Figure 1.5 a schematic of an X-ray tube of a model dating from 1913 is shown. The electrons are produced by thermionic emission 15 from a heated tungsten filament serving as the cathode; the electrons are accelerated towards an anode target which is watercooled. This type of tube can produce powers up to 18 kw. The generic X-ray spectrum from a source which generates X-rays by bombardment of a target with electrons is presented in Figure 1.4. On top of a broad feature ranging over several kev of photon-energies sharp features emanating from discrete atomic 13 That is, for instance, faster than Moore s law for the transistor density of integrated circuits. 14 The rate of publication in physics and chemistry was also growing faster than an exponential curve during the first part of the 20 th century[4]. 15 Discussed further in the context of electron guns for free electron laser below in Section 3.2 (see page 47).

24 1.2. Laboratory X-ray and UV/Vis photon sources 9 transitions in the target which generates X-rays with precisely determined energies. The broad smooth feature arises from bremsstrahlung from electrons that decelerate in the target and thereby emits X-rays. An improvement still upon this is the rotating anode source where the area of illumination is increased to allow more efficient cooling of the anode by letting it rotate in vacuum. It is desirable to keep the illuminated spot as small as possible to increase the brilliance of the source. Since the surface temperature of the anode can easily reach above 2000 C the cooling needs to be very efficient and the rotation speed kept high. Modern rotating anode sources can produce up to 100 kw of X-ray power thanks to this development. Rotating anode sources are a mature technology which therefore is used for medical purposes (imaging and therapy) and as laboratory sources both for scientific research and in industry for material diagnostic purposes. Synchrotron light sources First generation synchrotron light sources were particle physics electron storage rings where the synchrotron light produced in the dipole magnets (used to bend the electron beam in a quasicircular orbit) was used by others in a parasitic fashion. For particle physics experiments, the production of light in the accelerating structures is a, more or less significant, problem. The first observation of man-made synchrotron light was published in 1947 [5]. Second generation synchrotrons were built in the early 1970s to dedicatedly supply synchrotron radiation for a growing number of researchers from various fields; the multitude of scientific disciplines attracted by synchrotron radiation can in part be explained by that the emitted spectrum is from the infrared to the hard x-rays with an well defined polarisation. The light was still produced in the bending magnets that accelerates the electrons so that the electrons can be stored in a quasi-circular orbit. Third generation synchrotrons are used today and use insertion devices, such as wigglers and undulators[6] to produce radiation with even higher brilliance and power. The insertion devices are periodic magnetic structures (Figure 1.8) which, stated bluntly, makes the electrons turn more often which produces a higher radiation power than just one bending magnet. However, since a wiggler do not need to bend the orbit and thus ideally should not influence it the magnetic field can be much higher which not only increases the radiation power but also shifts the wavelength of the photons upward (which is why wigglers are sometimes called wavelength shifters). An undulator has generally a lot more magnetic periods than a Intensity Photon energy Figure 1.6: Typical intensity distributions from dipole (dashed), wiggler (red, solid) and undulator (filled) radiation. wiggler with weaker magnetic fields which keeps the deflections from the central orbit small such that photons emitted at an earlier instant can interfere with photons emitted at future times which produces a build up of emitted power at certain frequencies. In chapter 2, we will investigate with some detail and rigor the properties

25 10 1. Introduction of undulator radiation as this is a prerequisite for the understanding of the free electron laser formalism. Figure 1.6 presents how the general appearance of the spectra from different insertion devices can look like. In the case of the undulator there is sharp peaks where the condition for positive interference is fulfilled. The peaks are distributed at multiples of the first resonance (i.e. harmonics of the fundamental energy where the condition is first fulfilled). Synchrotron storage rings provide almost a continuous source of radiation with repetition rates in the 100 s of MHz something which gives rise to high average power. The high repetition rate is often too much for time-resolved measurements which is why synchrotrons are sometimes run in low filling modes where only one or a few bunches of electrons travel around the orbit which brings down the repetition rate to the order of 1 MHz. The bunches are still relatively long (in the order of picoseconds); experiments demanding short pulses can use femtosecond laser slicing of the electron bunches before they pass through a bending magnet, or undulator, this modulates part of the electron beam and causes that part of the beam to emit a short pulse which is separated from the radiation fro the majority part of the bunch. One can conclude that synchrotron radiation has many attractive properties which, as mentioned, have made its use widespread over a broad range of scientific communities, i.e. tunable light with an (extremely) well defined polarization (which can be linear, circular or elliptical) available over a very large range of energies. It also have an inherent timestructure that can be manipulated to provide relatively long x-ray pulses in the MHz repetition rate domain; in combination with lasers other timestrutures other types of time-resolved experiments are enables. A (significant) fraction of the light is also transversely coherent, which enable imaging experiments making use of for instance phase contrast at X-ray wavelengths. Lasers The theoretical framework for the Laser was laid down by Albert Einstein in his Zur Quantentheorie der Strahlung [7] from In this paper he detailed how light quanta are absorbed and emitted by atoms 16. By introducing probabilities for the processes of absorption, spontaneous emission and stimulated emission he was able to quantify how atomic spectral lines was formed. The processes of absorption and emission of light works in the intuitive way; Stimulated emission describes how the presence of electromagnetic radiation causes atoms in a higher energy state to decay into a lower one. One can then imagine a process where, if we were to pump atoms to a higher energy state, decays from this state will then in turn stimulate other atoms in the ensemble to decay to. If, in a medium, the number of atoms in the higher energy state is larger than the number in the lower energy state the amount of stimulated emission is larger than that absorbed in the ensable the amount of light in the medium is amplified. By placing this medium between two mirrors, an optical resonator, the light passes through the gain medium many times before it is extracted somehow, this gives rise to an even more efficient amplfication: we have a proper laser. The word (or acronym) Laser can be spelled out to Light Amplification by Stimulated Emission of Radiation. 16 Building on Max Planck s seminal paper from 1901 Ueber das Gesetz der Energieverteilung im Normalspectrum[8] considered to be one of the birthplaces for quantum theory.

26 1.2. Laboratory X-ray and UV/Vis photon sources 11 The first laser was built in 1960 by T. H. Maiman and consisted of an solid stateflashlamp pumped artificially grown ruby crystal (emitting red laser light at 694 nanometer wavelength)[9]. Shortly thereafter a laser with a gasmixture as a gain medium was demonstrated. The number of available laser media is large 17 and currently covers a wavelength range between millimeters down to below 200 nm. There is a multitude of non-linear optical processes that can be used to manipulate laser light. Of particular interest for the lasers to use together with free electron lasers is harmonic generation of shorter wavelengths. This phenomenon was first discovered in a quartz crystal in 1961[10], where integer multiples of the driving laser s frequency was observed. Third harmonic generation using a gas as a medium was observed a few years later[11]. The intensity of the generated harmonics drops very fast the process can be understood (in the regime of weak fields) as an atom absorbs several photons which in turn are emitted as one; the probability of absorbing n photons drops with n. High Harmonic Generation Lasers If one ventures out of the weak field regime there is a possibility for another process to occur: high harmonic generation. Laser light is shone into a gas sustaining high enough energy density (typically in the order of W/cm 2 a fraction of the laser power can be converted into (odd) higher harmonics of the original laser pulse. This allows for the creation of UV and even soft X-ray pulses. Typically the repetition rates for such systems range from a few Hz to KHz (the same as the driving laser) and even attosecond pulses can be created. High harmonic generation can be understood via a semi-classical picture[12]: A sufficiently strong laser field can perturb atomic potentials enough to allow the outermost electrons (illustrated as a red wave-packet in Figure 1.7). This allows the electron wave-function to tunnel out of the atomic potential into the continuum (2 in the figure) during the first half cycle of the laser pulse; during the second part of the laser cycle the electron wavefunction finds itself on a strongly attractive potential leading back to the atom where it came from upon recombination the system will emit the excess energy as a high energy photon with significantly higher energy than that of the driving laser. There is also the possibility of higher harmonics of this motion to occur and thence higher photon energies. Unlike in the weak field regime the intensity of the higher harmonics do not drop with the harmonic number in a simple decreasing manner. Indeed, the higher harmonics have roughly the same intensities up until a cut-off energy. This cut-off energy can be understood from the recombination model mentioned above, with the ionization potential of the medium being I p: E cut-off = I p U p and the pondermotive energy being the average energy of a free electron in the linearly polarized laser field E (with angular frequency ω. U p = e2 E 2 4m eω 2 17 Diagram of laser lines from commercially available sources: laser lines.svg

27 12 1. Introduction Laser field 3 X-ray photon 2 1 Figure 1.7: Illusration of the high harmonic generation process. This process is effective (that is, it works) for linearly polarized light elliptically polarized light accelerates the electrons in such a way that it misses the ionized atom on on the returning path so no recombination occur. At very high energy densities (10 16 W/cm 2 ) the magnetic term in the Lorentz force equation (Equation 2.5) becomes significant, which causes the acceleration to deviate from the intended return path. In the context of free electron lasers, ordinary lasers and high harmonic generation lasers are interesting both for experiments in combination with free electron laser radiation,i.e. two-color experiments as discussed in chapter 10, and as a way to increase the quality of the free electron laser light in ways that will be elaborated upon below (see page 15). 1.3 Free electron Lasers In a conventional laser the average output power is limited by how much of the unused power (which is significantly larger than the output power) that can be dissipated by the active medium. Moreover the light from a laser is seldom diffraction limited owing to heat effects in the lasing medium and non-linear processes taking place in the medium. Contrasting this is the free electron laser process which can be close to unity in efficiency. In a free electron laser the amplification of the electromagnetic field occurs by the interaction between an electron beam and the radiation field it creates when moving through a periodic magnetic structure. Hence the operating wavelength is tunable via machine parameters such as electron beam energy, and magnetic field strength. Figure 1.8 depicts three different ways of producing free electron laser radiation: bunches in a storage ring passes through a long undulator; an oscillator where the interaction where the electromagnetic radiation interacts with the electron bunches many times; an amplifier, where the electrons pass once through an long undulator structure the interaction between the electromagnetic field and the electron beam is strong enough for one pass to be sufficient.

28 Log radiation power 1.3. Free electron Lasers 13 Figure 1.8: Different ways of generating coherent laser radiation. From left to right, electrons are fed into a long undulator either from a storage ring or in a storage ring but with mirrors that reflect part of the pulse to modulate the electron bunch even further, or from a linear accelerator where the electron bunch gets modulated by the light field it generates. There is a number of free electron lasers operating in the world today (chapter 11), covering light wavelengths from the infrared to the x-ray regions. This book will cover free electron lasers that are providing light in the X-ray range, which are amplifiers operating in the high-gain regime. Sase The physical process that governs the function of a free electron laser is abbreviates Sase Self-Amplified Spontaneous Emission. In the next chapter we will discuss this in more detail, here follows a short introduction. The spectrum from the photons emitted from an electron bunch traveling through an undulator will contain a large degree of incoherent radiation and a small part of coherent radiation. The latter occurs since a small number of electrons, by chance, happen to be radiating coherently. In the undulator spectrum thus, a number of spikes will be seen on top of the broad spontaneous emission spectrum. As the occurrence Distance Figure 1.9: Growth of the radiated power in a Sase-mode as a function of travelled distance in the undulator. The process saturates when the microbunching is maximal.

29 14 1. Introduction Photons/s 0.03% BW Photon energy [ev] Figure 1.10: Computed Photon flux into 0.03% bandwidth at 3.63 ka at the Lcls at 1.5 Å wavelength. The two spikes are the 1 st and 3 rd harmonics of the fundamental Sase mode, which sits on a broad spontaneous radiation background. of the coherent radiation is random the number of coherently radiating modes per electron bunch will follow a Poisson distribution. The radiation field that is created from the acceleration of the electron bunch through an undulator in a storage ring is often considered to be weak enough as to not have an effect on the electron bunch, i.e. the electron bunches do not interact with the radiation field. This is true if the electron density is low enough and if the overlap between the radiation field and the electron beam is small. However, if the electron density is high enough and if the quality, (called emittance 18 ), of the electron beam is high the interaction between the electron beam and the radiated field can become substantial. If the interaction between the electrons in the bunch and the radiation field is strong enough a microbunching of the electron bunch occurs. This means that as the electron travels along the undulator structure the electron density becomes modulated with the wavelength of the radiation field. This enhances the coherent emission further, which in turn enhances the micro-bunching and amplifies the radiation field. The radiation mode thus gets amplified and the degree of coherence increases. The growth of the radiation mode s strength is exponential until the process saturates. Free electron laser radiation has a number of unique features owing to the amplification process outlined above. In Figure 1.10 an example of the brilliance from the Lcls free electron laser source is shown. The peak intensity and brilliance is many orders of magnitude larger than can be produced by other sources (Figure 1.3). The 18 See the discussion on emittance below.

30 1.4. Development of X-ray free electron lasers 15 average brilliance, which is limited by the (generally) low repetition rate of the driving linear accelerators are still orders of magnitudes above that of synchrotron storage rings. In the figure the two sharp spikes mark the fundamental and third harmonics of the Sase radiation modes. Those spikes sit on top of a significant spontaneous radiation background that encompasses several orders of magnitude of photon energies. Pulse lengths down to tens of femtoseconds are also orders of magnitude shorter than those of a synchrotron. Ordinary lasers and high harmonic generation lasers can surpass this figure but can not deliver the brilliance at X-ray wavelengths considered here. Free electron laser radiation has full transverse coherence (if the Sase process has reached saturation), i.e. it is diffraction limited. The Sase process only amplifies certain modes at the time (and possibly their harmonics) The spontaneous radiation spectrum extends very high up in photon energy, towards 1 MeV. 1.4 Development of X-ray free electron lasers The concept of free electron lasing was developed in the early 1970s[13]. The prediction that spontaneous emission from electron bunches traveling through a periodic magnetic field could experience exponential gain was demonstrated 1977[14]. The first free electron laser to reach saturation was the Leutl free electron laser located at the Advanced Photon Source at the Argonne National Laboratory, Illinois, USA[15]. During the 1980s and 1990s a significant research effort was conducted as to develop the theory for free electron laser as to investigate the feasibility of increasing the photon energies into the UV and X-ray ranges[16 18]. The first lasing of a hard X-ray free electron laser occurred in 2009[19]. Around the world there is a number of laboratories harboring free electron lasers operating with photon energies across the electromagnetic spectrum, from the microwave region to the hard X-ray regions. Facilities for the VUV/X-ray region demand rather high electron beam energies, thus linear electron accelerators (retired from use for particle physics experiments) have been fitted with undulators and hence converted to free electron laser; Flash in Hamburg and Lcls in Stanford are from this category. Dedicated facilites for the X-ray range are also being deployed, for instance the Fermi@Elettra in Italy and the Scss in Japan. In chapter 11 currently operating facilites and some of those under various stages of commissioning and planning are described in more detail. 1.5 Seeding schemes As discussed previously, the Sase process starts up from shot-noise in the electron beam thus, even though the transverse coherence is very good (optimal) the longitudinal coherence is poor. This means that the photon spectrum is different for each pulse, both regarding the number of modes that are radiating, which frequencies dominate the spectrum and the beam energy. This can be seen in Figure 1.12: the frequency and intensity distribution vary on a shot-to-shot basis. Intuitively this phenomenon can be understood by considering the

31 16 1. Introduction Name Radio Microwave Infrared Visible UV X-ray Gamma Wavelength [m] Buildings Humans Butterflies Needle Point Protozoans Molecules Atoms Atomic Nuclei Frequency [Hz] Corresponding temperature of radiating blackbody 1 K 100 K 10,000 K 10,000,000 K 272 C 173 C 9,727 C ~10,000,000 C Figure 1.11: Wavelengths and frequencies in the electromagnetic spectrum. Figure 1.12: The Sase photon spectrum from the Flash free electron laser. stochastic start of the amplification process; in the beginning of the undulator many modes radiate energy, those serve as seeding radiation for the duration of the traversing of the (long) remainder of the undulator. The modes that fit the resonance condition for the undulator spectrum will get progressively more amplified whereas those modes that are not radiating resonantly do not gain in energy. The resonance condition may be fulfilled by several modes simultaneously, more or less well which give rise to many spikes in the final spectrum. For each new bunch the process start

32 1.5. Seeding schemes 17 over again and thus a new set of modes arise from the stochastic start-up. Naturally there is a desire to have a more stable free electron laser photon spectrum. Both the jitter in time between pulses, the pulse energy and the spectral content prohibit the maximum performance of both the free electron laser itself and the possible experiments that can be performed. To circumvent the stochastic startup of the radiation-field amplification the most straightforward way at least conceptually is to pre-modulate the electron beam s energy with a strong laser field, then convert this energy modulation into a density modulation. The conversion between energy and density modulation can be done in a magnetic structure (chicane or wiggler/undulator) since the different parts of the bunch take different paths through such a structure. Figure 1.13: Energy modulation of an electron bunch. esase If the electron bunch are modulated with a laser in a wiggler and subsequently pass through an undulator structure significantly shorter gain length (and thus shorter undulators) can be achieved as compared to normal Sase operation (hence Enhanced- Sase)[20]. ESASE Modulator Radiator HGHG High-Gain Harmonic-Generation is a frequency upconversion scheme, designed to upconvert the fundamental frequency of the laser to a much higher frequency[21]. This scheme has been demonstrated[22] and it includes a short modulator where the energy-density conversion starts, followed by a chicane (two bending magnets that bends away and returns the beam along the orignal path). The chicane compresses the bunch further which enhances the density modulation even more before the beam enters the second undulator (the radiator) where the free electron laser process takes place. Since the electron bunch is pre-modulated when it enters the radiator the spectrum from this type of free electron laser is significantly more intense in the fundamental mode (up to 10 6 times) and narrow (since, ideally, all the spectral intensity is put into one mode and its harmonics). The shot to shot repeatability is also

33 18 1. Introduction much better as the free electron laser pulse is a up-converted version of the original laser pulse (at least the part of the spectrum arising from the part of the electron bunch that became modulated)[22]. The Hghg scheme can of course be cascaded, HGHG Dispersive section Modulator Radiator that is putting several stages in front of each other, to achieve increasingly shorter wavelengths. EEHG The Echo-Enabled Harmonic Generation free electron laser scheme[23] have recently been demonstrated experimentally at the Next Linear Collider Test Accelerator at the SLAC National Accelerator Laboratory, Stanford, USA[24]. The principle is similar to that of the Hghg scheme above with the important difference that two modulators with two different laser seedings is used before the undulator. This enables more intricate control of the path differences the particles with different energies takes in the two different chicanes allowing the density modulation of the electrons to occur at a shorter frequency than the original laser pulses; at the entrance of the radiator one can get a pre-bunched electron beam for a significantly shorter wavelength than any of those of the seed-lasers. Harmonic afterburners Harmonic afterburners consist of one or more undulators placed after the main radiator. They are either used to enhance the radiated power in a harmonic of the fundamental thus reaching shorter wavelengths[25]. Extra undulators can also be used to control the polarization of the emitted light to some degree[26, 27].

34 1.6. Definitions used throughout the book Definitions used throughout the book Brilliance and Brightness The intensity of a source can be regarded as the flow of energy per unit time per unit source area I = de dtdxdy The flux of a source Φ Φ = 1 di ω dω dω is defined as the number of photons per unit time, per unit surface area of the source. As figures of merit for a light source the intensity and flux are rather blunt tools since they say nothing about the directionality of the source. If we differentiate the flux with respect to the solid angle dω we obtain the brightness: B = dφ dω with units [photons/s/mm 2 /mrad]. Brilliance, or spectral brightness[28] is defined as the number of photons emitted per unit time, per unit solid angle, per unit source area inside a bandwidth chosen to be 0.1% B r = d2 Φ dωdω thus the unit [photons/s/mm 2 /mrad/0.1%bw]. This defines the brightness of a source inside a certain frequency envelope centered around a certain frequency ω. Spectral brightness is closely related to the emittance of the of the electron beam source. The emittance is the product of the beam divergence and the transverse size of the beam along each direction perpendicular to the propagation of the electrons. Emittance When an ensemble of charged particles propagates through an accelerator they move along an orbit through the accelerator structure (composed of guiding magnets and accelerating cavities etc.). Each particle in the ensemble move along a trajectory, i.e. the orbit is described by the ensemble motion is an average of the individual trajectories. The instantaneous position of an particle can be described by the tripple [x,y,s] (as defined in Figure 1.15). In a linear accelerator the ŝ direction coincides with the ẑ coordinate. For a complete description of the particle s state we also need to define coordinates that are proportional to the the momentum of the particles: [x,y,e], with x = p x/p, y = p y/p which describe the angular deviation, perpendicular to the direction of motion, from the ideal orbit. For relativistic particles the energy is approximately equal to the particle momentum E cp. In some instances it is more convenient to define the energy in terms of its deviation from the ensemble average, as this gives a measure which is independent of the total energy.

35 20 1. Introduction Potential energy surface and phase plot X X 1 2 Figure 1.14: Part of a quadratic potential energy surface with a phase portrait. The circles describe orbits with constant energy, i.e. a particle would move along those circles. A beam can thus be defined as occupying a certain volume in a 6-dimensional phase space. This volume stays constant if the ensemble s motion is such that the total energy of the system do not change (i.e. evolves according to Hamilton s equations of motion) 19. For convenience the phase space of the ensemble is usually represented by two-dimensional projections x,x ; Figure 1.14 shows a phaseportrait and a potential energy surface for a particle moving in a quadratic potential (for instance a gravitational force), the circles represent orbits with constant energy. Horizontal emittance (for instance along the x direction) ε x is the area of an ellipse encompassing the majority of the particles (usually this is taken to be the area of a root-mean-square (rms) sense). A measure of the average phase space area covered by the particles in the x,x -plane can then be computed, assuming a distribution along the ideal orbit such that x = x = 0 ε x = x 2 x 2 xx 2 This quantity is conserved as long as the motion in this direction is independent from the motion in the other directions (something which is common in accelerators)[29]. 19 As a consequence of Liouville s theorem, i.e. that the volume in phase space stays constant if the system evolves under the influence of conservative forces only. Forces that depend on position only are conservative, e.g. gravity and Coloumb forces. It is less common that forces that depend on the momentum are conservative, an important exception to the latter is magnetic forces which do not change the momentum magnitude, only its direction; thus magnetic forces are conservative.

36 1.6. Definitions used throughout the book 21 x 2 ˆx ŷ ŝ x 2 Figure 1.15: Definition of the rms width and angular spread of particles in a bunch. In Figure 1.15 the quantities inside the square-root are depicted. The emittance, as defined above, is also preserved as long as the particles are not accelerated. It is therefore customary to use the normalized emittance which makes the emittance comparable even if the beam has undergone acceleration[30]. The normalized emittance is related to the beam energy via the relativistic factors β = v and γ = 1 c 1 β 2: ε n = βγε which is invariant along the accelerator structure in the absence of radiation. Consequently, the transverse size of a charged particle beam shrinks as it gets accelerated as βγ. As will be seen below, the emittance needs to be very low for a free electron laser as the generated radiation needs to overlap substantially with the electron beam for the lasing process to occur. Together with the current and the beam energy the transverse and longitudinal emittances are very important figures of merit for accelerators.

37 22 1. Introduction Summary X-rays can be used to investigate the electronic and geometrical structure of matter by spectroscopic or scattering experiments respectively. Thus they are used by a broad scientific community for experiments, i.e. for both fundamental and applied investigations in medicince, biology, chemistry and physics. The brilliance (quality) of X-ray sources have developed exponentially since the discovery of X-ray radiation. Today the most brilliant, man-made, X-ray source is the free electron laser. Other X-ray sources are X-ray tubes, anodes, synchrotron storage rings and high-harmonic generation (HHG) lasers. Compared to solid state lasers and HHG lasers a free electron laser do not have any limit on the output power imposed by the laser medium, it being an electron beam in vacuum and not a gas or a solid. The basic process that governs free electron laser amplification is abbreviated Sase Self Amplified Spontaneous Emission. This process describes how the radiation field is amplified by a relativistic electron beam moving through a periodic magnetic field (i.e. in an undulator) when the radiation field modulates the electron beam density (microbunching). A nice introductory description of the free electron laser process can be found in Ref. [31]. Sase is a positive feedback process and the amplification of the radiation field can be exponential. The process reach saturation when the electron beam is microbunched with the periodicity of emitted radiation. The process starts up from electron shot-noise in the beam, thus the number of radiation modes follow a Poisson distribution. The spectrum of the emitted photons is broad (from incoherent spontaneous undulator radiation) with a number of sharp spikes corresponding to the coherent radiation from Sase-modes. The radiation in the modes have full transverse coherence and each mode is diffraction limited. The energy and intensity distribution from each pulse is unique since the process starts up from noise. Methods to manipulate the electron beam serving to enhance the shot to shot repeatability of the spectrum utilize lasers to seed the beam before entering the periodic magnetic structure (undulator). In fortuitous cases this can lock the radiation into a single Sase-mode which then becomes one million times more intense then the corresponding unmanipulated Sase-spectrum.

38 2. Synchrotron radiation and its properties Written by: A. Lindblad 2.1 Radiation from a moving charge This chapter contains certain elements of classical electrodynamics, which is needed in the following chapters. For the underlying framework and definitions see the book of Jackson and Schwinger s article from 1949[32, 33]. Maxwell s laws S2 Gauss law for the electric field states that the flux of the electric field through a closed surface S is proportional to the enclosed total charge: E da = Q S ǫ 0 (2.1) Analogously there is a Gauss law for the magnetic field B; the field lines of the magnetic field must be closed thus the net flux through a closed surface must be zero, i.e. B da = 0 (2.2) S This implies that there are no magnetic monopoles, if there were this equation would also have a source term as the equation for the electric field. For the electric and magnetic fields to be coupled the flux of either the electric or the magnetic fields S needs to change; if the flux of the magnetic field 1 E changes over time, then the electromotive force along a closed loop on the surface S is proportional to the flux: IS I B E dl = ΦB (2.3) S t Figure 2.1: Surfaces sharing the same The sum of the magnetic fields through a closed bounding contour S. loop on a surface enclosing a current is proportional 23

39 24 2. Synchrotron radiation and its properties to that current (Ampere s law): B dl = µ0i. However, as seen in Figure 2.1 it S is easy to construct a situation where the same bounding contour is shared by two surfaces where only one of the surfaces contain the current in Ampère s law, whereas the other one contains a changing electric field here we use a discharging parallelplate capacitor for this purpose; even though no charge flows between the capacitor plates there is still a current I D flowing inside the capacitor (although there is a vacuum between the plates here), by Ampère s law we have just stated there should be an induced magnetic field. Using Gauss law for the electric field, assuming a static surface, we can get: dq dt = I = ǫ0 ds E t E Sǫ0 t S S This current and the conduction current must be equal since they must sum to zero. We divide by the area of the surface element S and use current densities (i.e. divide I by the area as well, I/S = J) and we get the result: the Ampère-Maxwell equation: ( ) E B dl = µ 0 J+ǫ 0 ds (2.4) t S Equations 2.1, 2.2, 2.3, and 2.4 are the Maxwell equations that consitute the basis for classical electrodynamics; via Gauss and Stoke s theorems we can formulate them also in differential form as Gauss law E = ρ ǫ 0 Gauss law for magnetic field B = 0 Maxwell-Faraday equation Ampère-Maxwell equation E = B t B = µ 0J+µ 0ǫ 0 E t The electric and magnetic fields also couple via the force the fields exert on a charge moving in them in the expression for the Lorentz force equation: F = q[e+v B] (2.5) The energy flux of the fields can be found via the expression for Poynting s vector: S = 1 µ 0 (E B) = 1 cµ 0 E 2 ẑ (2.6) Charged particle at rest or moving with constant velocity A charged particle at rest surrounds itself with an electric field that can be written (Coulomb s law): E = 1 q 4πǫ 0 r 2ˆr This is a special case of Gauss law for the electric field, Equation 2.1. Since the electric field is static in the situation when the particle is at rest no magnetic field is induced (Ampére-Maxwell equation 2.4. In the case of a uniformly

40 2.1. Radiation from a moving charge 25 moving charge we have a constant current which creates a static magnetic field (Equation 2.4 again) no electric field is induced (Equation 2.3). In both cases considered here no change in the kinetic energy of the particle occurs, thus no energy exists that can be transferred to the electromagnetic radiation field. The fields from a charge in arbitrary motion Following Feynman[34, 35] we write the electric field from a charge in arbitrary motion as E = q [ ( ˆr r d ˆr + )+ 1c ] d 2 4πǫ 0 r 2 c dt r 2 2 dt 2ˆr (2.7) and the magnetic field cb = ˆr E. The primed quantites is to remember that we have to evaluate these quantites at retarded time t = t r this is a consequence c of the finite speed of light, at the observation point p in Figure 2.2 signals observed at time t was created when the charge was at t. The second term corresponds to a linear extrapolation of the Coulomb field (velocity times the time-delay r /c), such that when the velocity tends to zero we retain the normal Coulomb field. The first two terms are both proportional to the inverse squared distance and thus decays fast with respect to the distance, at least compared to the third term which is proportional to the inverse distance. Therefore, the last term in the equation above is called the radiation field since it survives even when r. Electric and magnetic field lines must be to be continuous; looking at the right-side of Figure 2.2 we can consider a charge that get accelerated a very short time towards a non-relativistic velocity (v c). The signal at X that was emitted at time t = 0 have its front at a distance c t from the signal that was emitted at t = t; for the electric field lines to be continuous there must exist a perpendicular component of the electric field which is proportional to the velocity in that direction (and thus the acelleration). The parallel component is given by the first two terms in the equation for the electric field above. p 1 ẋ r c ẋ r 2 r ẋt 2 1 ϑ ẋ ẋ c t E E Figure 2.2: Signalsreceived at the observationpointp attime twascreated atthe retarded time t. Equation2.7 attempts to account for the particles motion by linearly extrapolating the Coulomb-field to guess the particles current position.

41 26 2. Synchrotron radiation and its properties E /E = ẋ t c t = ẍ t t = ẍ t = {t = r/c} = ẍ r c t c c 2 The magnitude of the electric field outside the sphere is given by Gauss law, which gives the parallel component: E = q 1 4πǫ 0, yielding the perpendicular component r 2 we seek: E = q ẍ 4πǫ 0 c 2 r sinϑˆr = q 1 d 2 4πǫ 0 c 2 dt2ˆr (2.8) in the relativistic case we must take care to evaluate the derivative at retarded time. Radiated power from a charged particle in non-relativistic motion Equipped with the expression for the Poynting vector and the expression for the electric and magnetic fields for a charge in accelerated motion we are now equipped to find the expression for the radiated power. In Figure 2.2 we can see that we can write the radiation part of the electric field (the other terms will fall off as 1/r 4 in the expression for the Poynting vector and thus carry an insignificant energy flux compared to the radiation field) q 1 E = (2.9) 4πǫ 0c 2 rẍsinϑ with direction ˆr (ˆr ˆx). the magnetic field we get straightforwardly cb = ˆr E. Inserting this into Equation 2.6 we get: S = 1 c 4 q 2 (4πǫ 0) 2 ẍ 2 To get the total radiated power we integrate over all angles P = S ds = π This is the Larmor formula[36] for the total radiation power 1. Radiated power from a relativistic charged particle 0 r 2 sin2 ϑ (2.10) S 2πr 2 sinϑdϑ = q2 6πǫ 0c3ẍ (2.11) Equation 2.10 describes the radiation field from a charge in non-relativistic motion, with the typical sin 2 ϑ look of the power distribution (which is similar to that of a dipole-antenna); the left-side of Figure 2.3 shows the radiation lobes from a nonrelativistic charge moving along the z-axis that gets accelerated in the direction of 1 The Larmor formula is the result one obtains within the framework of classical electrodynamics. If one accounts for the quantum nature of the emitted photon, and thus the resulting recoil exerted on the electron, the radiated power is slightly less[33]: ( P = P Larmor 1 55 ) 16 ε 3 E with ε as the classical photon energy and E the total energy.

42 2.1. Radiation from a moving charge 27 the x-axis. We will now try to get a look-and-feel for how the radiation power is distributed upon acceleration at relativistic velocities. In the rest-frame of the particle (i.e. a reference frame moving with the same speed as the particle) S the radiation flux will look as in the non-relativistic case described above, that is a dipole-field; this is shown in the left side of Figure 2.3. A radiated electromagnetic wave with wavelength λ in a certain direction in the rest-frame will, will have a wavevector k in that frame. To see how this wavevector looks in our laboratory frame we must do a Lorentz-transformation. If we consider the velocity to be solely in the ẑ direction we can write the Lorentztransformation from the starred to the unstarred system as k z = 2γkz, where γ is the relativistic factor 1 = 1 v2 c β2. As we approach more and more relativistic velocities more and more of the radiation is focussed in the forward direction; the opening angle of the radiation cone shrinks: θ kx k z k x 2γk z = tanθ 2γ 1 2γ This is a very important property from the point of view of light producing accelerators, the more the particles get accelerated, the more focussed the radiation gets. It can also be seen from the bottom in the figure that smaller opening angles get shifted to higher frequencies than those with larger opening angles thus there will be a spatial frequency distribution of the electromagnetic radiation with the highest frequencies in the middle; this is a angle dependent Doppler shift of the radiation. To find the magnitude of the radiated power one must generalize Larmor s formula to take into account relativistic effects (see e.g.[32]); for the treatment here it suffices to know that for the same accelerating force leads to a factor γ 2 higher radiation power it is thus more economical to have light producing structures that accelerate the particles transversely rather than accelerating them longitudinally (at least from the light production point-of-view). This is also the reason as to why linear colliders are historically the weapon of choice for particle physics experiments where, notably for light particles, synchrotron radiation losses is undesirable since the particle energy is the critical parameter. If we let r cmc 2 = e 2 define the classical particle radius r c and ρ the bending radius of the orbit caused by the deflecting magnetic field, the total radiated power becomes: P γ = 2 3 rcmc2 cβ 4 γ 4 ρ 2 (2.12) InFigure 2.3 we see thatmost ofthe radiation will beradiated in theforward direction with a polarisation perpendicular to the bending magnetic field (σ mode) however, some of the power will be emitted in a mode off axis with circular polarization (π mode). It can be shown [37] that the relative power between the modes are: P σ = 7 8 Pγ, Pπ = 1 8 Pγ Frequency and coherence of synchrotron radiation Synchrotron radiation from a charged particle in a circular orbit at relativistic speeds is characterized by a searchlightlike lobe of radiation of width 1 = φ, this angular γ

43 28 2. Synchrotron radiation and its properties a a Θ ˆx ẑ θ v c v c k θ k z k x L k θ k z k x kx Figure 2.3: Nonrelativistic (left, starred quantities) and relativistic (right) dipole radiation fields. With k = 2π/λ we get from the starred reference frame to the laboratory (observers ) frame via a Lorentz transformation L. interval is swept during the time t during which the particle moves the length l = v t = v φ ω 0 all in the particles frame of reference. Due to the relativistic effects in play (length contraction and time dilation) an observer will measure a compressed pulse width of length: t = t l c ) (1 v 1 = c γω 0 = t v t = c ( )( 1 v c 1+ v c 1+ v c ) ) (1 v t = c 1 γω 0 [ ( ) ] v 2 1 c ) (1 v φ c ω 0 1 = 1 2γω 0 2γ 3 ω 0 In the last steps we have, since v c in an accelerator, made the approximation 1+v /c = 2. The spectral width of a pulse of duration t is ω 1/ t. Thus, in the case of synchrotron radiation we can expect to observe radiation with frequencies up to about ω Max 2γ 3 ω 0 The spectrum will consist of Fourier components nω 0 from n = 1 to n 2γ 3. A spectrum from a bending magnet in a storage ring will thus be a broad spectrum peaked at the critical frequency (see e.g. [32, 38]). The critical frequency is usually defined as the frequency where half the integral power lies below and half lies above this frequency. In a storage ring, or linear accelerator there also exist collective effects since there is a number of particles in the beam, say N; how the particles are distributed have a large impact on the emitted radiation. If we consider the case of a storage ring three cases can be discerned.

44 2.2. Radiation from a bending magnet 29 e 1 γ 1 γ t Figure 2.4: The time during which an observer is illuminated... The particles are evenly distributed in a constant current along the ring this leads to perfect cancellation of the radiation fields since their phases are evenly distributed. If every particle is closer than a typical wavelength (in a short bunch ) then their individual phase differences will be small and the field from each particle will be amplified N times leading to a N 2 fold increase in the radiated power. This is coherent radiation. If the particles are unevenly distributed in the ring then N of the particles will have phases that are not perfectly random 2. Then the fields from those N particles will amplify that of the N others which leads to that the incoherent radiation is proportional to N. In a synchrotron beam from a storage ring with bunches of N particles both incoherent and coherent parts of the radiation field are normally present (Equation 2.32). 2.2 Radiation from a bending magnet Asseen abovein Equation2.12, thepower is inverselyproportional totheradiusof the orbit squared. The upper limit for a single magnet is thus set by the strength of the deflecting magnetic field and the beam energy. To maximize the radiated power one thus needs to have smaller magnet gaps and higher magnetic field strengths combined with a high beam energy. Thus there exist a limit as of how intense radiation one can create with a bending magnet. For a single bending magnet there exist another side-condition that is that the magnet should not bend the electrons away from the orbit in the storage ring, thus a 2 Imagine that the emitted radiation is shot-noise thus characterizedby a Poisson distribution, then for a sufficiently large number of particles the signal to noise ratio will be the square root of the number of emitters, since the variance is N for a normal distribution which can be considered applicable since for large N the Poisson-distribution tends towards the normal distribution.

45 30 2. Synchrotron radiation and its properties too strong magnetic field can not be utilized. To circumvent this we can imagine an array of strong magnets that eventually returns the electron to the intended orbit. If the array of magnets are strong, such that the deflection from the central orbit is large so that the light pulses from different bunches do not overlap, we will get a spectrum similar to that of a single bending magnet but more intense and with the now stronger magnetic field shorter critical wavelength. Such a device is called a wiggler or wavelength shifter. The output power exceeds that of a bending magnet by twice the number of periods, i.e. 2 N. We can also imagine a device with a smaller magnetic field strength where the deflections from the central orbit is not too large, instead we employ many more poles to get the intensity stronger. In this type of scheme the emitted radiation field can positively interfere for certain wavelengths (this condition will be specified below) resulting in a spectrum with a fundamental radiation mode and its harmonics whose wavelength corresponds to a given combination of magnetic field strengths and beam energy. This type of device is called an undulator. In a free electron laser this device is a critical component which ultimately sets the properties of the emitted radiation. The output power exceeds that of a bending magnet by the square of the number of periods: N Undulator radiation The undulator was described already in 1951 as a source for synchrotron X-ray radiation [6]. In Figure 2.5 a schematic of the alternating-magnetic pole scheme of a permanent magnet undulator is shown usually the number of poles is much larger since the number of deflections for the electron bunch dictates the intensity and spectral quality of the radiation emitted (as we will derive below). θ ẑ λ u Figure 2.5: A schematic of the periodic magnet structure of an undulator. In yellow the electron path is shown. The undulator equation The undulator strength parameter K The magnetic field in an periodic magnet structure can be written, if we consider that we look at the structure from above as in Figure 2.5: ( ) 2π B(z) = B 0cos z ŷ = B 0cos(k uz)ŷ (2.13) λ u

46 2.3. Undulator radiation 31 Remembering the expression for the Lorentz force (Equation 2.5) and Newton s second law we can write dp dt = [ṗ] = e(v B) ṗx = evzby where in the last step we have used v = v zẑ; we have also used the approximation that the electric field created is weak enough so that the interaction is negligible later we will see what consequences occur when this is not the case (see section 2.5 at (see page 44)). this is the equation of motion for the electron in the periodic magnetic structure 3. If we insert Equation 2.13 into the equation of motion we get ṗ x = e dz dt B0cos[kuz] which after integration with respect to time gives: mγv x = eb0 k u sin(k uz) (the relativistic factor γ enters from the expression for relativistic momentum) which defines the undulator strength parameter K: v x = eb0 sin(kuz) = Kc sin(kuz) (2.14) m ek uγ γ If the deflection from the ẑ direction can be considered small we can use tanθ θ together with the approximation that v z = c to obtain: [ ] tanθ = vx vx θ = K v z c γ sin(kuz) Usually the non-dimensional parameter K is written as: K = λueb0 2πm ec B 0λ u (2.15) where the latter holds true if the magnetic field strength is measured in Tesla and the undulator period in centimeters. The condition of coherent emission In an undulator the transverse motion is small, thus significant parts of the radiation field emitted at different times will overlap as the electron transverse the undulator. This will result in positive and negative interference of certain wavelengths which are on or off resonance with the period of the magnetic field. The condition for a wavelength to experience positive interference can be derived without too much effort in terms of the undulator strength parameter, the relativistic factor γ and the deflection angle.

47 32 2. Synchrotron radiation and its properties A λ ucosθ θ B θ ẑ λ u Figure 2.6: Light traveling the path AB interferes with light emitted from A at an angle θ (path AB ). Considerthattheelectron emitradiationatthewave-crest 4 labelled AinFigure2.6 and at some later instance τ emit radiation at crest B. In Figure 2.6 the path through an undulator for an electron moving in the field described by Equation The relationship between the emitted wavelength λ s and the period of the undulator λ u can be found by considering the condition for constructive interference of the wavefronts emitted at A and B respectively. If we denote the average longitudinal velocity ṽ z then the time difference between thetopoints of emission is τ = λ u/ṽ z. The pathdifference between thetwopoints will be a multiple of some wavelength λ s of the emitted light; multiples of this wavelength will experience positive interference and will dominate the spectrum. c λu λ ucosθ = nλ ṽ }{{} z }{{} s AB n Z+ (2.16) AB We now need to seek the average longitudinal velocity. Remembering Equation 2.14, we have an expression for the velocity in the transverse direction thus we can write: v z = v 2 v 2 x = v 2 K 2 c2 γ 2 sin2 k uz where, by using β = v/c and γ = 1/ 1 β 2, one can by breaking c out of the square-root find: v z = c 1 1 γ 1 sin 2 k uz = c 1 1 [ K2 sin 2 k ] uz 2 γ 2K2 γ 2 Knowing that γ >> 1 and the McLaurin series for 1+x = 1+ 1 x x [ v z c 1 1 ( 1+K 2 sin 2 k ) ] uz 2γ 2 3 In an helical undulator the magnetic field can be written B = B u [ˆxcos(k uz) + ûsin(k uz)]. 4 The strength of the radiation is proportional to the acceleration, Equation 2.11.

48 2.3. Undulator radiation 33 which averaged over one half oscillation gives the sought average velocity 5 : [ ṽ z c 1 1 2γ 2 )] (1+ K2 2 (2.17) which, inserted into Equation 2.16, gives: nλ s = λ u 1 ( 1 1 2γ 2 1+ K2 2 ) ) (1 θ2 2 where we have expanded the cosine for small θ, for the first term we again use the 1 fact that 1/γ is very small: = 1 x 1+x+x2 +..., which gives the final result, for n = 1: λ s = [1+ λu 12 ] 2γ 2 K2 +(γθ) 2 (2.18) In a helical undulator the 1 2 K2 term becomes K 2. This equation is usually referred to as the undulator equation which defines the wavelength which satisfies the resonance condition upon which the radiation is experiencing positive interference. On axis (θ = 0) the total time of travel through the magnetic structure will be t = N u T, with N u being the number of poles this yields a linewidth of the ω ω = 1 radiation given by: N u. For future reference we note that owing to the properties of the Fourier transform: The pulse length will be increased if it is larger than λn u and the line width will be 1 increased if the energy spread of the beam superseeds A detailed look at the equations of motion in an undulator 2N u. To derive the frequency spectrum of undulator radiation it is convenient to know a bit more about the trajectories of the particles in the undulator, so far we only concerned ourselves with the transverse component of the motion as this gives us expressions for the wiggler/undulator strength parameter K and the resonance condition for the emitted radiation. It is here convenient to use Hamiltonian dynamics, as this will simplify our discussion later when we consider what happens when we can no longer make the approximation that the radiated electric field is de-coupled from the motion of the electrons. The Hamiltonian for an electron in an electromagnetic field with vector potential A can be written: H = (p ea) 2 c 2 +(mc 2 ) 4 (2.19) From Maxwell s equations it can be inferred that, since we know the rotation and curl of the electric and magnetic fields one can formulate them in terms of a vector potential A and a scalar potential φ. This is Helmholtz theorem of vector calculus; for the B field this relation is particularly simple B = A thus (with the aid of Equation 2.13) π 5 1 π sin 2 xdx = 1 2 0

49 34 2. Synchrotron radiation and its properties A = B k u sin(k uz)ˆx is the vector potential defining the undulator field. The Hamiltonian described above do not have any explicit time dependence in the coordinates; for such a system the Hamiltonian describes the total energy of the system, i.e. H = γmc 2. Moreover, as the magnetic field donot perform any work on the particles, as it only changes their trajectory we get an added bonus in that the canonical momenta in the transverse directions of the system is conserved, hence[39]: ṗ x = H x = 0, ṗ y = H y = 0 Both momenta are thus constant and we can choose this constant to be zero if we consider the electron s velocity upon its entrance in the magnetic structure to be completely axial. The trajectories are given by ẋ = H px eax = p x γm, ẏ = H py eay = p y γm We use the definition of the undulator strength parameter K and divide by c to obtain expressions for the velocities β x = K γ sin(kuz), βy = 0 from the definition of the relativistic parameter γ = 1/ 1 β 2 we can get an expression for the axial velocity β z as well: β z = K2 4γ 2 β 0 cos(2k uβ 0ct)+β 0 (2.20) where β 0 is the average longitudinal velocity (Equation 2.17). The longitudinal velocity is thus slowed down since a part of the kinetic energy is transferred to the transverse motion. It can be expected that the velocity in the forward direction will be much greater than the transverse deviations, thus we can consider the longitudinal trajectory as approximately given by β oct+z 0 in the integration of Equation 2.20 K 2 z(t) = 1 8β0 2 sin(2kuβ0ct)+β0ct+z0 (2.21) k uγ2 The transverse component can be obtained similarily as was done above: x(t) = 1 β 0 K k uγ coskuβ0ct+x0 In the rest frame of the electron it will therefore describe a figure eight motion.

50 2.3. Undulator radiation 35 Frequency distribution of undulator radiation Using the vector potential introduced above we are now equipped to derive the frequency spectrum from a relativistic electron in an undulator field. Another way to express the radiated power per unit solid angle is[32]: dp(t) dω = A(t) 2 thence the total radiated energy becomes the time-integral (assuming that the radiation field drops sufficiently fast for large times, past and future, so that the radiated energy is finite) dw dω = A(t) 2 dt The relativistic fields can be derived from the vector potential A and the scalar potential ψ, the Liénard-Wiechert potentials[32, 40] which takes care of the fact that the radiation perceived by an observer was generated at an earlier instant (i.e. at retarded time t = t R/c). [ c c ˆn (ˆn β) β ] A(t) = 4π [RE rad] ret = 4π (1 β ˆn) 3 the electric field here have some resemblance to the one described by Equation 2.8, however in the present case all the consequences of the relativistic velocity of the motion have been manifested. To analyze the frequency spectrum of the radiation it is convenient to express the radiated energy in terms of the Fourier transform, where we can make use of the Parseval theorem 6 dw dω = A(ω) 2 dω If integration is taken for positive values of the frequencies, since negative ones do not have any physical meaning, we can write, as the integrand: A(ω) 2 + A( ω) 2 = 2 A(ω) 2 where thelast equality hold if A(t)is real so thata( ω) = A (ω). Wemay formulate the argument of the integral as the intensity as the double derivative of the intensity, as perceived on the direction ˆn from the source ret dw dω = 0 d 2 I(ω,ˆn) dωdω dω 6 Loosely stated: the integral of the square of a function is identical to the integral of the square of its Fourier series, i.e. with appropriate units: the energy contained in a waveform is identical to the energy contained in the sum of its various frequency components.

51 36 2. Synchrotron radiation and its properties We need to find the Fourier transform of the vector potential to proceed [ e 2 ˆn (ˆn β) β ] A(ω) = e iωt dt 8π 2 c (1 β ˆn) 3 we should now change variables as to take explicit care of the retarded time, t + R(t )/c = t, we also assume that the unit vector ˆn stays constant in time that is, our observation point is sufficiently far away from the region in space where the acceleration takes place. The distance R(t ) x ˆn ˆr(t ). [ e 2 ˆn (ˆn β) β ] A(ω) = e iω(t ˆn ˆr(t )/c) dt (2.22) 8π 2 c (1 β ˆn) 2 it can be shown that one can rewrite the integrand in terms of time derivative [ ˆn (ˆn β) β ] = d ] [ˆn (ˆn β) (1 β ˆn) 2 dt 1 β ˆn with this in mind one can integrate Equation 2.22 by parts to obtain a significantly simpler expression for the frequency distribution e 2 ω 2 4π 2 c ˆn (ˆn β)e iω(t ˆn ˆr(t )/c) dt (2.23) On axis, the fundamental harmonic of the undulator will thus have a frequency distribution given by: ( ) d 2 I dωdω = e2 Nuγ 2 2 K 2 2 sinx1 ( ) 2 F 1(K) c 1+ K2 x 1 2 (2.24) where F 1 is a difference between Bessel functions such that F 1(K) = [J 0(κ) J 1(κ)] 2 where the arguments are written as κ = 2 ( K K ret Figure 2.7: Undulator-radiation in frequencyspace (amplitude scaled to unity) shows an oscillatory behaviour dominated by the sin x/x term. Furthermore ω ω r x 1 = πn u ω r where ω r is the resonant frequency obtained from the undulator equation above: ω r = 2ckuγ2 1+ K2 2 ).

52 2.4. Microbunching Microbunching Interaction between the electron beam and the radiation field Up until now we have considered the coupling between the electrons motion and the radiation field to be negligible. If we consider the possibility for energy to be transferred back and forth between the electron beam in an undulator and the radiated electromagnetic field we will find that free electron laser amplification can occur. In the following we will entertain this possibility and find out the conditions that enables this amplification to happen. An energy-modulation to occur along an electron bunch can be accounted for via the action of the part of the Lorentz force (Equation 2.5) containing the electric field: dw = F ds = ee ds = E v ds (2.25) In an undulator the electron velocity have components parallel to the electric field. E x(z,t) = Ecos(kz ωt+φ 0) (2.26) To find the flow of energy per time we need an expression for the electron velocity in an undulator this is given by Equation 2.14, hence: dw dt = ee ck 0cos(ks ωt+φ 0) γ sin(kus) = }{{} Eq = ece0k 2γ {sin([k +k u]s ωt+φ 0) sin([k k u]s ωt+φ 0)} = = ece0k 2γ [sinψ + sinψ ] (2.27) For the energy transfer between the electron beam and the radiation field to be efficient over the whole undulator structure, the phase between the sinosoidal terms within the brackets in Equation 2.27 needs to be constant, i.e.: 0 = dψ± dt = [k ±k u] ds dt 2 K 2 ω kc1+ ±k uc (2.28) 2γ 2 The resulting wavelength can thus be calculated: λ = 2π k = ± 2π (1+ K2 2k uγ 2 2 ) = λu 2γ 2 ) (1+ K2 2 (2.29) in the last step, the negative branch of solutions have been dropped since only wavelengths larger than zero make physical sense. Our hope is to make Ψ + constant to fulfill the resonance condition defined by Equation This is fulfilled if the electrons lag behind the radiation field one λ u per undulator period. The energy between the electron beam and the radiation field is exchanged with the same wavelength as spontaneous undulator radiation.

53 38 2. Synchrotron radiation and its properties ŷ ˆx v E ẑ ŷ ˆx 0 0 ẑ ŷ ˆx v E ẑ ŷ ˆx v E ẑ λ u λ r Figure 2.8: The interaction between the electrons in the beam and the radiation field give rise to a density modulation of the electron bunches. This occurs most efficiently if the the electron bunch lags behind the radiation field with one λ u per period. The electron velocity is parallel with the electric field twice per period there dw = 0. The pondermotive phase Ψ dt +, related to the negative branch as Ψ = Ψ + 2k us when dψ ± = 0, oscillates twice per period and on average cancels out, dt i.e. for a homogeneous e - -distribution half the electrons gain energy while the other half looses it. As a result the electrons, if bunched from the start, tend to become density modulated with the periodicity of the radiation field this process is called microbunching. The wavelength of the density modulation is thus given also by Equation With the resonant condition fulfilled the electron beam and the radiation field can exchange energy over several (many) undulator periods which, taken together with the microbunching, can lead to a net gain of energy in the radiation field. So far we have considered the electron beam to be monoenergetic it is instructive to consider also a beam with an energy spread (which will later be seen to relate to

54 2.4. Microbunching 39 other figures of merit for free electron laser beam). We denote the energy spread by γ, then we can write the pondermotive phase change as: dψ + dt = kc 1+ K 2 ( (γ + γ) 1 ) 2 γ 2 2k uc γ γ }{{} =η (2.30) where in the last step the relative energy spread has been defined. Knowing this we can formulate the energy transfer rate: dw dt = dη dt γmec2 (2.31) Using the two relationships found above we can write an equation system in the two variables Ψ and η: dψ + = 2k ucη dt dη = ee 0K dt 2m ecγ sinψ 2 with Ψ = Ψ + as the phase of the radiation field compared to the electrons with γ = 0 somewhere where dw dt = 0. The system of differential equations can be combined to a single second order differential equation: Ψ+Ω 2 sinψ = 0, Ω 2 = ee0kuk m eγ 2 For small oscillations (i.e. sinx x) this is nothing but an harmonic oscillator: ẍ+ω 2 x = 0. Large oscillations, where one needs to keep the sine-term intact, cause the frequency to decrease; analogous to, for instance, a swing that can make a full loop. For the electrons that deviate from the central energy more energy is lost than gained. This further drives the bunching since fast electrons slow down and slow electrons get accelerated. This longitudinal motion of the electrons reduce the coupling(contained in K) between the electron bunch and the radiation field, a correction need thus to be made, i.e. ( ( )] K 2 K 2 K K [J 0 ) J 4+2K K 2 For K close to unity the reduction caused by the Bessel functions within the brackets is 0.9 and tends toward 0.7 for large K. This correction is commonly written as [JJ] in free electron laser litterature. Exponential gain The radiated power in a spectrum emanating from spontaneous radiation is proportional to the number of emitters, i.e. no phase correlation exist. In a free electron laser beam ideally all electrons in the beam emit in phase, as stated previously such an ensamble s radiated power is proportional to the square of the number of emitters.

55 40 2. Synchrotron radiation and its properties In a storage ring, part of the electrons in a bunch emit in phase the number of such emitters can be enhanced by various laser slicing schemes, all striving to increase the number of coherent emitters. In general the power from such a mixed ensamble can be described by P = P 0 ( Ne +N 2 ef e ) ; [ F e = cos(2πz/λ)s(z)dz] 2 (2.32) where S(z) is the longitudinal density distribution of the electrons, The number of electrons in the storage ring case is N e In a free electron laser amplifier three collective phenomena contribute towards the quadratic dependence on the number of emitters: 1. Modulation of the electrons energies due to the interaction with the radiation field. 2. Change in the electrons longitudinal positions from path length differences in the combined potential created by the radiation field and the undulator field. 3. A, so far, ignored growth of the radiation field which enhance the two aforementioned effects. If we let e i2πz/λ iωt describe the radiation field (which develops according to the wave equation) and E = E 0e iφ describe the transverse oscillations of the electrons, one may formulate the three cooperating processes in a more specific language: ( c t + ) E = i µ0 z 2 aw j e iφ j γ j (2.33) The right hand side of this expression clearly have a maximum when the phases Φ j are the same, i.e. when the electrons emit in phase. Furthermore, the strength of this maximum is clearly larger with increasing number of electrons j. mc 2 dγ dt = ee0 a w γ sin(φ+ψ) (2.34) This equation describes how the energy transfer occurs between the electrons and the radiation field. Here a w describes ( the coupling on-axis in the undulator so that for a planar undulator λ u = λ 0 2γ 1+a 2 2 w +γ 2 θ 2), for a planar undulator a 2 w = K 2 /2. Lastly, the equation below describes the energy modulation of the electron beam which give rise to the microbunching of the electrons. If the longitudinal velocity β z differs from the resonant velocity β z the electron slips in pondermotive phase, electrons with higher velocity move forward while slower ones are retarded. dφ dt = 2πc ( ) βz 1 λ β z (2.35)

56 2.4. Microbunching 41 Scaled free electron laser equations The equations above can be formulated compactly by utilizing the Pierce parameter: ρ = λu 4π 2 j 0 Krms 2 A 2 jj (2.36) 4π I A λ u γ 3 where j 0 is the beam s current density, I A = mc 3 /e = 17 ka (the Alfvén current). A jj is the coupling coefficient between the electron and photon beams for a helical field it is equal to unity, whereas for a planar sinusoidal magnetic field it is a combination of Bessel functions of the first kind: A jj = [J 0(κ) J 1(κ)] with argument κ = Krms/[2 (1+K 2 rms)]. 2 To connect it stronger with the results above we may write it as function of the undulator parameters and properties of the electron beam: ( ) 2/3 F1Kγ 0Ω f ρ = 4cγrk 2 u with this we can write a detuning parameter describing how the electron beam s energy relates to the resonant energy of the radiated field: δ = γ2 0 γ 2 r 2γ 2 rρ γ γρ = η ρ where the approximation holds for small deviations from the resonant energy. The resonant energy is given by the undulator equation as: γ r = kr 1+K 2 /2 2k u 2 µ 0 N ee 2 c 2 γm e The Ω f is the plasma frequency which enters as a parameter in the space charge coefficient which describes the repulsion forces between the electrons in the beam something which counteracts the micro-bunching. The balance between the space charge effects and micro-bunching is one of the reasons why the amplification eventually saturates. The space charge coefficient is defined as: σ = Ω fγ 0 ck rρ 1 1+K 2 /2 We write our new set of variables, describing the energy-spread, field amplitude and position-time, following[41]: η = η ρ ( A = F1Kkr ik re iψ) 4γ rk uρ 2 z = 2ckrργ2 r t γ0 2 where in the second equation we have introduced the complex amplitude of the vector potential. For the details on the derivation not important for the following

57 42 2. Synchrotron radiation and its properties the reader is referred to Bonifacio et al. [41]. With the new variables above our equations 2.35, 2.35 and 2.35 can be normalized to the system of equations: θ = δ +η η = ( A+iσ 2 e θ ) e iθ c.c. A = e θ This 1-D system of equations can be solved analytically for a few idealized cases, otherwise we have to utilize numerical methods to solve them. Without energyspread and using the reasonable ansatz A e iλ z we find that the cubic dispersion relation: [ (Λ+δ) 2 σ 2] Λ = 1 reduces to Λ 3 = 1. This equation have three solutions describing the free electron laser collective instability: the real solution, which is oscillatory, and two complex solutions which is decaying and growing respectively. In the start-up phase the three solutions have comparable magnitudes, after a certain time the growing solution will dominate, and the field amplitude grows exponentially. Within the linear one dimensional framework we can not explain where this growth process ends (for instance via beam blow-up due to space-charge effects) as it is a non-linear process. Inserting z = 2 k uρz (using z = ct and no energy spread) into our ansatz gives the scales solution A e iλz/lg, defining the one-dimensional gain-length 7 : L g = λu 2 3πρ which is the undulator-length needed for the field to grow a factor e. As will discussed below, different factors combine to limit the gain after a certain length in the undulator it can be shown that this length is[31]: L s 22L g Significant effort is put to keep the gain-length (and thus saturation-length) as short as possible for economical reasons. The results here is valid for a mono-energetic beam, introducing energy-spread effects the gain negatively as it prevents the bunching of the electrons at the proper phase. The output power at saturation of the free electron laser can also be expressed in terms of ρ: ( ) γ Ipeak mc 2 P sat = ρp beam = ρ e Besides maximizing ρ to shorten the undulator, a large value of the parameter also give greater radiation output power. 7 By solving Re (iλ) = 3/2

58 2.4. Microbunching 43 Saturation limiting factors for the gain The Pierce parameter defined above shows up in several relations highlighting the demands on the quality of the electron beam for the free electron laser amplification to be efficient. Electrons transfer energy to the radiation field until they fall out of the bandwidth of the free electron laser and the synchronism condition is no longer fulfilled. We may thus formulate the efficiency of a free electron laser simply by restating the last equation as ρ = P sat/p beam the Pierce parameter is thus a measure on how good a machine is when it comes to converting electron beam energy to radiation energy. Among the limiting factors for the gain process (and indeed the free electron laser process as a whole) is: Energy spread around the resonant energy Deviation of the mean energy from the resonant energy The size and divergence of the electron beam, that is normalized emittance. Diffraction effects in the beam. In Equation 2.24 we found that the frequency spectrum of undulator radiation is proportional to ( ) sinw 2 w with w (γ γr)/γ r. The gain curve, showing how a mode with arbitrary energy will get amplified in the undulator, for the free electron laser process can be shown to be proportional to the derivative of that function, i.e. G(ω) d ( ) 2 sinw dω w The proportionality constant contains parameters that define the electron beam and radiation field properties as dictated by the list above a detailed treatment requires assumptions on the electron beam and the details would vary 8. 8 See for instance the books by Saldin and co-workers, or Wiedemann[42, 43], or for a more compact account the review in Ref. [44]. Said references also serve as good general references for this chapter for readers who want a more detailed and perhaps more stringent account of matters than presented in this introductory text to the subject at hand. 1 Gain w 1 Figure 2.9: The small-signal gain function for a free electron laser amplifier.

59 44 2. Synchrotron radiation and its properties In Figure 2.9 the derivative of the negative cardinal sine function is plotted, this is the functional dependence on the beam s energy for the gain curve as given by the equation above. It can be seen that a beam must have a certain, not too large, energy spread and ideally a small shift towards higher energies than the resonance energy to have a positive gain (for a nearly monochromatic beam the optimal shift is about +1.2 on the gain curve). An energy spread prevents efficient microbunching of all electrons with the same pondermotive phase, this smears out the electron bunch which prevents efficient transfer of energy into the resonant mode with (fundamental) wavelength λ r. The resonant energy being γ r = (λ u/2λ) (1+a 2 w) the initial energy spread σ of the electron beam should be kept σ γ r ρ The undulator resonant energy needs, of course, to be tuned to the beam energy, i.e. the energies needs to be matched: γ γ r γ r ρ Greater efficiency is obtained if the electron beam and the photon beam overlap exactly. An electron oscillates around the central path through and undulator with a period that is much longer than the undulator s period; this motion is called a betatron motion. Part of the electron s kinetic energy is thence partitioned into the execution of this betatron motion which slows down the electron, effectively acting as an energy spread. The betatron amplitude function β have a direct effect on the normalized transverse emittance of the photon beam which dictates the following demand: ǫ n 4γβ γ ρ λ u The beta oscillation needs to be optimized to strike a balance between a high electron density and space charge effects which degrades the emittance a good starting point is to set it equal to the gain length, β L g λ ρ. This gives us a condition on how 4π the emittances of the electron (ǫ) and the photon beam (diffraction limited λ/4π) should be matched: ǫ = ǫn γ < λ 4π If this condition is fulfilled neither beam diverges faster than the other. Diffraction effects in the beam softens the coupling between the radiation field and the electron beam, to account for those properly a more intricate three-dimensional model needs to be constructed[17]. A 3-d analogue to our one dimensional Pierce parameter can be found where the relations states are still fulfilled. 2.5 Sase So far our treatment of the free electron laser problem have been done without any assumption on the nature of the radiation mode(s) that are amplified. In the previous chapter, schemes aimed to create conditions for amplification of already coherently

60 2.5. Sase 45 radiation modes from the start were discussed. Such schemes were not employed in the X-ray range until recently at the free electron laser in Italy, which successfully demonstrated Hghg seeding in december The process of Sase utilizes the broadband spontaneous undulator radiation from the first few gain-lengths of the undulator section as a seed for the remainder of the amplification process. Owing to this the resonance condition is always fulfilled for some modes of the radiation, thus the number of radiation modes and their energy is sampled from a random distribution (within the bandwidth of the amplifier which is ω ω also related to the Pierce parameter: = ρ) on a shot-to-shot basis. The shot-to-shot fluctuations of the radiation pulse energy follows a Gamma distribution [45] whose free parameter M can be interpreted as the number of spikes in the final frequency spectrum. The length of the individual spikes is proportional to the gain-length and the wavelength of the radiation as λ/λ ul g. Shorter pulses increases the number of spikes as the energy content of such pulse is broader. The width of the Gamma distribution is inversly proportional to M; the fluctuation of the power is distributed as a negative exponential[42]. Coherence properties Coherence means that the relative phase of waves is fixed. Spatial coherence between two radiation sources means that the photons originating from them occupy the same volume in phase space. In practice this means that emitters within the coherence-length/area can amplify each other by constructive interference if the phase relationship means that they are equal. Temporal coherence can be thought of in the same manner: waves emitted at different times have a phase-correlation that is predictable. The time during which the phase-relationship remains locked is referred to as the coherence-time. Waves emitted during this time interval (e.g. from electrons along the electron bunch) can constructively interfere with each other if the phases are equal. The coherence time τ is intimately related to the spectral width λ of the source via: λ = λ2 cτ A long coherence time thus ensures a narrow spectral bandwidth of the source. This is the case for a normal Laser. In a Sase free electron laser many modes are excited with various coherence-times for each meaning that each mode give rise to a narrow spike in the spectrum, whereas the compound spectrum is broad[45]. Sase ensures very high transverse (spatial) coherence at the saturation point[45 47]; towards the end of the linear gain regime ideally all electrons in the beam radiate in concert. This makes the free electron laser extremely attractive for diffractive imaging[48] and other experiments relying heavily on this property of the X-ray source[49]. As we have seen earlier the ratio between the coherent radiation part of the radiation spectrum and the in-coherent (spontaneous) radiation can be extremely high in a free electron laser whereas in a storage ring the relationship the coherent part of the undulator spectrum is significantly lower[50].

61 46 2. Synchrotron radiation and its properties Summary Synchrotron radiation is radiation emitted from accelerated relativistic charged particles. This type of radiation can be produced in bending magnets in storage rings. The number of photons emitted and the quality of the photon beam can be optimized with magnetic arrays. Bending magnet magnetic field strength limited by the condition that the electrons should stay in orbit in the storage ring. The number of emitted photons is proportional to the beam energy and the curvature of the bend (denote this flux Φ). A wiggler can have a stronger magnetic field since it returns the electron beam to its original path it is a sequence of bending magnets. The photon flux is proportional to the numberof magnetic periods, i.e. N w Φ. An undulator have many magnetic periods that have smaller field strengths than the wigglers however the spontaneous emission can constructively interfere for certain wavelengths yielding a dependence of the flux that is proportional to the square of the number of magnetic periods, i.e. N 2 u Φ. In a free electron laser the electron bunches become density modulated with the period of the radiation field. The photon flux is therefore proportional to the number of cooperating electrons in the beam in addition to the undulator flux: N 2 u N e Φ. An undulator has a spectrum with harmonics of a fundamental frequency. The frequency spectrum is dominated by the sinc function sinx. The bandwidth of an undulator is inversely x proportional to the number of periods. The gain-function for a free electron laser amplifier can be described bythe derivative of the sinc function: we must have an electron beam with slightly higher energy than the resonance energy with a small energy spread for optimal gain. Sase starts up from noise in the beam resulting in a random selection of radiating modes giving rise to a broad spectrum with many spikes with poor longitudinal coherence. Each spike is diffraction limited. Short-pulses and low charge gives fewer radiating modes[51]. A monochromator between two undulator sections can be used to select a desired mode[52]. Seeding schemes serves to increase the micro-bunching before the free electron laser amplification takes place which increases the degree of longitudinal coherence. Simulations Genesis[53], Fast[54]. See for instance the start to end simulations of the Lcls facility described in Ref. [55].

62 3. Free electron laser hardware Written by: A. Lindblad 3.1 A prototypical FEL amplifier In this chapter we will have a closer look at what is actually inside the tunnel of a free electron laser facility. Key technologies will be presented and at which facilities they are utilized. A free electron laser consists, in principle, of four parts before the user experiments (and their optics): (1) an electron gun optimized for low emittance which injects a short intense electron bunch into (2) a linear accelerator structure followed by (3) one or more undulator section(s) where the free electron laser process takes place; in some cases the three first principal sections are followed in turn by an (4) gas-attenuator section. e - -gun Accelerating structure Undulator(s) Figure 3.1: Schematic of a free electron laser facility. Gas attenuator 3.2 Electron guns The electron emitter source at the start of the accelerator is commonly referred to as an electron gun. In the ideal case it produce a monoenergetic current spike with minimal spatial extent. This current spike (see Figure 3.2), produced with electron emission, is transported and focussed with an electric field (sometimes in combination with a magnetic field) to the exit of the gun. Since electrons carry charge they can not be compressed into an arbitrarily small beam. Space charge effects effectively limits the minimal size of the electron beam. As will be seen below this is one of the principal limitations when constructing guns for free electron lasers. 47

63 48 3. Free electron laser hardware y y x x I [A] I [A] Time [t] Time [t] Figure 3.2: Ideal properties of an electron gun (left) compared to real life properties. Electron guns can be divided into categories by the method of electric field generation (direct current (DC) radiofrequency (RF)), by the method of electron emission, i.e. thermionic, photocathode, cold emission or plasma source. A general division also exist for accelerators between hot and cold technology, i.e. normally conducting vs. superconducting both of which have their pros and cons. A direct current electrostatic thermionic gun is arguably the simplest: a hot cathode emits electrons through thermionic emission (i.e. the cathode is hot enough so that electrons can escape from the surface) cased by the heating from the direct current going through the cathode the electrons from the cathode are then accelerated away via an electrostatic field. Of course the accelerating field need not be static. Either an RF pulse provide the accelerating potential or a pulsed DC field can provide the same. For instance, the Scss free electron laser at the Spring-8 site in Japan a thermionic gun is used together with a pulsed DC field of 500 kv with a CeB 6 cathode[56, 57]. Neither cold emission (also called field emission) nor plasma source electrodes are used for free electron laser electron guns. Field emission emitters are though an area of current research[58]. Photocathode guns on the other hand are used both at Flash, Fermi and at the Lcls. A photocathode gun is constructed from a laser that can photoionize a cathode. General requirements Generally, the beam dynamics throughout the accelerator downstream from the electron gun can be described by independent longitudinal and transverse parts. In this approximation a few parameters are critical at the start of the undulator: charge per bunch, the geometrical transverse emittance and the longitudinal emittance. For lasing at X-ray wavelengts, the geometric emittance must be smaller than λ/4π (where λ is the photon wavelength), i.e.that the electron beam must overlap sufficiently/totally with the generated photon-beam. The geometric emittance is proportional to the normalized emittance divided by the beam energy[59] ε g = εn E thus, a small normalized emittance allow for a lowering of the beam energy of the accelerator which in turn lowers the total cost for the facility. The emittance of the electron beam is defined by the electron gun where the charge cloud to be accelerated is created. The ultimate performance of a free electron laser is ultimately determined by quality of the electron beam at the start of the accelerating

64 3.2. Electron guns 49 structure. More precisely the emittance of the electron beam needs to be low, as this quantity can in the best case scenario be conserved throughout the accelerator. Since performance (and cost efficiency) can be gained by constructing an low emittance electron gun a lot of effort have been (and still is) put into research and development in this area (for a recent overview see W. A. Ferrario[60]). The longitudinal emittance and the bunch charge define two important parameters for the lasing process: the energy spread and the peak current. The path difference of the electrons (caused by, for instance energy spread) in the undulator over one gain-length must be very small (very much smaller than the radiation wavelength) allow microbunching to occur. Table 3.1, constitutes a wish-list for electron guns suitable for X-ray free electron lasers. As will become evident, it is hard to find guns that simultaneously fulfill all of the mentioned points. The accelerator structure (normal conducting, superconducting) and user demands on the facility will guide the choices. Parameter Value & Comments Repetition rate Hz to 100 s of MHz Charge per bunch Tens of pc to nc Normalized emittance 0.1 to 1 µm Energy at gun exit 0.5 MeV E-field at the cathode 10 MV/m B-field compatibility emittance compensation Spatial distribution controllable Bunch length (rms) fs to 10 s of ps Vacuum mbar Load-lock compatibility Facilitate cathode replacement High reliability User facility operation Table 3.1: Some requirements for X-ray free electron laser electron guns. The design parameters of a facility vis-à-vis average brightness and flux sets the repetition rate and peak current; the desired radiation wavelength sets the electron energy and undulator energy and field; photon pulse length and radiation field intensity constrain choices of seeding schemes, peak current, total charge, etc. Choice of cathode materials range from pure metals to various semiconductor compounds (e.g. CeB 6[56], ZrC[61]). They are chosen with respect to their stability and quantum efficiency. With low repetition rates (up to about 1 khz) presently available lasers can in combination with a low quantum efficiency material (i.e. QE ) achieve a high enough photocurrent to be employed. Megahertz repetition rates require materials with higher efficiency in the order of percents. Thermionic emitters The normalized rms emittance of electrons emitted from a hot cathode of radius r c can be described by[62]: ε n = βγ x 2 x 2 = γ rc kbt 2 mc 2

65 50 3. Free electron laser hardware Figure 3.3: Thermionic emitter (left) and photocathode emitter (right) with a static accelerating gradient. with T being the cathode temperature and k B Boltzman s constant. Clearly the key to a low emittance is to have a small cathode to begin with. At the SCSS (Spring-8) a thermionic gun using a CeB 6 cathode operating at 1450 C produces a 3 A peak current with a emittance as low as 0.4π mm mrad[56]. Photocathode emitters The emittance from a photo-cathode depends strongly on material properties, thus materials in combination with laser technology is therefore an active area of research[63, 64]. Photocathode guns are used at the majority of free electron laser facilities around the world. Lcls: currently polycrystaline Cu, CsBr coated Cu being considered as a future alternative[65]. Flash: Cs 2Te. Semi-conductor cathode materials are more sensitive to degrading processes such as ion backscattering and surface degradation than their metal low efficiency counterparts. Nevertheless, by asserting proper vacuum conditions Cs : GaAs and Cs 2Te are operating at user facilities. For an comprehensive investigation on different cathode materials and a perspective of the current research efforts see[66]. The emittance can be reduced by cooling of the cathode[62]. Normally conducting guns Static (DC) acceleration In this type of electron gun the particles are accelerated by a static 1 (or pulsed field that is static during the duty cycle, i.e. when an electron bunch is to be accelerated into the accelerator structure), as depicted in Figure Cockcroft & Walton used an electrostatic linear acceleratorwhere an alternatingcurrentsource is rectified by diodes and capacitors to achieve a voltage multiplication over several stages. They used the machine to split lithium atoms with 400 kev protons the results were published 1932[67]; for this achievement they were rewarded the Nobel prize in physics 1951 for Transmutation of atomic nuclei by artificially accelerated atomic particles.

66 3.2. Electron guns 51 The charges are accelerated by a force proportional to the gradient of the potential, i.e. the voltage difference F = q φ. The energy gained is E = qu with the unit often given in electron volts (ev). With this type of voltage multiplication it is possible to reach voltages of 1-2 MV. Radio frequency (RF) acceleration An oscillating electromagnetic field can be used to accelerate charged particles. If the particles motion is matched so that they interact resonantly with the rf-field a very high amount of acceleration can be achieved (see page 52). Guns operating in the L- and S-bands 2 ( 1 2 GHz and 2 4 GHz) have already been constructed and successfully employed in photoinjector schemes, notably the Lcls gun at SLAC[68]. Normally conducting RF-guns can be considered a mature technology that exhibit several important performance parameters in-line with what is demanded from a free electron laser point-of-view: they are capable of producing a high field gradient (up to150 MV/m) which allow theextraction of high peak currents in short bunches; they permit the use of emittance compensation through the use of solenoidal magnetic fields; they are compatible with a large number of various cathode materials. The limiting factor is the power density exerted on the cavity walls when they are submitted to a high accelerating field gradient. A high radio frequency implies that the cavities are comparatively small which makes efficient dissipation of the generated heat through a cooling system technically challenging. Hence the repetition rate for is limited to a maximum somewhere between 100 Hz and about 10 khz (depending on the RF-frequency). The small cavities also imply that the apertures are small which can also impair pumping which may generate vacuum quality concerns. Below a certain frequency the heat load on the cavity walls becomes manageable in such a way (with lower RF frequency the cavities become larger which decreases the power density) that a continuous wave (CW) operation mode can be allowed[69]. Lower frequency implies a lower accelerating gradient which are still higher than the alternative varm technology direct current counter parts. The interest for this type of operation is large from the user community since it allows a higher repetition rate than stated above, even for a non-superconducting apparatus. Owing to the correspondence to RF technology employed at storage ring this technology is well matured which ensures reliability and simplicity hard to find in other schemes. Superconducting guns A scheme where superconducting radiofrequency (SRF) accelerator cavities are combined with photocathode laser electron guns can potentially allow for the production of electron beams of sufficient quality for usage in free electron lasers at very high repetition rates[70]. An overview of the current research and developments have been published by A. Arnold and co-workers[71]. 2 RF sources are classified into VHF, UHF, microwave and millimetre wavebands. The microwave bands are divided into the following categories: the L band, GHz; S band, GHz; C band, GHz; X band, GHz; K band, GHz. The millimetre wave band is between 30 and 300 GHz.

67 52 3. Free electron laser hardware The Meissner effect (exclusion of B-field from superconducting cavity walls) makes the inclusion of emittance reducing B-fields in the source region problematic. The use of higher order cavity modes that generate a magnetic component achieving the emittance reduction have been proposed and are under investigation[72, 73]. Summary Table 3.2 presents the current best beam performance as obtained from different gun technologies. The low emittance of the Lcls gun is achieved thanks to the low peak current operation. The PITZ gun has a 10 Hz structure with 1 MHz pulse substructure. The Rossendorf setup apparently suffers from a damaged cavity impairing the strength of their accelerating field. Gun Technology Rate Acc. Field E ε n C [Hz] [MV/m] [MeV] [µm] [pc] Lcls NC RF GHz PITZ NC RF > (Flash) 1.3 GHz JLab DC Scss Pulsed DC Rossendorf SRF Table 3.2: Performances of existing guns employing different technologies. Table obtained from W. A. Barletta et al. [74]. 3.3 Radio-frequency driven accelerators RF RF RF RF RF RF RF RF Figure 3.4: Different rf acceleration schemes. From left to right: in the betatron charged particles are accelerated in a spiral path in a static magnetic field; in the microtron the magnetic field is static but the orbit is stretched longer for each pass to adapt to the particles higher kinetic energy; in the synchrotron the magnetic field strength is risen per turn to compensate for the higher kinetic energy (in a storage ring the rf power is matched to the synchrotron radiation losses, hence the orbit is kept stable with a constant magnetic field strength). A linear accelerator successively accelerate the particles without bending their orbit. A radio-frequency (RF) accelerator use power from a single RF generator to create an alternating electric field gradient over the gaps of the accelerating sections. Figure 3.4 different particle acceleration schemes are presented, all can be understood from the Lorentz force equation (Equation 2.5): only an electric field can change

68 3.3. Radio-frequency driven accelerators 53 the kinetic energy of a particle, whereas an magnetic field can change the orbit of a particle (since it exerts a force perpendicular to the particle s velocity) 3. In 1924 G. Ising suggested that time-varying electric fields could be used for the acceleration of charged particles through a periodic structure of drift-tubes[75]. The first successful operation of a radio frequency driven linear accelerator was demonstrated in 1928 by R. Wiederöe[76]. In Figure 3.5 an accelerator of this type is outlined. The lengths of the drift tubes needs to be progressively longer as the particles velocity increases along the structure. However, when their velocity is sufficiently close to the speed of light they mainly pick up energy, thus after a while the length of the drift tubes need not to be increased. Since the length of the structures in a Wiederöe linac is βλ/2 it makes economical sense to choose higher radio frequency since the overall accelerator would become shorter. However, the structure radiates energy as P = ω rf CVrf 2 the losses thus increase with the radio-frequency ω rf, the gap capacitance C and the voltage squared. If the drift tube is placed in a cavity the electromagnetic energy is also stored within the structure in a magnetic field (owing to the cavities inductive properties). The resonant frequency of the cavity can of course be tuned (via the cavity radius) to match that of the accelerating field. The mass of an electron is 1832 times smaller than a proton, an electron thus achieves relativistic velocities much faster with the same accelerating force. Therefore linear accelerators for electrons generally have structures that have equal length since the velocity factor is β 1 already after the electron gun accelerating structure. The governing principles for linear accelerators using resonant acceleration are slightly more convoluted than those of the electrostatic accelerators mentioned above[77]. We will consider here only a few key features of their components necessary for understanding of accelerator parameters necessary for free electron laser. 3 At relativistic speeds v c the second term in F = q[e + v B] may be about 300 times larger than the first term already at 1 T magnetic strength (which is readily achievable technologically) βλ/2 Figure 3.5: Schematic of the cavity structure of a Wiederöe accelerator. To the right there is a source for the particles to be accelerated.

69 54 3. Free electron laser hardware The accelerating RF-field A good starting point to get a feeling for how the accelerating electric field within a accelerator cavity looks is to consider the field within a capacitor. If we, initially, assume the field to vary very slowly with the angular frequency ω we can write the field as: E = E 0e iωt (3.1) i.e. with the alternating field the charges on the plates gets depleted and accumulated sequentially. E Γ B Figure 3.6: A capacitor connected to an alternating current source stores both an electric and a magnetic field. The Γ contour (dashed) is an integration path. We know that a varying electric field induces a magnetic field (from the Ampère- Maxwell equation, eq. 2.4). Inside the capacitor we have no stored current and thus (Figure 3.6): c 2 = ΓB dl E ds (3.2) t S where S is the area enclosed within Γ. The contour is a circle with radius r. c 2 B2πr = t Eπr2, thus B = iωr 2c 2E0eiωt (3.3) Where we have made use of our definition of the oscillating electric field. If the time derivative of the electric field is identically zero (i.e. a static electric field) all energy in the capacitor was stored in the electric field. Now with a time-varying field there is the additional possibility of storing energy in the induced magnetic field. In the center of the capacitor (r = 0) there is no magnetic field, elsewhere there is an induced field that varies with the distance from the center. Since such a magnetic field is present there is a increasing perturbation of the electric field with increasing

70 3.3. Radio-frequency driven accelerators 55 r. It is now possible to construct a correction to the electric field that takes this into account using Faraday s law eq. 2.3: E = E 1 +E 2 (3.4) Γ 2 S 0 Figure 3.7: The capacitor viewed from the side, depicting the surface and integration path used for Faraday s law. The second term in the superposition is required to be zero in the center, it is also the only term contributing to the line integral in (Figure 3.7): E dl = ΦB Γ 2 t The flux of the magnetic field in a vertical strip of width dr is B(r)hdr (imagine that we split the surface S 0 into strips). The right hand side boils down to E 2(r)h: he 2(r) = h B(r)dr Here it can be seen that the correction field does not depend on the separation of the fields, only on the distance from the center. The equation above gives E 2(r) = ω2 r 2 E 4c 0e iωt, this gives us the corrected electric field in the capacitor 2 ) E = E 1 +E 2 = (1 ω2 r 2 E 0e iωt (3.5) 4c 2 Our obtained electric field now differs significantly from the one we started out with to obtain the magnetic field above. Since we are dealing with fields we can repeat the same procedure for the magnetic field, i.e. use the ansatz that B = B 1 +B 2 With B 1 = iωr E 2c 0e iωt. To find the correction term we may use the Ampère-Maxwell 2 equation again (as we did above in eq. 3.2): c 2 B 22πr = E ds t S

71 56 3. Free electron laser hardware The flux of the electric field is taken through the circle enclosed by Γ in Figure 3.6 and we get: B 2(r) = iω3 r 3 16c 4 This gives us a new correction to the electric field via E 3(r) = B 2(r)dr t We obtain a new term in the expansion of the electric field as: [ E = 1 1 ( ωr ) 2 1 ( ωr ) ] 4 + E 0e iωt 2 2 c c if we were to continue we would get an increasingly large expansion within the parenthesis which continues as (slightly rewritten): [ 1 1 ( ωr ) 2 1 ( ωr ) 4 1 ( ωr ) ] (1!) 2 2c (2!) 2 2c (3!) 2 2c This series is, bydefinition, thebessel function of the first kind(j 0) with argument ωr/c. The oscillating electric field in the capacitor can thus be written in the very compact form: E = J 0(ωr/c)E 0e iωt J0(x) r[c/ω] Figure 3.8: The Bessel function of the first kind. Bessel s functions are solutions to the wave equation in a cylindrical geometry. The subscript zero denotes that this solution is independent of the polar coordinate. In Figure 3.8 we can see that the function have a zero around 2.4 (it is actually 2.405). This implies that a pair of plates have a resonant frequency 2.405c/r of course there is also the possibility for harmonics of this frequency, functions that will 1 have additional nodes inside the cavity meaning that, 0. 8 the electric field and magnetic fields will exchange energy in an oscillating manner indefinitely (as a capacitor and an inductance coupled together). If the fields were enclosed in a cylinder with conducting walls this would hold if the walls were perfect conductors. Imperfect conducting walls implies that the oscillating fields gradually gets drained of their energy due to resistive losses. To describe a resonating cavity, we may imagine that the oscillating field occur in a hollow cylinder containing the same oscillating field as above (the solutions are basically the same). The lowest mode in such a cylinder is usually denoted TM 010 which can be written: E z = E 0J 0(k cr)cos(ωt k zz) The wave numberk z describes the dependenceof the field upon the cut-offwavelength λ c of the cavity only electromagnetic waves with wavelengths shorter than the

72 3.3. Radio-frequency driven accelerators 57 cylinder diameter can propagate through the structure: k z = k 2 kc, 2 where k c = 2π/λ c and the free space wavenumber k = ω/c. We require that the field vanish at the surface of the cylinder, letting the radius of the cylinder be ρ, thus k c = 2.405/ρ must hold (2.405 being the first zero of the Bessel function J 0). Ifanelectron wouldhavethesame speedas thephasevelocityofthewavedescribed above it would be accelerated, however the phase velocity of the wave is: v phase = ω c = > c k z 1 λ2 λ 2 c The condition of acceleration is thus possible to fulfill for a very short distance only after which the wave would reverse the field orientation and decelerate the electron again on average no net gain in energy would be possible. To overcome this, i.e. to make a working accelerating structure, the phase velocity of the wave can be slowed down for a certain frequency to match the speed of light by introducing irises along the cavity. Such a structure will naturally perturb the fields of the perfect cylinder, a working accelerating structure is obtained when the wavelength is chosen such that it is a multiple of the distances between the iris-discs, λ = nd (see Figure 3.9). The modes inside the disc-loaded cavities are usually named after the phase advance k zd = 2π/n of the wave per sub-cavity. Beam 2π/3 mode π mode d Figure 3.9: Two common modes used in disc-loaded cavities. Energy gain in a radiofrequency driven accelerating cavity If U 0 m ec 2 the electron speed is close to the speed of light. Let z = d/2 be the entrance of the cavity (corresponding to a time ωt = π/2), a particle entering the cavity may experience the electric field at a phase φ relative to the peak field (defining zero phase). Then the field on axis (in the ẑ direction with r = 0 in cylindrical coordinates) can be written: E z = E 0cos(ωt(z) φ) since, on axis the Bessel function J 0 is equal to unity. If the particle is at z the time is given by t(z) = z dzv(z). The energy gain is then: 0 U = qe z = q d/2 d/2 E 0cos(ωt(z) φ)dz We know that during the passage the change in velocity is small we may set t(z) z/v. With the use of a trigonometric identity we can have the phase angle outside the integration. Defining the accelerating gradient V = E 0d and transit time T U = qe 0dT cosφ = qvt cosφ

73 58 3. Free electron laser hardware the transit time T = sin(ωd/(2v)) is a correction to the particle acceleration owing to ωd/(2v) the time variation of the field while the particles transverse the cavity. is the energy gain of an electron passing an accelerator of length L. The phase φ is measured relative to that of the traveling wave. Often one does not operate the accelerators at the point of maximum acceleration since one wants to introduce a energy chirp (gradient) along the particle bunch to achieve a shorter bunch. Warm technology: Copper Accelerating structures built in Copper have been used for decades in both storage rings and linear accelerators, thus this technology can be considered to be very mature and solutions are often available commercially. Copper is chosen for its good electric conductivity coupled with a high thermal conductivity. The cheap cost per GeV (about 15 Million USD) must though be put against the limited average brightness that can be delivered to the users. Cavity structures for the L, S, C and X bands are currently being used for different purposes. Thanks to the cheap cost the technique is being developed for MV/m for the X-band, mainly for the TeV lepton linear collider but with obvious synergetic effects for linear accelerators for X-ray production[78]. C-band normally conducting copper structures operating at accelerating gradients of 35 MV/m are used at the Scss free electron laser. Superconducting technology Superconducting technology is vastly more expensive than the warm counterpart; however, the high average brightness required for larger facilities (especially those where it is envisioned that many experimental stations are served simultaneously, e.g. the European X-Fel) this might be the only way forward. Since the short duration and low emittance of the electron bunches would not be preserved in a synchrotron, Sase free electron lasers are based on linear accelerators, either employing normally conducting or superconducting rf structures as sketched in Figure 3.9. In contrast to the case of a constant current, the resistance of a superconductor does not completely vanish in the presence of an radiofrequency field, see e.g.[79]. It is nevertheless much smaller in superconducting niobium at e.g. 2 K than for copper at room temperature. Therefore, the quality factor Q of a superconducting cavity (where Q/2π is the ratio of the energy stored in the system and the energy dissipated per oscillation cycle) is of the order of , compared to below 10 5 for copper cavities. On the other hand, for 1Wof power lost in asuperconductingcavity at 2K, thecryogenic system requires almost 1 kw to keep the temperature constant. This together with the technological complexity and a fundamental limitation given by the critical magnetic field makes the choice not so obvious. It required a committee of international experts in 2004 to identify the superconducting TESLA technology as the best solution for the International Linear Collider [80]. At Flash, six acceleration stages, each accommodating eight nine-cell TESLA cavities used to accelerate the electron beam to 1 GeV[81]. The average

74 3.4. Undulators 59 h D y x z Figure 3.10: Schematic of an Apple-I variable polarization undulator. The short magnet in the start have λ u/8. electric field is about 20 MV/m with one meter cavity lengths. By optimizing cavity design and with the advent of new techniques to clean the cavity surfaces, fields larger than 50 MV/m have been demonstrated[82]. The European X-ray free electron laser will employ TESLA cavities with a field of 21 MV/m. Lcls at Stanford, on the other hand, is based on the normal-conducting SLAC linac, and some other projects, like the Scss XFEL in Japan for example, have opted for normal-conducting rf structures as well. Continuos wave operation with TESLA cavities have recently been demonstrated[83] 3.4 Undulators Most free electron lasers use planar undulators with a fixed undulator period, which then provide linearly polarized light containing a fundamental wavelength and its harmonics. If one desires to suppress the higher harmonics, for some reason, a quasiperiodic scheme can be employed[84]. A quasiperiodic undulator scheme generally degrade the performance of the undulator for the fundamental which makes such devices unattractive for the use in, at least, Sase free electron laser, since the cost is highly dependent on the undulator length and an decrease in photon density necessitates a longer gain length. However, often polarizations other than the linear is desired by the user community. By introducing a magnetic field parallel to the central path through the undulator (superimposing the vertical field) it is, in principle, possible to generate arbitrary polarization directions[85]. In Figure 3.10(adapted from Ref.[86]) a schematic of an Apple-1(Advanced Planar Polarized Light Emitter) undulator. Two magnetic fields (sinusoidal and helical) are superimposed on each other with variable strength and phase. The type II and III varieties looks similar but have different pole geometries[87, 88]. By placing a variable polarization device after the Sase undulator or using it directly as the primary undulator in the free electron laser elliptically polarized light can be delivered to the user experiments. The resonance wavelength in this type (Apple-1) of undulator looks slightly differ-

75 60 3. Free electron laser hardware ent than our expression found earlier as we now have two fields in the undulator: ( λ r = λu 1+ K2 x +K 2 ) y E 2 2 Here we obtain the resonance wavlength in Ångström if the undulator period is given in millimeters and the beam s energy in GeV. The coupling parameter between the undulator field and the radiation fields is also different with the [JJ] Bessel-function factor reducing to unity[17]. Undulator tolerances example Using the Pierce parameter ρ (Equation 2.36) one can estimate the accuracy needed to be achieved, with errors from different sources: temperature, alignment, undulator gap accuracy and flatness change upon undulator gap changes. The fundamental wavelength have to be tuned within ρ λ λ (3.6) For an error to have a large impact on the amplification process it has to be in effect for at least one gain length. As an example we can use the European Xfel which has a gain length of 10 meters and undulator sections that are 5 meters long the ρ = at 0.1 nm for this facility. If all error sources are equally severe, then one can obtain an idea of the tolerances required for an free electron laser undulator system[89]. We can express the bandwidth as a function of different errors impacting the magnetic field in the undulators: λ = λ B B 2 temp. + B 2 gap + B 2 flat (3.7) from this one obtains that for Equation 3.6 tobe fulfilled the alignment between undulator sections needs to be within ±100 µm; the temperature stability of the whole undulator system within ±0.08 K and that the gap adjustment accuracy and the flatness preservation upon gap changes needs to be better than ±1 µm.

76 3.4. Undulators 61 Summary The basic components of a free electron laser before the user s experiments are: An electron-gun. Which can be of thermionic, photocathode or field emission type. The electron gun defines the emittance and the number of electrons in the bunches. A linear accelerator. Defines the repetition rate of the system. Superconducting accelerators have higher repetition rates (khz-mhz) than normally conducting (100 s of Hz). Undulator(s) sets the wavelength and polarization of the X-rays. (Gas attenuator) - can be used to limit the intensity at the experiments.

77

78 4. X-ray optics The material presented here in this chapter is partly adapted from Survey of in situ metrology for the measurement of damage to FEL photon transport optics by A. J. Gleeson, Iruvx WP7, 2010 by A. Lindblad. It is a challenge to construct any optical system for X-rays. The requirements on optical elements at free electron laser is often different than those imposed at synchrotron X-ray sources because of the high peak-power rather than the high average power. The demands on precision is also higher since the photon beam from the free electron laser undulator(s) have a very high brilliance that one wishes to preserve to as high degree as possible. In the following sections we will investigate how stringent those demands are and the techniques that can be used to achieve this. Also connected to the high brilliance and fluence is damage to optical elements and methods to minimize/prevent it. This will be discussed below before the chapter end, containing descriptions of dispersive optics, monochromators and beam attenuators. If we write the index of refraction for X-rays in matter as: n = 1 δ iβ with δ and β as the refraction and absorption coefficients respectively a number of conclusions can be drawn. In the X-ray regime the reflection coefficient δ is in the order of 10-5 to 10-7, generally thus a refractive optic would not be very effective. The absorption coefficient is very high in the UV-soft X-ray region for all elements which present yet another tamper, however for materials constituted of elements with low mass (and thus small nuclear charge) this coefficient is small above 1.5 kev since the photoionization cross-sections become very low there. For instance, the deepest laying single-ionization threshold for carbon is around 300 ev. Absorption can be further traded into reflection by having a grazing incidence of the X-rays onto the optical elements[90]. In the soft X-ray region this is the general approach utilized. For hard X-rays reflection planes in crystals of low Z materials can be used. 4.1 Demands on optics precision at free electron lasers A real-life mirror is not perfect and imperfections of various kinds distort and degrades the mirror s performance. To analyze the impact of various errors one usually 63

79 64 4. X-ray optics compares with an idealized surface which perfectly transfer the source point to the image point. It can be shown that low frequency surface errors, between millimeters and λ, distort the wavefront but still image the incident wave into the image plane (often taken to be within the 1/e intensity points in a Gaussian spot). Higher frequency errors scatter the incident waves outside the image plane[91]. The authors of Ref. [91] have developed a model classifying an optical systems performance in terms of the slope error (deviation from ideal shape) and surface roughness the system coherence length describes the limit between high and low frequencies in a natural way: W = λ 2 Θcosϑ i treating Θ as the given angular radius for the image and ϑ i the incident angle relative to the surface parallel we have, as a function of the operating wavelength λ the wavelength W which is the surface spatial wavelength that diffracts intensity into the 1/e radius of a Gaussian spot. For a diffraction limited source (as is free electron laser and modern synchrotron storage rings) the W is roughly equal to the illuminated length (l) of the optical element. For the X-ray optics considered here this wavelength thus lies between λ and l. The degradation of transmission and image quality in the optical system due to mirror errors may be described by the deviation from the ideal case, the so-called Strehl-factor: I(0) I 1 8 ( ) 2 4π 0(0) Θ 2δ2 λ cosϑi σ 2 with δ and σ are the rms values of the slope error and surface roughness within the band-pass of the optical component[91]. Both the slope error and the surface roughness are integral properties of the surface, i.e. the accumulated error is what affects the beam: δ 2 = 4π 2 1/W 1/L df xs 1(f x)f 2 x; σ 2 = 1/λ 1/W df xs 1(f x) Owing to this property of the imaging system one is faced with an array of different problems when it comes to manufacturing and commissioning a device with such stringent demands on surface quality: Manufacturing Polishing a surface down to a few nanometers peak-to-peak roughness over a large area (typically the mirrors are above 25 cm long) Process such a large substrate to a determined shape. Metrology of the manufactured surface with high (sub-nm) accuracy[92, 93]. A detailed account of techniques and metrology methods for the manufacturing of X-ray optical elements is given in the book Modern developments in X-ray and Neutron Optics edited by A. Erko et al.[94].

80 4.2. Focussing mirrors back-reflecting geometry example 65 Moving and mounting the finished element into its position in the optical system of the facility without degrading the surface. One way to circumvent this problem is to make mirrors that have an mount where the surface can be mechanically distorted to compensate for the errors so called adaptive optics (see e.g. Ref. [95]). As an example we here take the offset mirrors at the Lcls, they have figure errors on the order of 2 nm (rms)[96] and because of the reflectivity condition on the grazing incidence they need to be of different lengths for the soft and hard X-ray regions: soft X-rays, 25 cm long, boron-carbide-coated a total of four. hard X-rays, pair of 45 cm long mirrors with SiC-coating and 25 kev cut-off. Allows the throughput of the 3 rd harmonic of the 8.3 kev fundamental. 4.2 Focussing mirrors back-reflecting geometry example So far we have only discussed plane mirrors, there is naturally a demand for focussing mirrors for experiments that utilize high photon-density. Figure 4.1 shows a princi- Figure 4.1: Spherical/Parabolic mirror used to focus the free electron laser beam. the focuspoint do not overlap with the incoming beam because of the beamstopper (black). ple for an experiment that uses a backscattering geometry with a focussing mirror that focus the photonbeam to a point. Such set-ups are utilized, for instance, when investigating multiphoton ionization of gases. One such experiment utilized a Mo-Si multilayer spherical mirror with 68% reflectance (this number is made possible by progress in EUV-litography[97]) which could then be focussed down to 3 to 5 µm focus diameters[98]. 4.3 Damage Because of the high peak powers and short pulses routinely achieved at free electron laser it is entirely possible that new kinds of damage mechanisms that degrade optical components in X-ray beamlines have to be considered. Often our knowledge for such mechanisms emanate from the world of storage ring synchrotrons where rather a high average power load provides the source for potential damage to optical elements and coatings. At a free electron laser the high peak power could potentially render an (costly) optical component useless within fractions of a second[99]. The research of various damage mechanisms caused by this kind of sources is therefore an active field[100, 101]. The empirical data for damage thresholds that exist are often very specific to a certain (synchrotron) beamline and are thus unique to the flux and operating wavelength

81 66 4. X-ray optics under consideration. Recently materials for optics and their coatings employed at X- ray free electron laser around the world have begun to be studied in a more systematic fashion[101, 102], notably the low Z materials B 4C and SiC[103]. Damage to opical elements at a free electron laser can be thought of as direct and in-direct: direct damage could be ablation cratering of the surface, distortion due to the heat-load caused by the pulse, etc. In-direct damage mechanisms are more subtle and include damage to multilayers by diffusion or chemical modification of surfaces and layers, changes to the refractive index. Careful monitoring of the beamline performance is thus important and the methods described in the second part of this book inherently give information that can be used to diagnose the optics. 4.4 Diffraction gratings A diffraction grating (henceforth taken to be synonymous to grating only) is a periodically structured surface that divides and diffracts a lightbeam into several beamlets propagating in different directions depending on their wavelength. This can readily be understood from the Huygens-Fresnel principle stating that each point on a wavefront act as an independent source and that by adding up the contribution from such pointsources the properties of any subsequent point can be found. Light reflected from an an ideal grating can be consideredt to equal to that from emitted from a set of infinitely long narrow slits spaced with distance d from each other. If we add up the beams from each slit at some point (far) away from the grating the optical path difference between the beams will casue positive and negative interference owing to the phase difference between the waves. If the path difference between the slits are some multiple of the wavelength d = n λ positive interference occur for a given wavelength this condition will be fulfilled at some angle ϑ away from the normal (taken to be perpendicular to the surface) dsinϑ = n λ Ifweallow for theincominglight s (considered tobeaplanewave)angle tobedifferent from that of the outgoing we get a generalization of the equation above: d(sinϑ out sinϑ in) = n λ (4.1) This equation is commonly referred to as the grating equation. Since the result was obtained using the phase differences this holds for regular structures, i.e. wavefront distortions occur through the irregularities of the grating. The solution corresponding to n = 0 is the zeroth order component mentioned before (this is akin to specular reflection at a mirror); the nonzero solution corresponds to different diffraction orders. A grating is thus a dispersive optical component that can be used in at normal or grazing incidence to deflect a certain wavelength part of the beam into a defined angle. At short wavelengths (in the EUV/soft X-ray regions) it is necessary to operate with grazing incidences since the reflectivity materials increase with decreasing angles. The zeroth order diffraction have the same diffraction angle as the incoming angle whereas the diffracted orders have a different angle as compared to the incoming light (angles α and β in Figure 4.3). Since the grating splits the beam, either the diffracted

82 4.5. Monochromators 67 orders or the zeroth order can be used for beam diagnostic purposes without disturbing the user s experimental stations downstream this aspect is further discussed below in chapter 5 (see page 73), Because of their dispersive nature gratings act as bandpass filters on the radiation and can thus be used to define the wavelength at the experimental stations (see below). Gratings that are blazed produce a maximum efficiency vis-à-vis reflectivity into a certain order (other than the zeroth) for the light that hit the grating. The higher reflectivity decreases the potential for radiation damage to the grating. 4.5 Monochromators Although the bandwidth of the radiation from free electron laser can be very small, e.g. at Flash it is about 1%[104], many experiments especially spectroscopic dittos have a more stringent demand on the spectral purity of the light. This is one reason why monochromators are present at some free electron laser other reasons include the increase of stability of the central wavelength as discussed below. Some experimental cevats concerning free electron laser radiation A Sase pulse from a free electron laser can be considered as being built up from a series of spikes arising from the radiating longitudinal modes that happended to be amplified as that pulse passed through the undulator structure. Each spike in the spectrum is transform limited 1 whereas the spectral distribution inthe pulseis chaotic in the sense that each pulse have a unique spectral composition. Thus a Sase pulse consists of many independently radiating modes whose intensity varies from pulse to pulse hence the median wavelength of the pulses change, as well as the spectral intensity distribution, on a pulse to pulse basis. Additionally, as seen in Figure 1.10, the radiation emitted in the Sase part of the spectrum sits on top of a large broad background of spontaneous undulator radiation. If the undulators are not perfectly helical (that is the electrons emits non-circularly polarized radiation) the spectrum will contain harmonics of the fundamental wavelength emitted. In certain instances this can be viewed as fortuitous since the harmonics will have shorter wavelengths (but then the intense fundamental becomes a problem at the experiment) or as a serious drawback if it is the fundamental wavelength that is to be used and the harmonics becomes a problem at the experiment side. Seeded free electron laser schemes (section 1.5, see page 15) improves upon the basic Sase scheme in various ways all striving to improve the quality of the emitted radiation by enhancing the microbunching of the electrons in various ways. To avoid timing errors between the seed pulse(s) and the electron bunch (timing jitter) the seed pulse is often significantly shorter than the electron bunch. Hence, only a part of the electrons experiences the additional density modulation owing to the seeding process, in addition to the seeded free electron laser radiation one thus obtains a Sase background from the rest of the electron bunch (as well as the background from spontaneous undulator radiation mentioned before). Eventhough the Sase part of 1 i.e. the spectral width is minimal for a given pulse-length. For a Gaussian pulse this implies that the time-bandwidth product is 0.44.

83 68 4. X-ray optics the beam do not reach saturation it can still carry significant power. The unseeded part of the beam can thus disturb downstream experiments both with the background itself and that it arrives before, and extends after, the main pulse. Benefits and drawbacks of from a monochromator A monochromator is a device that filters a photon beam with regard to wavelength acting essentially as a wavelength band-pass filter. Considering only the wavelength variation issue first, it is obviously beneficial to filter the photon beam with a monochromator since it resolves many of the issues mentioned above. A monochromator provides: Suppression of the spontaneous emission background. Selection of a narrow(er) wavelength range essentially translating central wavelength jitter to intensity jitter. The latter is significantly easier to measure on a pulse by pulse basis 2 to be used in the analysis of other experimental data. Selection of a single harmonic. Either filtering away the fundamental if higher harmonics and thus shorter wavelengths are desired, or suppressing the contribution from higher orders if the fundamental wavelength is to be used. Selecting the seeded part of the spectrum suppressing the spontaneous undulator emission and the Sase background. The spontaneous and Sase background which lies directly underneath the seeded part will not be filtered away and thus contribute to a intensity jitter of the monochromatized pulse. From a wavelength stability aspect it is thus very advantageous to insert a monochromator before the experiments. This is provided that the intensity jitter between pulses can be measured on a pulse by pulse basis which can be included in the data analysis of the experiments. Ways of measuring the intensity are discussed in chapter 7 (see page 99). The price to pay for the wavelength stability is that the transmitted power through the optical system gets smaller (per each new optical element) and that the pulses get temporally stretched. The time-stretch can be controlled or compensated at the cost of transmission as will be seen below. For high energy photons (larger than about 2 kev) it is not possible to use gratings because their cut-off energy prohibits transmission. Instead crystal monochromators can be employed which is constructed from channel cut crystals (often Si) optimized to transmit one photon energy optimally. At Lcls one such monochromator is built into the beam transport system that is optimized for 8.3 kev[96]. Time-stretching In the soft X-ray ranges the incidence angle on any optical element needs to be small (i.e. the beam impinges at the optic at grazing incidence). Thus there will be a time difference between the parts of the beam that hits the surface first and the parts 2 Otherwise the full spectrum of the pulse (i.e. both wavelength and intensity distribution) needs to be measured on a pulse by pulse basis. This is slightly more involved than measuring the intensity in this manner, as discussed in chapter 7 (see page 99).

84 4.6. Beam attenuators 69 that hit at a later time, as illustrated in Figure 4.2. The time-stretching can be reversed by letting the beam bounce off a second surface at the cost of reduced transmission, it can also be controlled as it is proportional to the number of grooves that are illuminated by the beam[105]. By illuminating the grating parallel to the grooves (off-plane mounting) the time-stretching can be reduced also[106, 107]. Figure 4.2: Time stretching of a pulse arising from the grazing incidence. α β β α 0 th order Figure 4.3: A time-stretch compensating double grating setup. The beam moves from left to right in a Z-shaped path and the outgoing beam is parallel to the incoming. 4.6 Beam attenuators Although not a proper optical element per se, gas attenuators are a integral component of the beam transport system of free electron laser providing a robust mean of controlling the intensity of the radiation at the experiments. The intensity can be controlled in a continuous manner over several orders of magnitude with the limit set essentially by vacuum considerations, i.e. how good the differential pumping is. Beam attenuators and filters based on metal foils and metal/ceramic windows free electron laser beam can be used at higher energies provided that they can withstand the fluence of the X.rays. There is strong indications that, at least, gas attenuators do not distort the wavefront [104] thus conserving the coherence properties of the x-ray beam. Figure 4.4 describes a generic attenuator, at the Lcls there are solid attenuators included whereas at Flash and Scss only the gas attenuator is needed (owing to

85 70 4. X-ray optics Intensity detector Gas input Intensity detector Pumping Solid attenuators Pumping Figure 4.4: Schematic of a gas attenuator with intensity monitors before and after. their wavelength ranges). Intensity monitors are usually put before and after the attenuators 3. The gas attenuator at Flash is 15 m long and sandwiched between intensity monitors. It is operated either with nitrogen for the wavelength ranges nm, and for smaller wavelengths xenon or krypton can be employed. The differential pumping system is fast and changes of transmission of up to four orders of magnitude can be provided by the attenuator within minutes[104, 108]. At the Scss a smaller gas-cell is used with argon as attenuator gas[109, 110]. Lcls employs a 4.5 meters long gas attenuator using nitrogen for operation between 800 and 2000 ev photon energies. The pressure range is up to about 10 mbar and thus provide an attenuation span of four orders of magnitude. A set of solid beryllium attenuators (0.1 to 32 mm thickness) provide the attenuation for the harder X-rays up to 8 kev. 3 Intensity diagnostic devices will be discussed further in section 7.2 (see page 100).

86 4.6. Beam attenuators 71 Summary The demands on X-ray optical elements for free electron lasers are more stringent than those utilized for e.g. storage ring lightsources owing to the, in most instances, higher peak power of free electron lasers compared to the high average power exerted from storage ring synchrotrons. Damage on optical elements changes the properties of the radiation at the user stations vis-á-vis spectral content, intensity, coherence and temporal structure. Optical elements used at free electron lasers generally suffers damage primarily from ablation caused by the high peak brilliance of the source. In the VUV and soft X-ray regions diffraction gratings are universally adopted as the dispersive optic necessary to provide wavelength selection in monochromators. Simulation codes: Shadow[111], Xtrace[112], Spectra.

87

88 5. Beam-splitting methods The material presented here in this chapter is partly adapted from Survey of beam splitters by M. A. Bowler, A. J. Gleeson, D Laundy, and M. D. Roper. Iruvx WP7, 2010 by A. Lindblad. 5.1 Introduction The number of beamlines, where experiments can be carried out, at Free Electron Laser (FEL) facilities is much less than on synchrotrons, and may not be enough to meet user demand. One possibility of increasing the number of users being able to carry out experiments on free electron lasers is to split the radiation in a beamline into two or more separate paths allowing more than one experiment to be carried out simultaneously. This could be achieved by splitting the photon beam, or if the pulse repetition rate is slow enough, by kicking the electron bunches into different paths. This chapter is mainly concerned with the former technique, and gives a survey of techniques for splitting a photon beam. The type of beam splitter used will depend on the wavelength range over which it is required to operate. This chapter concentrates on the wavelengths from the vacuum ultra-violet (VUV) to the soft X-ray (SXR) regions. However, mention will be made of techniques employed at other wavelengths, at harder X-ray energies of relevance for example to XFEL, and at much longer wavelengths in the infrared regime of relevance to existing free electron lasers and possible future far infrared (FIR) sources. Beam splitters are also used to partition the radiation for pump-probe experiments, for sending a small fraction of the radiation for diagnostic purposes, and for input to interferometers. Beam splitters designed for these and other uses have been included as they may be able to be adapted to fullfil the requirements for allowing multiple end-stations to be used simultaneously. Beam splitters can be divided into two main categories. Firstly, there are those that divide the amplitude of the radiation, such as: partially transmitting mirrors - metallic foils, multilayers, pellicles, beam splitter plates beam splitter cubes thin crystals 73

89 74 5. Beam-splitting methods diffraction gratings wire grids Secondly, there are those that divide the wavefront, such as knife edge mirrors or crystals Fresnel bi-mirror slotted or perforated mirrors structured arrays In the case of a pulsed source, it is also possible to divide the beam in time by using moving mirrors (translating, rotating, vibrating) to deflect pulses in different directions. Each type of beam splitter is discussed in turn, and in section 5.6 a list is drawn up of those which may be suitable candidates for splitting a main free electron laser beam for multiple experiments for different wavelength regimes. General points for the specification of a beam splitter are given in section 2 before the survey of the different types. 5.2 Beam-splitter specification A sample specification is given in Table 5.1 for a beam splitter on an XUV-FEL. The full specification of a beam splitter will include the maximum power loading, overall efficiency, relative intensity of the split beams, minimum angular separation, polarisation and wavefront preservation. The required power handling and efficiency to a large extent will determine the incident angle and the material(s) used. The incidence angle will have a large impact on the size of the optic. Cost and ease of manufacture of the component are also important considerations. FEL radiation has a high degree of polarisation and coherence. In considering the suitability of different types of beam splitter, the starting assumption is that the quality of the incident beam is to be preserved in the split beams, i.e. polarisation, wavefront shape and pulse duration are preserved as far as possible. However, it may be that in order to increase the efficiency these assumptions have to be relaxed, at least in one if not both of the beams. Obviously the exact beam qualities required will depend on the experiment and preserving all properties may not be important in all cases and such a relaxation may not matter. Different splitting techniques will compromise different aspects of the beam and the correct choice will depend on the experiment; there is unlikely to be a universal beam splitter. The minimum required efficiency will be set by the ability of the optics to handle the power load or beam fluence. The efficiency requirement as determined by the flux needs of the experiments falls outside the scope of this survey. It is however assumed that the experiments on each branch will be equally demanding of photon flux and so the beam should be split roughly into equal parts. It is however noted that for some applications the free electron laser be may be too powerful, and it may be that a beam splitter could be used as an attenuator on one beam path. A further point to note is that he space available for the beamlines may well also limit the maximum angular separation and in general it may not be practical to have very large angular separations between the beams.

90 5.2. Beam-splitter specification 75 Parameter Value Comments Photon energy ev Average power W Depends on rep. rate Beam fluence 50 mj/cm 2 Value at 100 ev, normal incidence Grazing angle < 5, preferable 3 Determined by reflectivity requirements and ablation threshold Size mm by 50 mm Depends on grazing angle Overall efficeny > 50% This may increase if power loading becomes problematic Intensity split Roughly equal in each branch Polarisation Ideally small/negligable This will be difficult for lower energies Wavefront distortion Ideally the modal structure of the beam should be preserved Minimum angular 5 mrad (0.3 ) separation of beams Vacuum compatibility UVH bakable hydrocarbon free for operation near the carbon edge Table 5.1: Sample specification for a beam-splitter for XUV radiation.

91 76 5. Beam-splitting methods 5.3 Amplitude division beam splitters Partially transmitting materials Partially transmitting mirrors can be made from metallic foils or multilayers. When these are deposited on glass they are termed plate beam splitters, or on a thin (of the order of µm thickness) stretched polymer membranes, they are termed pellicles. Thin crystals are also used as beam splitters in the harder X-ray regime. Plate beam splitters, by their nature of being deposited on glass, operate mainly the visible and near infrared (NIR) but their range can be extended to 200 nm using UV grade fused silica as the substrate. They will normally have the beam splitter coating on the front face of the plate and an anti-reflection coating on the back to prevent ghosting and the substrate will be slightly wedged to eliminate interference fringes. They can be either polarising or non-polarising. Polarising beam splitters use bi-refringent materials and/or are operated near the Brewster Angle. Plate beam splitters can be made for high power applications, but those that are readily available are mainly single wavelength, single angle devices, made for specific laser lines. As an example, ESCO[113] make a range of beam splitters with a 10% bandpass, damage threshold W/cm 2, designed to work at 45 incidence for a range of laser lines from the UV to IR. Broadband dielectric plate beam splitters are available in the visible and NIR, e.g. Newport[114] provide beam splitters covering the wavelength ranges nm, nm, nm. These operate at 45 angle of incidence and all are slightly polarising. The damage threshold is quoted as typically 500 W/cm 2 CW, 0.5 J/cm 2 with 10 ns pulses. Conventional plate beam splitters may not be applicable for ultra-fast use due to dispersion in the transmitted beams. Newport provide thin (3mm) ultra-fast plate splitters made from UV quality fused-silica operating over nm for s-polarised light and nm for p-polarised light. Again these operate at 45 angle of incidence and split the radiation nearly 50:50 and are usable for pulses in the 100 s of fs regime. Pellicles Pellicles operate in the wavelength range nm. They have the advantage over plates in that there is no ghost image due to their extreme thinness (except for extremely short pulses which would only be a few cycles long at these wavelengths). For uncoated pellicles the reflectivity is about 10%, transmission about 90%, but coatings have been made which increase the reflectance up to the order of 50 %. Typical damage thresholds are 2 W/cm 2 CW and 1 J/cm 2 with 10 ns pulses for uncoated membranes, which makes them unsuitable for free electron laser beamlines. The thin membranes are also susceptible to vibration and interference fringes. For further details see for example: [114, 115]. As an extension to what is normally considered to be a pellicle, a beam splitter for an FTIR spectrometer has been made for the THz free electron laser at KAERI by coating a polyester film with silver [116]. At 3 THz, the absorption of the polyester film is about 2%, and the balance between reflection and transmission was obtained by coating the film with several tens of nanometers of silver to create the beam splitter.

92 5.3. Amplitude division beam splitters 77 In an analogous manner, thin foils of a low-z material might be used at soft x-ray and shorter wavelengths. For example, Lcls propose to use 30 µm thick polished beryllium foils at a grazing angle ( 1 for energies around 8 kev) above the critical angle to reflect a small ( 0.01%) part of the beam to a diagnostic instrument, while transmitting 99% of the radiation[117]. Because low-z materials give a sharp reflection cut-off, achieving a more balanced split will require the grazing angle to be adjusted to suit the photon energy and hence the angle of beam separation would be a function of photon energy. At lower photon energies high transmission will not be possible e.g. it is effectively zero below 1 kev for a 30 µm Be foil. Extension of this technique into the XUV would require exceptionally thin foils where the challenge of manufacturing and supporting a surface of sufficient quality for good reflection would be very severe indeed. Where absorption is high, there is also the concern of radiation damage. Multi-layer beam splitters Multi-layer beam splitters can be made for the XUV and shorter wavelengths, however in general they only operate for a given wavelength and incident angle. Multi-layers are usually formed onsic, SiNor Si 3N 4 membranes butobviously for thetransmission multi-layers required for beam splitters, absorption in the membrane is a problem at XUV wavelengths. Much work has been done in the nm wavelength range for applications in lithography using multi-layers on Si 3N 4 membranes, however in general the overall efficiencies are not very high. Some examples found on the web with overall efficiency greater than 20% include: Near-normal incidence (10 ) Mo/Si multilayer - reflectivity 28%, transmission 32% [118] Ru/SiNbilayeroperatingat17.5 incidence -reflectivityandtransmission about 11% [118] Mo/Si multilayer on silicon nitride at 7.2 incidence - reflectivity 20%, transmission 22% [119] Some work has been done on manufacturing free-standing multi-layers. For example, Haga, et al. [120] report the manufacture of a 10 by 10 mm 2 Mo/Si multilayer where the silicon nitride membrane is etched away. The outer Mo layers were replaced by Ru which was much more resistant to the etching process. They also investigated the effect of the substrate smoothness on the efficiency of the multi-layer. Measurements using synchrotron radiation revealed that the multilayer worked as a one-to-one beam splitter whose reflectivity and transmittance for s-polarised radiation at 13.4 nm are both 27% at an angle of incidence of 45, i.e. the efficiency is similar to supported multilayers. More recent work on free-standing multilayers has not been identified. By varying the thickness of the multi-layers with depth, the wavelength and/or angle range can be increased, e.g. for reflecting multi-layers a reflectivity of larger than 40% is expected over the energy range 4-9 kev using 20 Mo/Si bi-layers with five different spacings on an SiO 2 substrate[94]. If these multi-layers could be made on transparent substrates, their use as beam-splitters could be investigated. Note again there may be a problem of dispersion which may preclude their use for very high time resolution application[121].

93 78 5. Beam-splitting methods Radiation damage is an area for concern for the use of multilayers in free electron laser beamlines. Recently Bajt, et al. [122] reported that a normal incidence parabolic Mo/Si multilayer mirror with a reflectivity of about 60%, used to focus 13.5 nm radiation at Flash did not show signs of damage. This efficiency is similar to the overall efficiency of some of the beam splitters mentioned above. Obviously more work needs to be done in this area. However, it is unlikely that a multilayer beam splitter would be used for the current application due to the wavelength specificity as well as possible power handling issues. Beam splitter cubes Beam splitter cubes onsist of 2 right-angled prisms, made of fused silica for UV applications, normally cemented together with an epoxy. Broadband cubes, with bandwidths of nm, are available over the wavelength range nm, and may alter the polarization of the light by about 10%. There are nonpolarizing cubes designed for specific laser lines in the UV, for moderate power laser operation. The epoxy absorbs radiation and hence cannot be used in high power applications. However, cubes which do not use adhesives to cement the prisms together have been recently designed for high power laser applications, e.g. Showa Optronics[123] market a cube for the UV over the range 193nm nm with a damage threshold at 248 nm of 1 J/cm 2 and Precision Photonics Corporation[124] make cubes for high power applications (damage threshold of 10 J/cm 2 at 1100 nm) in the visible and IR. Crystal diffraction beam splitters Perfect crystals are commonly used as monochromating elements for hard X-rays (working at X-ray energies above about 2 kev). An X-ray entering a perfect crystal scatters from the regularly space atomic planes - a process known as dynamical diffraction[125]. This leads to a very sharp reflectivity curve with a bandpass ( E/E) for a given angle of incidence (Bragg angle) that is typically less than The bandpass depends on the crystal material (diamond is narrower than silicon which in turn is narrower than germanium), on the crystal planes used (planes with lower order indices generally give narrower reflections) and on whether Bragg or Laue geometry is employed. In Bragg reflecting geometry, the X-rays enter and exit from the same surface of the crystal while in Laue geometry, the X-rays enter and exit from different surfaces. In Bragg geometry, the X-rays penetrate a short distance into the crystal and the reflectivity curve is given by a Darwin curve, which approximates to the ideal top hat shape. A general consequence of the narrow bandpass associated with dynamical diffraction is that the temporal profile of a short X-ray pulse is affected. When the radiation source bandpass is larger than the crystal reflection bandpass, as is the case with X-ray FEL radiation, a crystal monochromator can be used as a beam splitter. This method uses a crystal to deflect a small energy band from the broader band source to one experiment while the remaining transmitted radiation is passed onto a second experiment. Thin crystals are normally used to minimise absorption. Crystal reflections are sensitive to heating from the radiation which can result in changes in lattice parameter and lattice orientation which may degrade the deflected beam. The ideal beam splitter crystal should have low X-ray absorption to minimise losses to the X-ray beam and to reduce X-ray beam power absorbed inside the crystal.

94 5.3. Amplitude division beam splitters 79 This method of splitting beams for multiple experiments is used on some undulator and high-energy wiggler X-ray beams at synchrotron radiation sources. In the lower X-ray energy range, diamond is often used as the beam splitter as it has low X- ray absorption and also good thermal conductivity that allows the heat to dissipate efficiently, reducing thermal distortion of the crystal. The difficulty of obtaining diamond crystals with high enough perfection for use as monochromators is a problem that has been recognised[126]. A second monochromator crystal may be used to deflect the beam back into the incident beam direction and if the first reflection is a diamond (111) reflection it is possible to use a germanium (220) reflection as the second reflection as the d-spacings of the two reflections are very similar. Using a germanium reflection for the second crystal has the advantage that the reflection has a broad width making alignment easier and reducing loss of X-ray flux caused by strain within the diamond crystal. The addition of a second crystal may also allow the X-ray energy to be changed while maintaining almost constant X-ray beam direction. This method of X-ray beam splitting is used at the ESRF on the Troika beamline ID10, which has three undulator segments and has available a selection of monochromator crystals - diamond (111), diamond (220), and silicon (111) - allowing a variation in bandwidth on two side stations. Another example at the ESRF is the macromolecular crystallography beamline ID14 which has three diamond (111) and germanium (220) monochromator pairs, in line, to give three 13.3 kev fixed energy stations and a single variable energy station using the straight through transmitted beam. In the higher X-ray energy range, X-ray absorption is lower and silicon or germanium may be used as the beam splitting crystal. This allows the bandpass of the reflection to be varied by applying a bend to the crystal. An example of this application at the ESRF is the high-energy beamline ID15 which can use two bent crystals to deflect beam from the wiggler source to two side stations at X-ray energies from 30 kev up to 300 kev. Where beam splitting is required for X-ray interferometry, perfect crystals are used. Laue interferometers[127] use the forward transmitted and reflected beams at the crystal exit surface to split the beam. Interferometric beam splitters using multiple reflections[128] or the beams reflected from and transmitted through a crystal whose thickness is less than the extinction depth can also be used. These techniques might be useful where multiple low-bandpass ( E/E 10 5 ) beams are required, though there could be thermal problems since the radiation out of this bandpass will be absorbed in the crystal. A similar application to that of X-ray interferometry is the use of crystal beam splitters in optical delay lines. A splitter/delay line at 8 kev has been designed for the Lcls using Si (400) crystals[129]. A 10 µm thick Si (400) crystal has 80% reflectivity in a bandpass of E/E with a transmission outside this region of 75%. The reflected and transmitted beams are sent via different sets of crystals to be ultimately recombined on a common path but with a variable delay created by translating one set of crystals. Two pulses are created by tuning the crystal sets to wavelengths that differ by more than the bandpass of the crystal reflection but with both contained within the bandwidth of the free electron laser pulse. A similar device working at 8.39 kev with Si (511) crystals and 12.4 kev with Si (553) has been constructed at HASYLAB and tested on beamlines at DORIS-III, PETRA-II and the ESRF[130, 131].

95 80 5. Beam-splitting methods Gratings Gratings provide a very simple way of splitting a beam, though there are a number of practical limitations and consequences. A grating divides an incoming beam of a given wavelength into a series of orders spaced around the zeroth order beam, which has a diffraction angle equal to the incidence angle. Inside orders have a diffraction angle (measured from the grating normal) smaller in magnitude than the incidence angle and outside orders have a diffraction angle that is larger in magnitude than the incidence angle. By convention, diffraction angles that are on the opposite side of the normal are negative. For a beam splitter, one could choose to use either one of the first order and the zeroth order beams, or the first inside and the first outside order beams. Higher diffraction orders are unlikely to be used as they have lower efficiency. A possible advantage of using the first inside and outside orders is that the grating acts as a monochromator for both. Conversely, the zeroth order contains all the spectral content of the incident beam up to the cut-off determined by the reflectivity of the grating coating and so a second grating would be needed to give a monochromatic beam. However, this would allow independent choice of wavelengths for the two beams. The relative intensity of the first diffracted to the zeroth order depends on the shape of the diffraction grating grooves. A careful choice of the groove profile based on modelling the efficiency with a code such as Gradif 1 can give a certain degree of tuning of the relative intensity, but one cannot expect perfect control if the grating is to operate over a wide range of wavelengths. One should also remember that the required zero order efficiency could be, and probably will be, at a wavelength that is unrelated to the first order wavelength. Therefore, a comprehensive set of calculations would have to be performed to give not only the first order efficiency as a function of wavelength, but also the zeroth order efficiency as a function of both wavelength and incidence angle. There is thus no unique value to the efficiency at a particular wavelength into the zeroth order beam as it depends on wavelength of the first order beam and hence angle of the grating. Any requirement to tune the grating leads to the most significant practical problem with using a grating as a beam splitter. As the grating is rotated to select a different wavelength, the angle between the first and zeroth orders will change. Similarly, the angle between the first inside and first outside orders that have the same wavelength will also change. (Conversely, the wavelength into a fixed outside order direction will change in the opposite direction and at a different rate to the wavelength in a fixed inside order direction). This is very inconvenient for a beam splitter that is to feed fixed end stations from a fixed source. One solution is to place a plane mirror, which can both translate and rotate, after the grating. This mirror intercepts the zeroth order beam and steers it always to a fixed output path. The disadvantages of this are that the path length will change (so changing the overall beam timing) and that the mechanism is complicated and so prone to introducing small errors giving temporal and spatial jitter to the beam. An alternative approach is to use the SX700 type of variable included angle grating mount. In this, a plane mirror rotates about an axis not in the mirror surface and allows the included angle at the grating to be varied by just a single rotation. The 1 Gradif is an update of the LUMNAB code of M. Nevière, et al. [132]

96 5.3. Amplitude division beam splitters 81 mechanically simpler mount will work with less mechanical error, but there is still a path length change, and so the overall beam timing is a function of wavelength. Providing the grating is working in collimated light, there can a free choice of included angle without changing the focusing properties of the monochromator. This free choice of included angle can be used to either keep a fixed angle between the first diffracted order and the zeroth order, or to keep the first inside and first outside orders at a the same wavelength with a fixed angle between them. In the case where the angle between the first and zeroth order is to be fixed, one also finds that this is the same constraint for scanning a blazed grating on-blaze and thus has a potential advantage in optimising the first order efficiency. This would naturally be at the expense of the zeroth order efficiency at that wavelength, but this will not be a problem if the two branches are to operate at different wavelengths. If the angle between the first inside and zeroth order beam is ψ, then the grating equation under the constraint that ψ is fixed becomes Nmλ = 2sin ( ψ 2 ) cos ( ψ 2 β ) (5.1) where β is the diffraction angle. For a blazed grating operating on-blaze, the blaze angle should be ψ/2. A similar expression is obtained if the angle between the first inside and outside orders is to be kept constant and both orders are to pass the same wavelength. If β + is the diffraction angle of the first inside order and β the diffraction angle of the first outside order, then the angle between them is and the grating equation for constant ξ becomes ( ) ( ) ξ ξ Nλ = 2sin cos 2 2 β+ ξ = β + β (5.2) (5.3) which gives the diffraction angle of the inside order for a given wavelength, from which the incidence angle and diffraction angle of the outside order can be calculated. In both these modes of operation, the tuning range will be limited if the grazing angles at the grating are not to become large (and hence the efficiencies low). In general, the angles between the orders (ψ or ξ) will have to be < 3, and low line density (a few hundred lines per mm maximum) gratings used. A disadvantage of using a grating as a beam splitter with very short pulses is that the pulse is temporally stretched in the diffracted orders due to the path length difference across the beam in the dispersive direction as discussed in chapter 4 (see page 63). Since the pulse stretch is λ/c for each groove illuminated, one way to mitigate this effect is to use very low line density gratings. At shorter wavelengths and relatively long pulses, this may be sufficient to prevent the pulse stretch becoming significant. At longer wavelengths and shorter pulses, it may not be possible to illuminate sufficiently few grooves and a second grating must be used to reverse the stretch of the first. The second grating must work with incident angle equal to the diffraction angle of the first and in the opposite order of diffraction. Therefore, if a variable included angle mounting is being used for the first grating, it must be replicated

97 82 5. Beam-splitting methods for the second grating with consequent impact on the cost and further path length variations. The system with a translating and rotating plane mirror that intercepts with just the zeroth order beam after the grating would be simpler in this respect as both the grating mounts could simply be fixed included angle type. Alternatively, conical diffraction mounting can be used to reduce the pulse stretch (since the effective number of illuminated groves is reduced when compared with the classical mount). The further advantage of the conical mount is that the diffraction efficiency should be much higher. However, in the context of a beam splitter, the conical mounting leads to difficulties. It is normal to operate the grating in fixed altitude mode as this allows the grating to be tuned with just a simple rotation (about an axis parallel to the grooves). Unfortunately, in this mode, the zeroth order (for example) changes direction in both the horizontal and vertical planes. Capturing and steering the zeroth order beam into a fixed direction will be very difficult. Fixed azimuth mode would make capturing the zeroth order beam easier, but scanning the grating requires translating and rotating mirrors. A scheme for using diffraction gratings as a beam splitter has been proposed for FERMI@Elettra for wavelengths around 40 nm. Light from the 0 and +1 orders is used. For the 1st order radiation, a second grating followed by a translatable plane mirror allows the pulse stretch to be compensated and gives a fixed position for the output beam[133]. An efficiency of about 30% has been estimated for both the zero and first orders using at 100 lines/mm grating, 84 incidence angle, over the wavelength range of nm. This design requires the manufacture of a long (60 mm) grating to a very high specification, as well as a translating mirror hence it is technically challenging. The above applications are all for reflection gratings. Transmission gratings can also be used to split the beam with the advantage that, since the gratings are used at (or near) normal incidence, the geometry of the split beams is much simpler. Manufacturing transmission gratings that can work in the XUV to x-ray region is of course a major technical challenge. Achieving adequate dispersion (and hence beam separation) at short wavelengths requires the grating period to very small. The aspect ratio (depth/width) of the grating bars is inevitably quite high if the gratings are to be robust and they are therefore not suitable for strongly divergent light. The risk of ablation of the grating in a free electron laser pulse is also a major concern. In the XUV, a transmission grating will almost certainly behave as an amplitude grating, since it will be difficult to make the grating bars anything other than 100% absorbing. Strong absorption means the grating must also be made unsupported, which is very difficult. Assuming a perfect amplitude grating can be made, the maximum first order efficiency occurs when the groove width is half the grating period and is just 10% and the zeroth order efficiency is 25%. Conversely, for hard x-rays, it is difficult to make the aspect ratio of the grating bars high enough to be perfectly absorbing and the grating will function as a phase grating. The efficiency depends on the grating material and bar profile, and this offers scope for tuning the grating performance. Weitkamp, et al. [134] used a Ronchi phase grating to make an x-ray shearing interferometer. The grating is made by electron-beam lithography from silicon and has a groove period of 2 µm and depth of 9 µm. They operated the grating at 12.4 kev (1 Å), but were only producing a small shear in the beam. The phase shift of the grating was tuned by tilting the grating about an axis perpendicular to the grooves and the beam axis so as to vary the effective thickness of the grating. This allowed

98 5.4. Wavefront division beamsplitters 83 the phase shift to be increased to π and hence the zeroth diffraction order eliminated and first order efficiencies maximised. Naturally, this technique can only be employed when the grating bars have sufficient transmission, and is thus only applicable for harder x-rays due to the difficulty in manufacturing very thin gratings with such a fine structure. Gratings can also be used to send a small part of the beam (in first order) to a spectrometer for measuring the spectral content of the beam, while most of the beam is in the zeroth order and is passed down the beamline to the experiments. The groove profile of the grating is tuned to give just sufficient intensity in the diffracted order for the spectrometer to work (thus maximising the beam intensity to the experiment) and the line spacing is varied to give a flat field for the dispersed spectrum on the detector. Such an instrument is being installed at Flash [135]. A point of concern for operating gratings in free electron laser beams is the effect of the structured surface on the likelihood of ablation since parts of the surface may make very steep angles to the incoming beam. The effect of the groove shape on the ablation threshold is not understood. If this were to be a problem it would be exacerbated with classical grating mounts where the grating is likely to operate at quite a steep angle to the beam at long wavelength part of the spectrum. In this regard, conical diffraction in constant altitude mode has an advantage as the beam strikes the grating at effectively the same grazing angle even as the grating is tuned. Grids Wire grids can be used as polarising beam splitters for FIR radiation and are used in Fourier Transform Infra-Red (FTIR) spectrometers. Radiation with polarisation parallel to the wires is reflected, whereas the component polarised perpendicular to the wires is transmitted. As an example, the Millimetre-Wave Technology group[136] in the Space Science and Technology Department of the UK Science and Technology Facilities Council (STFC) has manufactured wire grids for a FTIR spectrometer to be used on the THz beamline on ALICE, the energy-recovery-linac-based developmental light source at Daresbury Laboratory. 5.4 Wavefront division beamsplitters Beamline apertures The simplest method of splitting a beam by wavefront division is to use apertures to divide the beam into two spatially separated parts, as is often done on synchrotron sources where there is a large fan of radiation(e.g. from dipoles or wavelength shifters). The disadvantage of this is that the angular separation of the two beams is determined by the natural divergence of the source, which will be rather small for a free electron laser. Nevertheless, the technique might be suitable for separating off a small part from the extremity of the beam to pass to a beam monitor or some beam diagnostics, or for coherent scattering experiments from small samples. If greater separation is required, a mirror could be used to deflect one beam downstream of the aperture, though this is effectively the same situation as the knife-edge mirror described below. As with other methods that divide the wavefront, edge diffraction effects are likely to

99 84 5. Beam-splitting methods be significant. The design of the aperture would have to eliminate the risk of radiation damage. Knife-edge mirrors The radiation can be split by inserting a mirror part way into the beam to deflect a portion of it. As an example, a grazing incidence (3 ) knife-edge mirror is used as part of an autocorrelator system designed at BESSY for use in soft X-ray pump-probe experiments at Flash[137]. The autocorrelator was designed to work up to 200 ev, and the slope error on the mirror is required to be less than 0.5 mikro-rad. This slope error must be maintained up to the cutting edge of the mirror and this is very difficult to achieve with conventional polishing techniques as there is always some roll-off at the mirror edges. The required quality was achieved by cutting away the end of the mirror after polishing to remove the roll-off region. Alternatively, the edge of the mirror could be masked with an aperture (see above). 6 Beam splitter 3 Figure 5.1: Schematic of knife-edge grazing incidence mirror beam splitter for soft X-rays. For harder X-rays, the grazing angle needs to be smaller to maintain a high reflectivity. The required minimum beam separation of 0.3 in the sample specification above means that the grazing angle must be greater than For carbon, the reflectivity is greater than 98% for energies from 1 kev to 10 kev at this incidence angle, but the mirror could become very long. For slightly larger angles the cut-off in reflectivity with increasing energy will be the main limiting factor in the usable wavelength range, e.g. the reflectivity of carbon decreases rapidly above about 3 kev for a grazing angle of 0.5. Using a coating with higher atomic number (nickel, rhodium) will give a reflectivity cut-off at higher energy for a given angle, but such materials do not have as high a damage threshold as carbon. The main concern about using a mirror as a beam splitter is that edge diffraction could have a significant effect on the wavefront, especially as the beam is being cut in the middle where the amplitude is likely to be highest. This type of beam splitter cannot therefore be expected to produce two beams that are lower intensity replicas of the original beam. Knife-edge crystals To achieve higher angular separation at shorter wavelengths, the knife-edge mirror could be replaced by a knife-edge crystal. For example, the Bragg angle of the silicon (111) reflectionat8kevis14.3, whichgivesabeamdeflectionangle of28.6. Doublecrystal arrangements could be used to give a deflected beam with a fixed exit direction as the crystal is rotated to tune the photon energy. The splitting crystal would have

100 5.4. Wavefront division beamsplitters 85 to be translated orthogonally to the beam direction or rotated about its cutting edge if the fraction of the beam it intercepts is to remain constant. Edge diffraction and the impact on the wavefront would still be an issue, especially as it may be difficult to maintain a perfect crystalline structure to its edge. There would also be a change in the pulse length of the beam deflected by the crystal due to the monochromating action of the crystal, and the reduced bandwidth will also limit the overall efficiency for the reflected beam. Fresnel bi-mirror Fresnel bi-mirrors consist of two flat mirrors, normally joined along one edge and inclined at an angle to each other see Figure 5.2. In general they are used in interferometers where the radiation reflected from the two parts of the mirror is inclined towards each other, resulting in interference. An example is their use in an interferometer on SU7 at SUPERACO[138], where silica mirrors at a grazing angle of 3 6 were used for 4.4 nm. While bi-mirrors could be used to cross the beams over each other and separate them, it is hard to see any advantage over the use of a single grazing incidence knife-edge mirror a p a Fresnel s bi-mirror Figure 5.2: Basic design of the Fresnel mirror interferometer. Rays a and a create an interference pattern when they add up. Slotted or perforated mirrors In this method, the incident wavefront is coherently split on a microscopic scale with the use of holes or slots cut in a mirror. This method is easier for longer wavelengths, but has been realised in the XUV regime, e.g. a slotted mirror has been used in an interferometer on beamline on the ALS[139]. This is similar to the proposal for a prototype beam splitter to be made for IRUVX by AZM at BESSY[140], in which arrays of small holes will be machined in a grazing incidence mirror. An area of concern is the ability to manufacture high aspect ratio holes to a great enough precision and surface quality. The effect on the coherence of the radiation must also be considered.

101 86 5. Beam-splitting methods Losses in reflection due to diffraction as well as filling factor have to be taken into account for mirrors with holes in them. One such example in the field of microelectromechanical systems (MEMS), an area of considerable research effort, has been found. A key component for future nanoscale optical devises is the freestanding micro-machined mirror as shown in Figure 5.3. Figure 5.3: A MEMS free-space optical reflector. Taken from Zou, et al. [141].Note the scale at the top of the figure the line is 200 µm long. The holes in the mirror surface serve no useful purpose regarding the function of the reflective surface. They are commonly referred to as release holes and allow release etchant to flow behind the mirror once the micromachining process is finished, releasing the component from the bulk material. In[141], the losses in the reflectivity due to the filling factor and diffraction are calculated for light of wavelength nm as a function of hole size from 5-23 µm and spacings of µm. For the case of 21 µm square holes spaced at 30 µm, the filling factor is 50%, and the loss in reflected light due to diffraction was estimated to be 14%. For the same spacing, as

102 5.4. Wavefront division beamsplitters 87 the hole size decreases, the diffraction loss increases, so that for a 10 µm hole size the filling factor loss is 11%, and the diffraction loss 15%. Much bigger holes relative to the wavelength were used in the beam splitter for the ALS interferometer, designed to operate between 60 ev and 100 ev. Slots were cut in a highly polished (rms roughness 3 Å) single crystal silicon wafer. Based on the coherence properties of the incident X-ray beam, the width and spacing of the slots were set to 50 µm and 100 µm respectively. The slots were 15 mm in length and created by chemical etching. The completed assembly was then coated with molybdenum. A major concern in the manufacturing was to keep the mirror flat to within 1 µrad, and to maintain the surface smoothness. Structured arrays A 1-D capillary beam splitter has been designed to work around 13.9 nm (89 ev) on a plasma-based XUV source[142]. It consists of a stack of 20 µm thick plates, 7.9 mm long and separated by 130 µm. The plates are tilted at a small angle (grazing angle of ) with respect to the incoming radiation. Light can either pass unhindered between the plates, or else undergo a single reflection, causing two beams to emerge at different angles. At 0.8 angle of incidence, all the light has to be reflected to get through the device. The transmittance (efficiency of the direct path) varies from 85% to 0% depending on the angle of incidence. The efficiency of the reflected light varies from 0% to 75% and 15% of the light is lost by absorption on the front edges of the plates. If a similar design were to be used for splitting free electron laser beams, the stack would need to be designed to absorb a smaller fraction of the radiation. The effect on the wavefront would also need to be investigated. Capillary arrays have been used in the kev regime to suppress higher order harmonics passed by a monochromator on a bending magnet beamline at BESSY[143]. This device uses a double reflection in the array, the grazing angle of 3.6 mrad giving an 89% efficiency at each reflection, so the reflected light is in the same direction as the incident; however this example shows that single reflection capillary plates could be used at this wavelength. An alternative construction scheme could be to adopt the same technology used to form Multilayer Laue Lenses (MLLs)[144]. The x-ray lens technology developed by Argonne National Laboratory consists of many individual layers precisely sputtered onto a silicon wafer. The multilayer stack is then sliced to form a thin transmission element in which the stacked diffracting surfaces are oriented almost parallel with the optical axis. Although developed as a Fresnel lens structure for micro-focus applications, it is foreseeable that the same technology could be used to create a beam splitter, either by employing a similar geometry to that used in the capillary beam splitter stack or as a knife edge diffractive element redirecting a proportion of the beam. Possible drawbacks for this unproven technology include radiation damage to the multilayer structure and achieving the necessary manufacturing tolerances for both the microstructure fabrication and material slicing.

103 88 5. Beam-splitting methods 5.5 Time-based splitting An alternative to splitting the wavefront in space is to send alternate pulses or trains of pulses to different beamlines. One scenario is to send hours/minutes worth of pulses to one experiment while the other endstation is changing samples, checking data, etc. This could be done simply using a switching mirror. At the other end of the time scale, is may be possible to use vibrating mirrors or alternating mirrors and slots on a rotating disc to send alternate pulses to two end-stations. The feasibility of this will depend on the repetition rate of the free electron laser. An early example utilising a disc rotating at 25 Hz was designed and used at on a synchrotron radiation source at DESY. A grazing incidence mirror occupied a segment of roughly a quarter of the disc area, with an equally sized slot occupying about another quarter. The system operated for wavelengths ev, the grazing angle of the mirror being 4 [145]. In order to increase the repetition rate, one could use the fact that the free electron laser beam is much smaller than those from a synchrotron radiation source and consider a system of several mirrors and slots on a disc, and also increase the rotational speed of the disc. High-speed slotted discs have been designed for use as beam choppers. For example, a beam chopper for operation at photon energies below 50 ev has been built by Forschungszentrum Jülich GmbH for use on the synchrotron radiation source at BESSY. The disc is aluminium alloy with a diameter of 338 mm and has 1252 slots cut in the edge. It uses magnetic bearings and is designed to spin at about 1 khz. It was reported at the SRI meeting in 2008 that the chopper had been successfully tested at 1 khz and will be commissioned with photon pulses in the autumn of 2008[146]. Asecondexample, inthiscaseusingairbearings, isthechopperwhichwasdesigned to chop the 4.3 MHz pulsed beam from the VUV-FEL on proposed 4GLS facility to 100 khz. The disc would have to have withstood a high heat load from the 400 W of beam power as well as high mechanical stresses from the high speed rotation. Consequently, martensitic stainless steel was chosen for the disk material. The disc had a polished chamfered edge to reflect the unwanted light at 2.5 grazing angle. A prototype chopper with just 2 slots has been built and tested by Fluid Film Devices Ltd[147]. The disc has a diameter of 134 mm and was tested up to 500 Hz, half the design frequency, before the project was discontinued due to 4GLS being replaced by the NLS project. If one wanted to use the chamfered edge to reflect the light into a beamline for use by an experiment, the edge would need to be polished to an optical quality surface. An alternative would be to attach mirrors to the disc. Both options require further feasibility studies. For the martensitic steel prototype described above, the manufacturer was not able to polish to the edge to optical quality, though the main aim was simply to reflect as much of the incident power as possible to prevent it from being absorbed in the disc. Distortions at the edge of the disc could also be a problem. For the second option, the feasibility of having mirrors bonded onto a high-speed rotating disc would need to be investigated. Furthermore, this technique would be difficult to apply to X-rays since the very grazing angle required for good reflectivity would lead to a thick disc and very high mechanical loads. At Flash the X-ray beam can be switched between two user experiments by a mechanically switching mirror. This reduces the repetition rate at the user experiments

104 5.6. Summary 89 to 2.5 Hz (with maximal switching frequency). The stated accuracy of the movement back and forth is a few µ m in the position and about 1 arcsecond in the angle[148]. 5.6 Summary As the preceding sections have shown, there is a wide variety of techniques that can be used divide a photon beam. Some of these techniques are very well established, whilst some are more developmental. A key issue for free electron laser sources is that the properties of the radiation produced extend into new ground when compared with conventional laboratory or synchrotron sources. The short wavelengths, high transverse coherence, short pulse duration and high pulse energy all mean that there is some element of development required for any splitting technique. Two lists of techniques are presented for further consideration for use mainly in the soft x-ray regime. The first list gives those techniques that would seem amenable to rapid development into practical beam splitters. The second list gives the techniques that show potential but will require more extensive development to over come the technical challenges. In all cases, the properties of a beam splitter derived from a particular technique will be somewhat specialised and so there will be no universal beam splitter. The technique chosen will depend on the nature of the photon beam being split and the particular needs of the experiment. Techniques requiring the least development Diffraction gratings Reflection gratings give amplitude division and since they can be made to very high tolerances, splitting with good wavefront control should be possible. Polarization effects will be present but should only be significant at VUV and XUV wavelengths. At least one of the beams will be monochromatic. Additional optics are required to keep the output beam directions constant if tuning of the photon energy is required. Pulse stretch is inevitable for ultra-short pulses, but can be corrected with a second grating. In general, flexibility is high, but the systems are likely to be complex and optimizations will give a more restricted operating envelope. The likely operating range is from the VUV to the soft X-rays. Infrared gratings are also feasible, though there are arguably easier splitting techniques for this part of the spectrum. Knife-edge mirrors A knife-edge mirror is one of the simplest techniques and also offers a very flexible splitting with minimal constraints. Both beams are essentially spectrally unmodified, though the reflected beam will be filtered at wavelengths shorter than the mirror reflection cut-off. Very low grazing angles will thus be required for hard X-ray operation, and so the splitting angle will become very small. (Bragg reflection from a crystal will give larger angles but with the disadvantages of reduced bandwidth and the need to rotate the crystal for wavelength tuning). The splitting is achieved by wavefront division and so the main disadvantage is that neither beam is a replica at reduced intensity the incident beam since diffraction effects at the edge will distort the wavefront. However, pulse lengths should be preserved. A key technical challenge

105 90 5. Beam-splitting methods is achieving a mirror with an edge that does not badly degrade the beam at the division region. Knife-edged mirrors could be designed to operate over the entire spectral range from infrared to X-ray wavelengths (though not necessarily in one device). Slotted mirrors A slotted (or perforated) mirror may overcome the key disadvantage of the knifeedge mirror by dividing the wavefront periodically in space (thus making each beam closer to a less intense replica of the incident beam) whilst maintaining the advantages of transparency (to the pulse properties) and flexibility. The technical challenge of making the mirror is however much more severe. There is no inherent restriction on spectral range, though the technical challenges will become more severe at shorter wavelengths and the devices may be limited to the soft X-ray regime and below. Crystal diffraction beam splitters These are mainly applicable to use at shorter wavelengths (< 6 Å), but have the advantage in this range over mirror type splitters of allowing much greater angular separations. Wavelength tuning requires a rotation of the crystal and hence additional optics to maintain a constant output beam position. Laue and Bragg reflections are always highly monochromatic (unless one distorts the crystal lattice) and so the full bandwidth of the free electron laser is not preserved. Accompanying this is a stretching in the pulse length and whilst this stretching should be small (a few femtoseconds), it cannot be reversed as is the case with a grating. Only in the case of very thin crystals can a broadband transmission be achieved, though there will be a missing component matching the bandwidth of Laue/Bragg reflection of the split beam. The most important area for technical development is in achieving higher quality diamond crystals, which are attractive due to their high thermal conductivity and resistance to radiation damage. Techniques requiring more development Multilayers A transmission multilayer is the most likely way that a plate beam splitter can be realized at short wavelengths. In fact, the multilayer beam splitter will be more akin to a pellicle. The technical challenges are thus making a membrane that is robust and flat but has adequate transmission. If the membrane is small, this will be easier but then the beam fluence will be high if the beam must be focussed onto it in order to fit through it. A larger membrane would allow operation in the diverged light but may be challenging to keep flat and vibration free. Structured arrays These devices have similar properties to slotted mirrors but differ in the approach to fabrication. Operational range will depend on the fabrication technique (e.g. the overall thickness of the structure is linked to the angular acceptance). Wavefront quality will be very dependent on the manufacturing and thus development is required.

106 5.6. Summary 91 Time-based splitters Mechanical switching to direct alternate pulses (or trains of pulses) to different beamlines is a logical approach for an inherently pulsed source. The potential advantage to the experiment is that all received pulses contain the full free electron laser output and can (in principle) be unchanged in all other properties. The difference is a lowering of the repetition rate or pulse structure (e.g. the change from a uniform pulse train to a macropulsed train). For some experiments this may offset the advantage of the intact pulse single pulse energy. In any case, there is a considerable engineering challenge of achieving a mechanical based system that can deflect alternating pulses or pulse trains at rates of the order of a khz or higher. High speed operation will probably be restricted to the VUV/XUV to ease the challenge of making a fast moving mirror that can deflect a complete pulse.

107 92 5. Beam-splitting methods Summary Splitting the photon beam can be done to serve several experiments in parallel, it also enables the use of part of the beam for diagnostic purposes. The trade off is that less (in some sense) of the beam gets handed out for the various purposes. A beam can be split in the amplitude (using e.g. a semitransparent mirror), frequency (a dispersive optic is needed) and temporal (using for instance a moving mirror) domains. Of the techniques listed in this chapter not all are suitable for the use at free electron laser. Often the limiting factor is the intended splitting techniques robustness when it comes to withstanding the high peak power at X-ray wavelengths. In some instances the following techniques are already in use at free electron laser whereas some need some kind of adaptation for the purpouse: Diffraction gratings (dispersive). Induces a pulsestretching whose length depends on how many grooves are illuminated. Pulse-stretch gets reversed if two gratings are used, at the expense of lower transmission. Crystal diffraction splitter effective below 6Å wavelengths. An attractive material is diamond crystals, owing to their high thermal conductivity combined with good radiation hardness[149]. The diffraction in the crystal causes a non-reversible pulse stretch of a few femtoseconds. Knife-edge mirrors Slotted mirrors Other techniques have been employed for specific purposes and proven to be applicable in the free electron laser regime of experimental conditions. Introducing them for general utilization require further development and research: Multilayers Structured arrays Time-based splitters

108

109 Part II Beam diagnostics

110 6. Introduction Written by: A. Lindblad Since the Sase-process starts up from white noise i.e. the initial shot-noise in the beam is uniformly distributed, each light-pulse will have different temporal, spatial and spectral properties. Over the course of many shots said properties average out and the machine attains its average properties in terms of intensity, pulse-length and spectral purity; it is therefore natural that beam diagnostic methods are an integral part of any free electron laser-project (see, for instance Ref. [89]). Diagnostics of the photons (and electrons) also provide valuable feedback to the accelerator part of the machine. This feedback is essential to ensure stable operation and long up-time for the users. The various schemes that exist to enhance the overall shot-to-shot repeatability, e.g. HGHG, EEHG 1, may seem to loosen the demand on diagnostics however the delicate problem of overlapping a laser pulse (which can be of HHG type also requiring its own diagnostics) with the electron beam still requires a strict characterization of the light as in the Sase case. In this chapter the various categories of diagnostics are presented, as well as the different subcategories that we can sort them into. 6.1 Diagnostics categorization Figure 6.1 gives an indication of how we can categorize the different diagnostic methods that needs to be employed to characterize the free electron laser photon beam. Beam cross-section Transverse (also along the beam path to discern the focus-size) Longitudinal Pulse arrival time The jitter between pulses Intensity / Pulse energy 1 Sections 1.5, see page 17 and 1.5, see page

111 96 6. Introduction y x I t z Figure 6.1: Photon pulses needs to be diagnosed vis-à-vis spatial and temporal extents. Spectral properties can be inferred from the temporal distribution. Spectral content Median energy The beam s size in space, and how it varies along the optical system is important to characterize since those properties needs to be known to know the focus points along the beam both for simulation purposes and experiments. The longitudinal cross-section of the beam gives the pulse length and shape. This is connected both to the spectral content and the pulse to pulse arrival time jitter. For experiments that are considering temporal properties of matter (pump-and-probe) this is crucial information. The pulse energy (or intensity) follows a gamma-distribution depending on how many radiating modes that are present[104] hence a shot-to-shot measurement of the intensity is necessary to have at a free electron laser facility. The centroid of the photon energy fluctuates about 0.5% at Flash[150], obviously a shot-to-shot measurement of this needs to be provided, both to the users and to the staff handling the accelerator itself. Spectral diagnostics (Intensity and energy) are discussed in chapter 7 below. Various methods concerning the measurements of the transverse spatial extent of the photon beam are described in chapter 8 (see page 109). A survey of pulse length, profile and jitter diagnostics can be found in chapter 9 (see page 151). Subcategorizations Shot-to-shot / Average Many properties of the free electron laser photon beam needs to be known at a shotto-shot basis. A spectroscopic experiment, for instance, needs to know the incoming photons energy and intensity per pulse as to allow sorting of the experimental data. Knowing just the average intensity and photon energy does not allow this post-experiment analysis of the data. Average properties, on the other hand says a lot about the long term stability of the free electron laser and may also serve as a measurement of the condition of transport optics. Averaging measurements are usually more stable than their shotto-shot counterparts and can thus be used to calibrate other diagnostics.

112 6.2. Conclusion 97 Transparent/Opaque/Blocking A diagnostic can be, more or less, invasive, i.e. how much it affects the photon beam s properties for experiments and other diagnostics downstream. An position measurement based on the photo-current generated on a slit will cut away parts of the beam, thus reducing the available intensity downstream from the diagnostic. As can be inferred from the title, we can divide the degree of invasiveness of a diagnostic tool into transparent, opaque and blocking. As on-line diagnostics it is preferable to have transparent diagnostics since they have least effect on the beam. For commissioning of diagnostics, beam-transport elements, calibrating of diagnostics and accelerator conditioning opaque and blocking diagnostics can be used. As discussed previously (chapter 5) it is possible to split off part of the beam to be diagnosed in parallel to the downstream experiments/diagnostics. Hence even a blocking diagnostic that otherwise have the needed specifications can be used to provide information to the downstream activities. Photon-energy range Physical processes that may be used as basis for a diagnostic can be challenging to find. For infrared and THz beams it is not possible to photo-ionize a gas, whereas for UV and soft X-rays the cross-section for this processes is very large and in turn, for hard X-rays the cross-sections for photo-ionization become very small. Hence, the photon-energy range(s) of interest needs to be taken into account in designing the diagnostic array for a facility. 6.2 Conclusion There is no such thing as an perfect diagnostic, i.e. a device that measure a property on a shot-to-shot basis in a transparent manner for any photon-energy with negligible error. Thus we have torely on acombination of diagnostics tomeasure thedesired unknowns of the photon beam. To ensure the integrity of the resulting diagnostics array one needs to calibrate them against each other (and possibly additional diagnostics).

113 98 6. Introduction Summary A diagnostic needs to be more robust and more user friendly than an experiment, as the information provided is used to analyze experimental data for users, as feedback to the running of the accelerator and for commissioning of the transport optics. Diagnostics can be divided into: Beam cross-section transverse and longitudinal Arrival time, jitter Intensity and Pulse energy Spectral content Median energy Any diagnostic method can also be further characterized by: its ability to measure on a shot-to-shot basis or if it provides an average measurement of the property. if it is transparent, opaque or beam stopping/blocking for a downstream experiment. what photon-energy range it can be used in, i.e. infrared/thz, UV, soft X-ray and hard X-rays. No perfect diagnostic exists (neither an universal that measures everything, nor optimal for all photon ranges). Thus a judicious combination of diagnostics needs to be composed into a diagnostics array distributed along the beam-path that can be used to Measure during the course of other experiments Calibrate other diagnostics during commissioning Cross-check the integrity of the diagnostics array Beam-splitters allows the use of opaque/blocking diagnostics in parallel to other experiments and diagnostics.

114 7. Spectral diagnostics: Intensity & Energy Written by: A. Lindblad In this chapter some ways to infer the spectral properties (or some spectral property) of the free electron laser light. During the course of Part I of the book we have gotten the indication that both seeded and Sase free electron laser provide light that need to be diagnosed on a shot to shot basis. The Sase process start up from current shot noise in the beam that is subsequently amplified with a few radiation modes contributing to the final spectrum at/after saturation. Each pulse is therefore unique and for an experiment to be meaningful the mean intensity and mean-energy of the pulses can be considered tobe the minimal information to be provided to the user. In various seeding schemes the quality of the pulses needs to be monitored to ensure stability. The harmonic content of the pulses and the spontaneous emission background levels needs to be diagnosed as well. Ideally the full spectrum of the pulse should be measured on a pulse to pulse basis in a manner that is transparent to the users of the beam. This is often not practically possible, as will be seen in the following, but this can be overcome by dividing the beam between the experiment and the diagnostics utilizing, e.g. a beamsplitting device as discussed above in chapter X-ray spectrometry The obvious spectral diagnostic of the fel beam is to measure it, or parts of it directly with an X-ray spectrometer. With one or more gratings it is possible to disperse the photon beam converting energy spread into a spatial distribution. In most instances variable line spacing gratings is used to focus a higher order diffracted beam onto a focal plane, passing the 0 th order reflected beam for the experiment (Figure 7.1). Rewriting the grating equation (Equation 4.1) in terms of line density sinα sinβ = n λσ 0 one can vary the groove depth according to a third degree polynomial (with x along the grating) as: σ(x) = σ 0 +σ 1x+σ 2x 2 +σ 3x 3 99

115 Spectral diagnostics: Intensity & Energy focal plane Incoming FEL pulse α β O th order Figure 7.1: A variable line space grating disperses different wavelengths along the same focal plane. λ range 6-40 nm nm central line spacing 900 l/mm 300 l/mm fraction in 1 st order 8-0.5% % diffraction angle Res. power (CCD) > 7000 > 4000 incident angle coating C, Ni C Table 7.1: Design parameters of the flash VLS grating spectrometer as given in Ref. [104]. Then one can choose σ(x) so that the abberation and spectral defocusing effects are minimized. With proper materials chosen between one and ten percent of the radiation is dispersed onto the focal plane (this percentage also depend on the wavelength). This kind of spectrometers provide the full spectrum around a certain photon energy harmonics are usually filtered away by the grating. The detection can be done either by CCD camera or strip detectors. At Flash the spectrum is recorded by a Ce:YAG screen imaged by a CCD camera. The camera can record images at a rate of 5 Hz[104]. Similar set-ups are used at Lcls[151] and at Fermi@Elettra[152]. 7.2 Intensity/Beam energy Earlier we discussed the use of monochromators in combination with the free electron laserbeam in section 4.5 (see page 67) as a means to convert the spectral jitter (wavelength and intensity fluctuations per pulse) into intensity jitter. Intensitycan be measured on a per pulse basis or as an average property over many pulses, of course a fast enough detection scheme can be made to integrate over many pulses if one needs to measure the average intensity. As free electron laser pulses are often in the order of tenths of femtoseconds (or shorter) a measuring on a pulse by pulse basis poses quite a challenge as will be seen below. As for most diagnostics we can roughly divide intensity measurements into opaque and transparent as seen from an imagined experimental station downstream from the diagnostic. Diagnostics which are, more or less, transparent are possible to distribute along a beam path leading up to an experimental station, whereas opaque diagnostics

116 7.2. Intensity/Beam energy 101 needs to use either a part of the free electron laser beam using a beamsplitter, or be placed after the experiment (provided that the experiment is somewhat transparent). Besides the gas monitor detectors and solid state devices described below a way of discerning the average energy of the free electron laser beam have been invented at the Lcls[96]. By determining the energy loss for different trajectories of the electron beam through the undulators a measure of the average pulse energy can be determined within 1 and 5%. Gas monitor detectors Ion/electron detection To provide a transparent diagnostic of the intensity at the Flash free electron laser a an intensity monitor based on photoionization of gases and detection of ions and electrons have been developed [153] at Flash. These detectors are placed before and after the gas attenuator[104]. The latter is places immediately before entering the experimental hall. By measuring the yield (electron or ion) from a known density of a gas it is possible to conclude the intensity of the photon beam via: N = N γ ρ σ(e) l (7.1) relates the number of particles ionized (N) with the number of photons N γ; the target density (ρ); the photoionization cross-section at the photon energy in question σ(e) and the length of the interaction volume l. -V + +V Figure 7.2: A Faraday cup counts the ions and electrons produced by photoionization of a target gas to produce a measure of the intensity of the FEL photon beam via Equation 7.1. The gas monitor detector scheme is shown in Figure 7.2. The charged particles (electrons and ions) created by the ionization of the gas is separated and accelerated by a homogeneous electric field, and can thus be detected separately. The gas pressure is typically held at 10-6 mbar, as to disturb the downstream experiments minimally. The charged particles are detected by Faraday cups. With this type of detector it is possible to measure the pulse intensity with an error less than 10% with a jitter between pulses of 1%. The latter is dominated by the signal statistics and holds for more than photons per pulse.

117 Spectral diagnostics: Intensity & Energy It is important to note that, since the detected intensity depends on the crosssection 1 for photo-ionization the sensitivity of the detection scheme varies strongly with photon energy. This is an issue to consider when this type of detector is to be used for hard X-rays, where cross-sections are several orders of magnitude lower than in the VUV/soft X-ray region. The sensitivity of the scheme when it comes to the detection of intensities of higher harmonics in the free electron laser pulses are therefore also impaired. Photoluminescence detection At the Lcls a gas monitor detector have been developed that detects the fluorescence of nitrogen with two photomultiplier tubes[96, 154]. Magnetic coils around a 30 cm long and 8 cm wide pressure chamber (with mbar of gas pressure) confine the photoelectrons produced by the free electron laser beam, these electrons excite the surrounding nitrogen gas. The de-excitation of the molecules occur by the emission of photons in the UV range between 300 to 400 nm. During the course of detection of cosmic rays it have been concluded that the yield in this spectrum depends weakly on the exciting electron energy. Calorimeters A calorimeter (also called radiometer in the present context and will henceforth be denoted thusly) measure, in principle, the integral spectral power impinging on it. Hence, the sensitivity is equal for the harmonic content in the pulses. Standard for measuring radiated power from UV/X-ray lightsources around the world (i.e. at PTB[155] in Germany, NIST[156] in the USA, and NMIJ[157, 158] in Japan). The device consists of a cryogenically cooled temperature sensor in front of a target upon which the radiation impinges on (Figure 7.3). The pulse energy is given by: E = T s f (7.2) where the temperature difference ( T) is the temperature raise in the absorbing cavity, f is the repetition rate of the source and s is the thermal response of the system. The radiated power is then simply P = E f. The thermal response of the system can have more or less inertia, but the time constant for transition from one equilibrium of the system to another upon changing absorbed power is measured in minutes. Hence, average energies per pulse can be obtained, however with small systematic errors (dominated by the intensity fluctuations of the radiation). A radiometer of this kind is also effectively a beam stopper and needs to be placed at the very end of the beam transport system, i.e. after the experiment(s) or operate at a split of branch of the beam. This type of diagnostic can therefore be used as a standard which to calibrate other intensity diagnostics against, for instance the gas monitor detectors mentioned above, or during commissioning runs and as a machine diagnostic. 1 Cross-sections for the noble gases have been tabulated by K. Tiedtke and co-workers for the noble gases up to 300 ev photon energy[153].

118 7.2. Intensity/Beam energy 103 Liquid He Liquid N 2 Photon beam Temp. sensor Heater Figure 7.3: Illustration of a cryogenic calorimeter setup. Solid state devices Photodiodes Photodiodes, commonly employed at synchrotron laboratories for intensity diagnostic purposes have shown to exhibit quite large errors when employed at free electron laser, at Scss in Japan one such measurements yielded an error of about 30% of the intensity. Bolometers A solid state bolometric sensor that can withstand the power from a free electron laser laser beam can be realized from a device where the resistance change of a colossal magneto-resistance thermistor film upon absorption of electromagnetic radiation. With a sufficiently efficient coupling to a cooling substrate the operation can be fast enough to allow very precise measurement of the beam energy on a pulse to pulse basis since they can be operated close to their metal-insulator transition where the resistance changes are very large. At low temperatures the contributions from thermal noise in the circuit is also lower. The resistivity and the temperature of such thermistor films can be varied depending on their composition[159]. The sensitivity of the resistance upon temperature R T changes (understood as 1 ) can be as large as 10%/K. R Assuming that the sensor is efficiently coupled to the cooling substrate then the current signal S from a voltage biased sensor is proportional to the total X-ray energy and inversely proportional to the heat capacity of the substrate C: T E fel C (7.3)

119 Spectral diagnostics: Intensity & Energy Assuming that the noise in the circuit mainly arises from thermal noise (i.e. Johnson noise) of the sensor and the readout (i n,e n) we can write the signal to noise ratio (S/N) during an integration time τ[159]: R S V bias τ = T N R 2 4kBT/R+i 2 n +(e n/r) 2 (t) τ (7.4) For low resistances and low temperatures this expression is maximized. Low noise operational amplifers have e n as low as 1 nv/ Hz and i n in the orders of pa/ Hz. Signal to noise ratios of can be obtained for integration times of milliseconds. Neodynium strontium manganese oxide (NSMO) sensors grown on a silicone substrate can be used to measure the total energy on a pulse to pulse basis with very small errors[96, 160]. Even-though this diagnostic interrupts the beam (which can be worked around as seen earlier) the devices can be absolutely calibrated with an ordinary pulsed laser. Lastly this kind of detectors have a sensitivity that is linear over three orders of magnitude of incoming beam energy. This kind of detectors are currently in use (and being further developed) at the Lcls free electron laserwhere they also serve as to calibrate the photoluminescence detectors described above. At 8.3 kev the average energy is determined with a pulse to pulse jitter of about 8%[96]. 7.3 Photon-energy Measuring the photon-pulse directly, as outlined above in section 7.1, needs the beam to be split (in amplitude or in frequency) or to be placed at the very end after an experiment that, in turn, needs to be transparent to the diagnostic. In various circumstances this is not desirable or even possible either because the experiment is photon-hungry and can not afford to use the loss of transmission from a beam splitting device, and/or the experiment is opaque (i.e. effectively a beam-stopper). One way to circumvent this is to measure the time-of-flight of the ions and/or electrons in a manner similar to the intensity measurement with the gas-monitor detectors described above (section 7.2). Since the arrival time of the pulses at the diagnostic is known (or can be inferred from other diagnostics) we can measure different aspects of the ionization processes occurring in, for instance, a rare gas via the time-of-flight of the produced charged particles in a homogeneous electric (and/or magnetic) field. Ion time-of-flight The time of flight of ions through an electric field is proportional to their mass and charge for a small source region the flight times for different charge to mass ratios are deterministic and depends only on electric field strengths and the geometry of the apparatus, usually referred to as a Wiley-MacLaren spectrometer[161]. Ion time-offlight is thus a mass-spectroscopic measurement, in essence. The resolution of a Wiley-Maclaren setup (spatial and temporal) can be analyzed, let us spell it out in detail: define U t = qses +de d, k = Ut se s qse s

120 7.3. Photon-energy 105 s d 0,E 1 d 1,E 2 D Figure 7.4: The field in the drift tube is zero. The ratio between the fields is uniquely determined by the geometry given by s,d 1 and D. With T as the total flight time, zero initial kinetic energy and starting position s, the position where ions having s± 1 δs pass each other can be found where 2 ) dt ds = 0 D = 2sk (1 3/2 1 0,s k + d k s This focus condition is the same for all ions and is independent of the systems total energy. Hence, if s, d, and D is given, the ratio E d /E s since k can only have one physically reasonable value. T(U,s) has either a maximum, minimum, or an inflection point where dt ds 0,s = 0, the latter can be found with: d 2 T ds 2 = 0, d ( ) k 3 D 0,s s = k 2s For the parameter values chosen for best resolution, two-field systems are operated at the maxiumum, i.e. with the d smaller than the righthand-side. s Spatial resolution Let M s be the largest mass for which the flight times are discernibly different, ( T m+1 T m = τ Tm s ) 2 2m Ms 16k s The latter is true whenever k 1 and k d/s. This shows that the distance to the sourcepoint s must be larger than the spread s for space resolution to be made adequate this, in turn, is dependent on D being large since D/s determines k. Increasing d (thus increasing k) improves space resolution.

121 Spectral diagnostics: Intensity & Energy Energy resolution Consider two ions at the same initial position s but with opposite velocities along the spectrometer axis, equal in magnitude, then the turn-around time is T = mU 0 qe s Then the maximum resolvable mass becomes, with D/s given by the focusing condition: M E = 1 ( ) Ut k +1 k +1 4 U 0 k k + d k s To find the overall resolution a compromise between M s and M E has to be found. Higher order focussing can be achieved by having additional drift-sections and fields[162] for those the flight times, etc. can still be calculated analytically[163]. Ion time-of-flight as a diagnostic A precise way of determining the charge to mass ratio of photo-ions allows us to measure the photon-energy. The photoionization cross-section depends on photon energy, i.e. one can measure it directly via the intensity of one charged state; a much more stable measurement of the photon energy is obtained via the ratio between singly and doubly charged ions (or higher charge states). All this assumes that the crosssections as functions of energy and charge state are known beforehand. Moreover, the photon-density must be low enough to ensure that only single-photon events occur something which is usually fulfilled for an unfocussed free electron laser beam[153]. Juranić et al. have used a Wiley-MacLaren spectrometer to measure the photon energy at Flash with uncertainties staying below 1% up to 150 ev photon energy[164]. Ion time-of-flight measurements can be shielded from perturbing magnetic fields easier, and provides higher countrates than the electron measurements described below. The time-of-flight times are also longer since the particles have higher mass which makes the measurement less demanding with respect to the data-acquisition. Electron time-of-flight The time-of-flight for the electrons can be converted into kinetic energy with the aid of known ionization energies of atomic states hence this is a spectroscopic measurement. If performed at high enough resolution electron time-of-flight can thus give information on the spectral content of the pulse as well as the mean energy. Potentially this spectrum also give access to the pulse length[165] as discussed in chapter 9. This allows for measurement of the photon-energy and the fluctuations of it, as have been done near 93 ev at Flash[150]. The resolution in the spectra for the He 1s photoelectron line was about 100 mev. The limitation of this photo-electron spectroscopic measurement is the relatively low countrate (in the order of thousands of electrons per pulse). The kinetic energy of the electrons is also not invariant with changing intensity of the free electron laser beam, where the attractive forced from the positively charged ions cases the kinetic energy to be lowered for the electrons which, if not accounted for, induces an apparent decrease in photon-energy with increasing photon-densities.

122 7.3. Photon-energy 107 However, the lower cross-section at higher energies lowers the Coulomb attraction between ions and electrons, since the number of electron-ion pairs(for single-ionziation events) is: N paris = N photons n gas σ gas l (7.5) where l is the length of the interaction region and n = p/k BT for an ideal gas. The non-ideality of the gas can be accounted for via a correction using the mean-free path[150]. For higher photon-energies thus, electron time-of-flight measurements can be a viable option for determining the photon-energy and its fluctuations.

123 Spectral diagnostics: Intensity & Energy Summary The beam energy (or intensity) is a critical parameter for user experiments and other diagnostics. Gas monitor detectors analyze the total yield occurring from photoionization (which is proportional to the beam energy) of a target gas by accelerating them in an electric (and possibly an magnetic field). This is a diagnostic that is transparent. Another transparent diagnostic is photoluminescence measurements of, for instance, nitrogen gas. Calorimeters (Radiometers) is a measurement that gives the average intensity of the pulses in a very exact manner. This is an opaque diagnostic which can also be used to calibrate other intensity diagnostics. Bolometers provides a measurement of the beam energy over a large photon range for instance with 8% error at 8.3 kev photon energy at the Lcls. Diodes have shown to have rather large errors when used at free electron laser, e.g. 30% at the Scss. Bolometers and diodes are opaque diagnostics and thus require splitting or a transparent user experiment. X-ray spectrometry measures the dispersed fel beam from a (VLS) diffractive grating. Thus obtaining the full spectrum of the free electron laser beam on a shot to shot basis. Ion time-of-flight measurements diagnoses the photon-energy of the beam with relatively small errors assuming that the cross-sections for the ionized gas is known as a function of energy and the various charged states. Electron time-of-flight can provide a measurement of the spectrum of the pulse and provides a way of discerning the fluctuations in photon-energy. Electron and ion time-of-flight measurements that are transparent to the user s experiments. Time-of-flight measurements utilize photoionization for which the cross-sections drops fast after ev i.e. for higher photon-energies they may be impractical due to low countrates.

124 8. Beam cross-section diagnostics The material presented here in this chapter is adapted from Survey of diagnostic techniques for measuring the beam cross-section of ultra-short photon pulses by M. A. Bowler, A. J. Gleeson and M. D. Roper. Iruvx WP7, 2010 by A. Lindblad. 8.1 Introduction By measuring the profile of the generated photon-beam many important parameters important for the beam transport towards the experiments can be learned. The beam-profile is also an important diagnostic for the machine and as an parameter for experiments (e.g. the spot-size determines the energy density at the experiment). The specific information that is required is: The transverse intensity distribution of the pulse allowing the source size, position and quality factor (M 2 ) to be calculated from the second moment 1. The centroid (first moment) of the transverse pulse profile giving beam position and (in combination with a second measurement of the same pulse at different longitudinal distance) the beam angle. The pulse wavefront giving a complete description of the spatial properties of the beam. The focused spot size of the beam critical for optimizing adaptive mirrors to give the best focusand for achieving high fluences for non-linear studies. The ideal cross-section diagnostic Any measurement that gives a full beam profile can be used to calculate the beam centroid but a measurement that gives only centroid information gives no profile information. Centroiding measurementsare nevertheless useful where they are less 1 The quality factor for a diffraction limited gaussian photon beam at wavelength lambda is λ/π. For a real beam the product of the minimum waist-size of the beam with the divergence of the beam in the far field is called the beam parameter product (BPP). The ratio between the BPP and λ/π is the quality measure M 2. For a diffraction limited beam this ratio is unity; for real beams this measure is larger than unity. 109

125 Beam cross-section diagnostics invasive or can give pulse by pulse information. For a free electron laser source, the ideal diagnostic would have the following properties: A sub-µm spatial resolution to allow the focused beam to be measured. A field of view of 1 cm to allow the unfocused beam to be measured. Non-invasive give negligible disruption to the beam. Sensitive to allow a single pulse to be measured. Wide dynamic range with linear response to measure attenuated and fullpower beams, focused and unfocused, fundamental and harmonics without damage, or excessive noise. Large bandwidth to measure every pulse up to MHz repetition rates in real time. Broadband work at THz/IR or from the VUV to hard X-rays. Spectrally discriminating to separate signals from e.g. fundamental and harmonics. The number of these properties that a given practical monitor will need will depend on the particular application or location in the photon transport system. For example, sub-µm resolution is only required to measure the size of the beam at a focus, it will not be necessary for a monitor to be able to wavelength-discriminate if it is situated after a monochromator, and diagnostics situated after the experiment do not need to be non-invasive. Distribution of diagnostics along the beam feedback to source On-line centroid monitors for beam position and angle Centroid monitors for mirror alignment Wavefront sensor Beamline optics Source Focus spot-size monitor Profilin monitors for quality factor analysis Profiling monitor for commisioning Figure 8.1: A schematic on how to distribute various diagnostics to determin transverse beam properties. Figure 8.1 shows schematically how the various diagnostics might be distributed along a beamline. Before any optics it will be necessary to have non-invasive (or minimally invasive) on-line diagnostics that give at least beam position and angle information continuously and individually for every pulse. These monitors could be used in feedback control of the machine to ensure the photon beam is stable in position and angle. There should also be diagnostics that can give a full pulse profile at three or more positions such that the source position and size and beam quality factor M 2 and can be determined[166]. The main application here would be during commissioning and so the monitors could be invasive, though if that were case it

126 8.1. Introduction 111 would not be possible to calculate the quality factor for a single pulse. Therefore a non-invasive measurement is preferred, but it need not work at the full rep rate of the free electron laser since statistical methods can be used to infer the overall beam quality. After each optical element a beam position monitor is required to ensure the beam alignment is correct. These might just give centroid information and may average over a number of pulses. Ideally, they would be on-line so the beam stability can be constantly monitored, though this may be unnecessary. Additional profiling monitors will also be available specifically for commissioning and diagnosing problems; these can be invasive. At the experiment it is necessary to determine the position and quality of the beam focus to: Ensure multiple beams can be overlapped spatially Optimise adaptive mirrors Achieve the highest beam fluence Position the sample at the focus It would generally be acceptable for these measurements to be invasive since, with a stable source, they would normally only be needed during commissioning and experimental set-up. Depending on need, the measurements could either be averaged over many pulses (e.g. for positioning) or measure just a single pulse (e.g. focus quality). If a measure of every pulse is needed outside the realm of commissioning then a noninvasive detector or a detector remote from the sample position is needed. The latter is quite easy with gas-phase experiments (which are almost transparent to the beam) since the detector can be placed after the experiment. It would not be possible to measure the focus directly, so the wavefront would have to be measured and reverse-propagated to reconstruct the beam focus. Direct measurement of the wavefront would be the optimal way to measure the beam as it allows for simulated propagation to arbitrary positions along the transport path, e.g. back to the source. However, wavefront measurement is invasive and so cannot be a general on-line diagnostic. Furthermore, accurate propagation across an optical element requires detailed information on the element surface shape at a large range of spatial frequencies and thus the accuracy of any prediction will fall as the simulation traverses more optical elements. Content of this chapter In this chapter, a broad survey of the range of techniques that have been used to profile non-visible photon beams is presented. In the VUV to X-ray range, most existing diagnostics have been developed for use on synchrotron radiation sources. The challenges there tend to be rather different, and the techniques may not be easy to modify for free electron laser use. Specific problems for FEL beams include: Damage from ablation rather than high average power. The need for pulse resolved rather than time averaged measurements. The need to avoid beam disruption through coherent diffraction effects.

127 Beam cross-section diagnostics It is worthwhile to describe briefly several common techniques that are used in the diagnostics as follows: Scanning in which a scan through the beam section is made, recording the intensity in a step-wise manner to build up the profile Imaging in which the entire intensity profile, in one or two dimensions, is measured in one shot Sampling in which a small part of the beam is extracted and the required information deduced from this whilst the bulk of the beam passes on to the experiment Replicating in which the beam profile information is transferred to another medium and that measured to give the actual profile. In some cases a mixture of these techniques is used, for example in imaging a replica of the beam. In the THz and IR ranges, diagnostics at existing free electron laser sources tend to be limited to characterizing the beam at the experiment rather than having distributed diagnostics along the transport system. The available means of detecting IR and THz radiation restrict the range of diagnostic techniques that can be applied, in particular because the long wavelength radiation cannot directly ionize materials. For the near and mid-ir, techniques can be adapted from the visible regime. In section 8.4 will be described those techniques that can give a profile of the beam intensity. In some cases this will be along a single axis (or two axes with two instruments situated orthogonally), and in others a complete 2-dimensional map of the beam intensity will be recorded. Section 8.10 will describe those techniques that give only information about the position of the beam centroid ( centre of gravity, or first moment, of the intensity). How the complete wavefront can be measured is described in section 8.11 and specific applications of beam profiling to determine the size and quality of the focused beam are described in section 8.8. Diagnostics for IR and THz wavelengths will be described collectively in section Definitions In this chapter we will look into various schemes as how to determine the transverse (x,y) distribution of photons in the beam 2. Most of the methods also carry over to more applications of particle beams in general. Let us define the problem more specifically, consider the particle beam to have a Gaussian distribution in the x,y plane orthogonal to the direction of the beam (the s direction) N(x,y) 1 e 1 2 (x 2 /σ x+y 2 /σ y) σ xσ y Along the s-axis the distribution is ideally a step function. The measurement of this profile will be covered more specifically in chapter 9. Various schemes can be envisioned on how to measure the profiles concerned, each with its own merits as a first rough division we can divide them into invasive and non-invasive methods: 2 Diagnostics concerning the longitudinal (s) extent of the pulses will be covered in chapter 9.

128 8.3. Direct imaging of the beam 113 y I x x I s y Figure 8.2: Projection of the spatial density distribution in the x.y plane (left) and onto individual coordinateaxes (right). invasive or direct measurements Direct imaging of the beam Wire grids Scanning wires, slits, knife-edges, pin-holes non-invasive or in-direct measurements rest gas ionization photo dissociation synchrotron light Compton scattering 8.3 Direct imaging of the beam The simplest way to image the transverse footprint of a photon beam is to directly illuminate an array detector such as a CCD with the beam[167, 168]. Providing the detector is sensitive to the photon wavelength, a direct readout of the beam profile is achieved. If the array is two-dimensional, then a complete transverse map of the beam can be recorded. The spatial resolution of a CCD detector is determined, in principle, by the photo-site size and spacing in the detector array. In practice this limit cannot be achieved due to diffusion, where electrons created in one pixel are collected in an adjacent pixel. To record an image of every free electron laser pulse individually, the frame rate of the camera must of course match the pulse repetition rate. Extremely high-speed cameras are available for optical imaging (e.g. 600,000 fps with the NAC Memrecam GX-8 3 ) and commercial high-speed X-ray imaging services are available (e.g. Speed Vision Technologies Inc. offer frame rates of 1000 fps 4 ). Speeds for scientific applications are typically much lower

129 Beam cross-section diagnostics For example, Princeton Instruments 5 manufacture CCD cameras for both direct and indirect (q.v.) X-ray imaging that have readout rates of 2 MHz or 100 khz depending on the sensitivity and signal to noise ratio. This rate equates to roughly the rate at which a single pixel can be read out since all the data passes through a single serial register. Thus the frame rate depends on the number of pixels. They offer a 512 x 512 pixel camera (with 13 µm pixel spacing) which could thus be read out at only 7.5 fps. Nevertheless, it is clear that higher speeds are achievable, though the balance of sensitivity and noise needs to be considered. We might therefore reasonably expect to be able to record every pulse at repetition rates of about 1 khz. For single pulse imaging at repetition rates above the detector frame rate, the camera would need to be gated to record just one pulse in the Figure 8.3: A typical scintillator screen setup. frame cycle. Gating at the nanosecond level is available with optical cameras, but is presumably achieved using electro-optical shutters which are not available for X-rays. A mechanical shutter would be needed to pick just one pulse and this would be also be challenging to design and synchronize. The high fluence of a free electron laser pulse also raises significant concerns over ablation, radiation damage, and linearity / saturation effects. The saturation level is a compromise with spatial resolution since if the pixels are made smaller then they can hold less charge and will saturate earlier. In fact, CCD detectors are not often used to measure the direct beam on synchrotron sources because they saturate too easily. Fedotov in 2000[169] reported that an old 1200LC1 type CCD would saturate with 500 photons at 10 kev compared with 5-50 photons for more modern CCDs. Therefore, a conventional CCD is limited to the direct measurement of only attenuated or spatially dilute beams. Direct detection with solid-state arrays offers the potential of energy discrimination, which might allow the fundamental and harmonics to be distinguished. However, this may only be possible if each pixel collects no more than one photon[167]. Another factor to consider is the wavelength sensitivity of the CCD. A standard front illuminated CCD detector will be insensitive to VUV photons as they cannot penetrate through the inactive layer on the detector surface. Conversely, the sensitivity can drop with harder x-rays as they can pass straight through the depletion layer of the detector. Different types of CCD are thus needed for different parts of the spectrum,for example back thinned for soft X-rays less than 2 kev, ordinary front illuminated from 2 to 10 kev, and deep depletion type for X-rays above 10 kev. Imaging a replica of the beam A common approach for imaging techniques is to measure indirectly via the production of a replica of the beam. One way of achieving this is by illuminating a luminescent screen with the beam and then imaging the luminescence through a viewport on the vacuum vessel with an optical camera[170]. This allows for higher ultimate 5

130 8.3. Direct imaging of the beam 115 Viewport Source Mirror pinhole array YAG Camera Beam profile Figure 8.4: The use of a YAG screen together with a pinhole array for X-ray beam profiling as described by Boland and co-workers. spatial resolution than with direct CCD imaging. The resolution is determined by the quality and thickness of the screen, the magnification and aberrations of the camera optics, and the camera sensor resolution. The ultimate limit is set by diffraction of the visible light through the camera optics, and is thus 0.5 µm. The viewport must be of high optical quality if it is not to degrade the image. On the Australian Light Source diagnostic beamline, Boland et al. [170] placed a pinhole array before a YAG screen (Figure 8.4) so that several fully resolved images are recorded and this allows the beam divergence as well as the profile to be measured. This approach could be useful with a free electron laser since it would simplify single-pulse measurement of the beam divergence. With traditional powder phosphors a grain size of c. 1 µm is available and the resolution as defined by the line-spread function is approximately equal to the thickness of the phosphor layer[171]. But if the phosphor layer is made too thin (less than a few µm) then the light yield decreases dramatically and performance is compromised. Optically transparent luminescent screens, or scintillators, are a better choice for achieving high spatial resolution. Since the camera is now focussed on a transparent screen, the screen thickness and depth of field of the camera optics play an important part in the resolution. The scintillators must therefore be thin, have a surface of high optical quality, and contain high Z elements to increase absorption. Cerium doped aluminum garnets are most often used. Koch et al. [171] used 5 µm YAG:Ce on 170 µm undoped YAG crystal in combination with diffraction-limited microscope objectives and achieved spatial resolutions of less than 1 µm in micro-imaging experiments at the ESRF. Tous et al. [172] achieved resolution of about 1 µm with an anode X-ray source using YAG:Ce and LuAG:Ce, both of 20 µm thickness. The bandwidth of such a system will be limited by the camera read-out rate and ultimately by the decay time of the luminescent material. The decay time of some luminescent materials can be roughly 1 µs, but the visible luminescence from YAG:Ce is very fast at 70 ns[173] and is thus fast enough to resolve single pulses at even 1 MHz. As discussed above, cameras with frame rates up to 600,000 Hz are available, though not with continuous output at that rate. It would need to be checked that they would have the sensitivity to record the luminescence from a single free electron laser pulse (the monochrome sensitivity of the Memrecam GX-8 referred to is 20,000 ISO). With slower frame rates, it should be possible to select just one pulse in the frame cycle by gating the luminescence with a high-speed electro-optical shutter such as a Pockels cell. Clearly, the total number of photons collected from the screen in this mode will be low and so an image intensified camera may be required. These are

131 Beam cross-section diagnostics available commercially, for example the Lambert Instruments LI2CAM 6,which has a frame rate of just 15 fps but can be gated down to 2 ns. Itis also possible tocreate anelectron replicaofthephotonbeam profilebydirectly illuminating a multichannel plate with the free electron laser beam. A phosphor screen placed near the plate converts the electrons to visible light whilst preserving the spatial origin of the electrons, and the luminescence from the screen is imaged by a CCD camera. This approach was used by Yang et al. to image the profile of the X-ray pulses from a Compton back-scattering source[174] (though the image was integrated over many pulses due to the very low intensity). The spatial resolution will be determined by the channel pore size, which at 10 µm would give a similar resolution to direct CCD imaging. The sensitivity would be determined by the photoemissivity of the channel plate, which is dependent on wavelength. Coatings can be added to enhance the photoemission at long wavelengths. At shorter wavelengths, the efficiency drops as the X-rays are absorbed more in the bulk of the channel plate material. At very short wavelengths, the X-rays may penetrate through the pore walls and this will reduce the spatial resolution. The bandwidth will still be limited by the camera frame rate, but the ultimate limit will also be influenced by the time of the avalanching process in the pores, as well as the luminescence decay. The bandwidth could be greatly increased by replacing the phosphor screen and camera with an anode array. Assuming parallel readout of each anode, the detector response could be reduced to the multichannel plate response time, which could be in the nanosecond region. This would allow every pulse to be measured, but the spatial resolution would be limited by the anode array size. Alternatively, the charge pulse from the multichannel plate as the photon pulse strikes it could be used to trigger the gating of the camera to select a single pulse. This would obviate the need for synchronization to the X-ray beam itself. If this is not possible, the timing trigger from the free electron laser pulse could be used to gate the multichannel plate. A refinement of this approach would be to illuminate a photo-emissive material (e.g. a metal foil) and image the emitted photoelectrons. A key requirement for this to work is preserving the spatial information encoded into the photoelectrons whilst they transported to the multichannel plate. Similar problems face the techniques described in sections 8.6 and 8.7. An imaging detector based on the photoconductive effect in Type IIa CVD diamond has been developed at the APS byshu et al. [175]. This detector is an extension of work done on quadrant detectors (q.v.). A 127 µm thick diamond disc was patterned on both sides with sixteen 0.2 µm thick and 175 µm wide aluminum strips. The patterns on the two sides are orthogonal such that a 16 by 16 pixel array is created with 175 µm by 175 µm pixel size. The strips on one side are connected to a bias supply via a 16-channel switch, whilst those on the other side are connected to sixteen discrete current amplifiers. The disc has a high transmission for hard X-rays (around 10 kev) and thus the monitor can be used on-line for constant beam monitoring. When the X-ray beam passes through the diamond, the localized conductivity rises in proportion to the absorbed X-ray power. Thus, the current passing through the diamond when the bias is applied is highest where the incident X-ray beam is most intense. In order to build up a two dimensional picture of the beam intensity profile, the bias is applied to each 6

132 8.4. Scanning techniques 117 strip on one side in turn and the current from the sixteen strips on the other side recorded. The spatial resolution is naturally fairly low, but sufficient to give a true beam profile assuming the beam is not highly structured and overlaps with enough of the electrode strips. The bandwidth is limited by the need to apply the bias voltage to each strip in turn. Nevertheless, the data acquisition system was able to scan at 300 to 3000 columns per second (from 19 to 190 Hz). Of course, this still means that the system will give only aline profile and not a full image of a single free electron laser pulse; the electrode structure would have to be modified to give simultaneous readout of all 256 channels for single pulse image. Summary of imaging techniques All the imaging techniques described above are invasive. Direct imaging with a CCD and direct illumination of a micro-channel plate will stop the entire beam and so could only be used during commissioning or if the experiment is transparent (e.g. gas phase) so that the detector can be placed after the experiment. The other techniques could be made partially transparent. For example, hard X-rays could pass through a sufficiently thin luminescent screen without excessive loss. The luminescent intensity is proportional to the number of photons absorbed and so some losses are required for the detector to work. On the other hand, since photoemission is essentially a surface phenomenon, a very thin and thus highly transmitting foil would give the same signal as a thick one. In any case, the disruption to a coherent free electron laser beam as it passes through a screen or foil would probably be unacceptable. There are also concerns over radiation damage, ablation,linearity and saturation with high-fluence, ultra-short free electron laser pulses. The risk of ablation would need to be controlled by using these techniques only where the beam is spatially dilute, and this might also be sufficient to prevent saturation and non-linear effects. The wavelength response of the detectors needs to be considered. It is obviously desirable for the detector to work over as wide a range of photon energies as possible. However, a broad-band response can cause problems if it is very non-linear. For example, photo-emission yield is much greater at VUV than X-ray wavelengths and this can distort an X-ray beam profile if there is low level VUV light with a different spatial pattern to the X-ray profile. 8.4 Scanning techniques Scanning wire This is perhaps, at a glance, the simplest solution to the present problem: scan a wire through the beam. A thin metal wire (such as tungsten) is step-scanned through the beam and the beam intensity deduced from, for example, the drain current in the wire[176], the intensity of electrons emitted from the wire, or the intensity of scattered or fluorescent light from the wire, all of which should be proportional to the beam intensity hitting the wire. The signal at each position in the scan is the result of an integration of the beam intensity along the illuminated length of the wire, i.e. in the direction orthogonal to the scan. The measured profile is thus a convolution of the actual beam profile and the illuminated length of the wire. This means the

133 Beam cross-section diagnostics scanningxwires.eps Figure 8.5: Working principle of a scanning crossed-wire monitor, after Ref. [178]. measured profile will be distorted when the orthogonal beam section is not uniform such that the illuminated length varies through the scan[177]. This will occur, for example when the wire is tilted relative to an elliptical beam. The resolution of the wire type monitor depends on the step resolution of the scanning mechanism, the diameter of the wire relative to the beam width, and the straightness and uniformity of the wire. Radiation scattering from the edges of the wire will degrade the resolution. Thin wires give higher resolution, but are harder to cool. If a wire gets too hot, thermionic emission can occur even before melting and this will distort the profile when electron detection is used to infer the beam intensity. Scanning crossed wires Two wires are crossed at 90 and scanned through the beam along a direction at 45 to each wire see Figure 8.5. In this way, two orthogonal profiles can be derived in one scan, but detection is limited to drain current to allow the signals to be distinguished. Each profile is still an integration in the orthogonal direction.the instrument developed by Fajardo and Ferrer[178] has a reported resolution of better than 5 µm, limited by mechanical reproducibility and vibration in the scanning mechanism. The finite response time of the amplifiers results in a difference in apparent position on forward and backward scans if the scan speed is too high; this effect was not observed at a speed below 1 mm/sec. Scanning slit A fine slit is scanned through the beam and the transmitted intensity measured by a detector (e.g. a photodiode, a micro channel plate, or a luminescent screen and video camera combination)[179].again, the intensity in the orthogonal direction is integrated by the length of the slit. The result is analogous to the scanning wire but the technique is more invasive, though easier to cool. Scanning slits are however

134 8.4. Scanning techniques 119 useful for probing aperture related aberrations in optical systems, though the beam spread after the slit caused by diffraction can confuse the results. Scanning pinhole A refinement of the scanning slit in which the beam profile is not integrated along the direction orthogonal to the scan direction and so true line profiles through the beam can be made. With two-axis control of the pin-hole motion, line profiles in arbitrary directions through the beam can be made. The pin-hole is commonly achieved by using either two slits crossed at 90 to make a rectangular pinhole or with four jaws making the two orthogonal slits. The advantage of the latter is that the size of the pin-hole can be easily changed, though a 4-axis drive is needed and very small pinholes are not realizable because of diffraction at each jaw and the necessary longitudinal separation between them. Scanning knife-edge A blade is scanned through the beam such that it successively obscures (or reveals) more and more of the beam. The intensity passing the blade is recorded by a detector such as a photodiode or mictro-channel plate[180]. The recorded signal is the integral of the profile in the scan direction and the deduced profile is integrated in the orthogonal direction. If the profile is being measured at a focus, a wire of diameter greater than the beam size can be used instead of an edge[181]. This has the advantage that it is easy to achieve a smooth edge with a wire than with a blade. Summary of scanning techniques The most important drawback when applying these techniques to a free electron lasersource is that they cannot be used to measure a single pulse due to the step-wise nature of the measurement. In addition, the techniques are invasive (i.e. disruptive to the beam), especially as the coherent nature of the photon beam will mean the disruption will be enhanced due to diffraction effects. Therefore, in the context of a free electron laser source, these techniques are useful neither during commissioning (when the invasive nature would not be an issue but the inability to resolve single pulses is), nor during operation (as the invasive nature makes them unsuitable as online monitors). In addition, the high pulse intensity of an unattenuated free electron laser fundamental gives serious concern over the damage to the scanning elements. With a free electron laser source, there are two modes of damage, viz. melting and ablation. At low repetition rates (less than 1 khz) melting is unlikely as the average power is less than in a synchrotron beam, but ablation is likely unless the pulses are attenuated (for example with a gas absorber, as discussed above in chapter 4 see page 69). Without attenuation, there is also the possibility of reaching non-linear regimes where the measured signal is no longer proportional to the incident intensity, e.g. through space charge effects.

135 Beam cross-section diagnostics 8.5 Ionization beamprofile detectors The beam-profile from a high-energy beam of particles (photons, electrons, neutrons...) can be measured by detecting the ions (or electrons) resultant from ionization events occurring in a residual gas intersecting the beam. By accelerating the ions in a homogeneous electric field towards a multichannel plate detector (see Figure 8.6) combined with a position sensitive read-out anode an image of the beam can be recorded. From Equation 2.5 one would expect the ions to get accelerated in straight lines towards the detector since the force on the charged particle is directly proportional to the electric field strength; the ionized particles, however, will have velocity components in other directions besides normal to the detector this will give rise to a broadening of the profile which can be minimized by applying a stronger electric field. A microchannel plate detector also have a finite resolution since the actual channels are in the order of 10 µm in diameter. There is also a possibility that several channels detect a single event which will blur the image further. Ion MCP 1 Anode MCP 2 Output signal Figure 8.6: Microchannel plates mounted in a chevron geometry with voltages coupled to detect ions. When an ion hit a microchannel plate it gives rise to several secondary ionizations the electrons from those ionizations, in turn, gives rise to other secondary electrons, thus an amplification occurs. The resulting charge cloud hits the anode and gives rise to an electric current which can be read out. An alternative to this scheme exist where a phosphor plate is mounted behind the anode which can be read out optically with, for instance, an CCD camera. At Flash this type of beam position monitor, using a phosphor screen together with a camera, gives a reported spatial resolution of c. 50 µm[182]. Obviously this type of detector also gives the position of the beam. 8.6 Imaging ion chambers An established technique for profiling particle beams in high-energy accelerators is to image the beam path through the residual gas (or gas added at a very low pressure gas, i.e. less than 10-5 mbar) in the beam transport system. As the beam passes through the gas, it will ionize it and the ion density is proportional to the particle density in the beam. Thus, if the ions can be channelled linearly to a luminescent screen with a uniform electric field, the intensity of luminescence is also proportional to particle density and the beam profile can be recorded with a video camera. The ion

136 8.6. Imaging ion chambers 121 signal is usually amplified by generating multiple electrons for each incident ion with a micro-channel plate placed in front of the screen. The benefit of this system is that, when using just the residual gas, the monitor is completely non-invasive. However, the achievable resolution has tended to be rather poor, of the 1 mm. This is mainly due toperturbation of the drifting ions bythe electric field of the particle beam, which causes themtospread awayfrom theregions ofhighion density,andsobroadeningthe recorded image. Ions, rather than electrons, are usually detected since their greater mass means they are less susceptible to these perturbations. Nevertheless, Fischer and Koopman were able to improve the resolution by measuring the electrons[183]. They achieved this by placing the ion chamber in a uniform magnetic field parallel to the electron trajectories. The emitted electrons will precess about the field and so can be channelled more linearly. The resolution was improved such that an actual beam width of 1 mm RMS could be measured without instrumental broadening (implying a resolution not worse than a few hundred µm). The same measurement principle can be applied to an X-ray beam, with which there is the advantage that the beam will not perturb the electrons and ions directly once created. However, preserving accurately their spatial point of origin is still difficult. The approach used by Ioudin et al. [184] is to encode the point of the spatial origin of the ions onto their kinetic energy by accelerating them with an extraction field see Figure 8.7. The further the ions are from the cathode when created, the greater the kinetic energy they gain during the acceleration. The ions are accelerated towards the entrance slit of an electrostatic energy analyzer, which disperses them in kinetic energy onto a micro-channel plate. Thus position along the plate corresponds to spatial coordinate of ion generation. The multi-channel plate amplifies the ion signal, which is imaged using a phosphor screen and video camera. This instrument, called the Beam Cross-section Image Detector (BCID), gives a profile of the beam in two axes the section along x is mapped along the microchannel plate as shown in the figure, X 1 = 2XE e/e a, whilst the section along y is mapped in the orthogonal direction on the plate. The spatial resolution is determined by a number of factors.ions generated at longitudinally adjacent positions a and b to q 2 in Figure 8.7 are mapped to different positions on the channel plate despite having the same kinetic energy. The slit width determines the longitudinal acceptance and hence the positional spread on the plate and must thus be kept small to control this blurring. The analyzer resolution is determined by the energy dispersion and the camera spatial resolution. Aberrations in the analyzer will distort the measured profile. The accuracy in the y-direction is determined by how linearly the ion chamber / encoder can preserve the transverse position along the length of the slit and the linearity of the analyzer response in the plane orthogonal to the dispersion plane. The ultimate resolution is limited by the extent to which the ions acquire extra momentum in the y- and z-directions as the result of inter-ion scattering and the influence of stray external (especially magnetic) fields. These effects will be reduced by increasing the gradient of the extracting field to increase the kinetic energy of the ions. But, if the kinetic energy is too high, then the analyzer performance will be degraded. The sensitivity of the technique is limited by the number of ions generated in the residual gas and the detection efficiency. Ion generation is more likely at VUV than X- ray wavelengths and thus the spectral content of the beam will influence the recorded profile. To measure the X-ray profile in, for example, the beam from a synchrotron dipole source would require the long wavelength components to be removed by a filter

137 Beam cross-section diagnostics Extraction field E e y + q 1 x z X - q 2 X-ray beam Phosphor screen MCP X Analyzer field E a Figure 8.7: The beam cross-section image detector (BCID) as described by Ioudin et al. [184]. such as a beryllium window[185]. This would however facilitate the addition of a gas such as argon or xenon at a low pressure to improve the ion count. In all cases, the necessity for a small analyzer slit limits the total count rate and all reported measurements of X-ray beams have been done with a gas pressure of 10-5 to 10-3 mbar and by integrating up to 256 frames with frame rate of 12.5 Hz [185, 186]. It is thus debatable whether the technique could have sufficient efficiency to record a single shot of a free electron laser beam. There is little information in the references on the spatial resolution achieved with the BCID. A residual gas beam position monitor is also being developed for use as an X-ray beam position monitor at PETRA III at HASYLAB. The RGBPM as described by Ilinski et al. [187] uses a layout similar to the original particle beam monitors, i.e. the kinetic energy encoding approach of Ioudin is not used and the spatial coordinate of the beam is mapped directly onto the detector. The generated ions or electrons are drifted in an applied electric field to a micro-channel plate (MCP) which produces an intensified image on a phosphor screen Figure 8.8. The beam profile is recorded in one axis only, this being in the direction perpendicular to both the drift field and beam direction. The profile is recorded for a finite length in the propagation direction

138 8.6. Imaging ion chambers 123 X-ray beam Guide electrode Repeller electrode Phosphor Profile axis MCP Guide electrode Field axis Propagation axis Figure 8.8: Schematic of PETRA-III RGBPM; a vertical profile of the beam is measured. of the beam determined by the longitudinal aperture of the detection system. Improvements in the resolution come from close attention to the quality of the electric field, initial kinetic energy of the ions or electrons, resolution of the detector system, and data processing. To quote: The electrical field has to be uniform in order to provide aberration free beam profile. Broadening of the beam profile occurs due to electrical field non-uniformity and presence of the transverse component of the electrical field. This broadening should not exceed the broadening of the beam profile which is caused by the initial transverse kinetic energy of the ions or electrons. The resolution of detection system is defined by the MCP, the phosphor screen, optical coupling and signal background ratio. A proper data processing allows for sub-pixel resolution. The guide electrodes shown in Figure 8.8 are designed to improve the repeller field uniformity. A prototype RGXBPM was tested on ID6 at the ESRF at 29 m from the centre of a straight containing three undulators. The monitor was located after a diamond window of 300 µm thickness. Two readout systems were tried, viz. optical by imaging the phosphor screen with a CCD camera, and current by using a multi-channel plate with a split saw-tooth electrode. The channel plate had a channel diameter of 12 µm and the CCD camera had a resolution of 15 µm/pixel. With the optical readout, each CCD frame had an integration period of 300 ms and the beam centre of gravity could be calculated for each frame with a ring current of 68 ma and a residual gas pressure of 10-7 mbar. A 5 µm step in the RGBPM position could clearly be resolved. The noise was not quoted, but looked to be 2 to 3 µm. The resolution with the splitelectrode detection was about twice that with the optical detection, with a 10 µm

139 Beam cross-section diagnostics step being resolved. An important limitation of these devices for measuring X-ray beams is that the cross-section for creating ions is much greater at VUV than at X-ray wavelengths and thus the sensitivity of monitor is strongly dependent on the beam spectral content. This is a real issue on synchrotron sources where the long wavelength halo around an undulator beam will give a false broadening of the measured profile even thoughit is at a low intensity compared to the on-axis X-rays[187]. In both the measurements of Ioudin and Ilinski, windows in the X-ray beam acted as high-pass filters. Such filtering is unlikely to be possible on a free electron laser source (because of the ablation risk and beam disruption) but the spectral content in such a source should not contain the long wavelength components anyway. Nevertheless, it is important to consider any possible sources of stray light (from dipoles, steering magnets etc and the spontaneous radiation from the undulators) that might propagate with the free electron laser beam. It should also be noted that the RGBPM is principally being designed to measure the centroid of the beam, this being achieved through measuring and analyzing the beam profile. Thus, a small amount of profile broadening can be accounted for. Of course, bi-axial profiling requires a second monitor. There is also the need to further improve the resolution and speed of the monitor if it is to meet the requirements of a free electron laser beam position monitor. Fluorescence detection in residual gas monitors When atoms in a gas are excited or ionized by VUV to soft X-ray photons, the dominant decay process is Auger emission. However, at hard X-ray wavelengths, decay by fluorescence becomes a significant process.there is therefore the option of recording the beam profile by imaging the fluorescent light. The principle is the same as with imaging the ion or electron emission. The density of fluorescent photons is proportional to the density in X-rays in the beam. With fluorescence, there is the advantage that the photons will not be perturbed once emitted since the probability of scatter in a low-pressure gas will be negligible. However, the photon emission is not instantaneous with the atom being excited by the x-ray. Thus, by the time the atom emits, it will have moved under the influence of the space charge of all the ions. The average motion will therefore be away from the beam centre and this will result in a broadening of the fluorescence profile. This broadening effect is much more significant when measuring charged particle beam profiles since the ions are also under the influence of the beam space charge. This effect has been observed when measuring the profile of proton beams[188]. When measuring an X-ray beam in a low pressure gas, the effect of inter-ion repulsion is probably negligible. The ions will still move randomly before emitting the photons, and statistically more will move away from the beam centre than towards it. Thus, there can still be some broadening effect that will depend on the lifetime of the excited state, which will in turn depend on the gas being ionized. This type of monitor is in use at the Cornell synchrotron CHESS, where the monitors are called video beam position monitors (VBPM). The layout is shown schematically in Figure 8.9. The beam tube is filled with helium at atmospheric pressure. Whilst this undoubtedly increases the fluorescence intensity, it would seem the main reason for this is that the entire beamline is gas filled after a window of unspecified material which isolates it from the machine vacuum. (These are of course hard X-ray

140 8.6. Imaging ion chambers 125 Horiz. profile camera Vert. profile camera He gas X-ray beam Figure 8.9: Schema of the CHESS VBPM system. beamlines). The video cameras image the fluorescence via plane mirrors to prevent them being damaged by scattered radiation coming through the viewports. One issue that affects the resolution of the VBPM is the depth of field of the video camera lens. The depth of field of the vertical profile camera is smaller than the horizontal beam size and so edges of the beam are not in focus. The blurring of the image leads to a broadening of the recorded beam profile. This is not an issue when the main purpose of the monitor is to determine the beam centroid, as in this application, but would be if accurate profiling were required. The spatial resolution is also dependent of the lens magnification and camera CCD pixel size, which need to be chosen with the size of the beam to be measured in mind, and the number of digitization levels and overall signal to noise ratio. The camera system was tested to have an accuracy of 0.4 µm fwhm. The imaging system of the VBPM runs at 15 frames per second and the intensity map is usually averaged over 10 frames. This low data rate is not an issue with an essentially continuous source like a synchrotron, but would be unacceptable for a free electron laser source. A faster camera could of course be used; the main concern is whether enough fluorescence can be generated with a single free electron laser pulse to be measurable. Enhancement of the signal byadding agas at a low pressure should be feasible; most X-ray free electron lasers have a windowless gas attenuator anyway (c.f. chapter 4, p. 69). But the pressure limit will be determined by absorption, vacuum

141 Beam cross-section diagnostics contamination (the gas cell cannot be isolated with windows) and self-modulation of the intense photon pulse as it passes through the gas. 8.7 Sampling techniques The ideal sampling process would be to extract a time slice from the beam so that the full spatial profile can be measured of the slice whilst allowing the majority of the beam to pass onto the experiment. Unfortunately, extracting a time slice of a femtosecond duration X-ray pulse is not practical. Therefore,sampling in the spatial domain has to be used, for which there are two approaches. One can remove just a small part of the spatial extent of the beam, which leads to only centroid information (see section 8.10), or the beam can be sampled by uniformly removing part of the overall intensity, which allows a profile to be measured. Clearly, the main objective is to remove as little of the overall beam intensity as possible to maximize the intensity reaching the experiment. Profiling by sampling requires an intensity beam splitter, whichisdifficulttoachieveinthevuvtosoftx-rayrange. Thusmostdemonstrations of this approach have been at shorter wavelengths. In an effort to make an effectively non-invasive profiling measurement, van Silfhout developed a replicating technique in which the bulk of the X-ray beam passes through a thin featureless foil angled in one plane to the beam whilst a small fraction of the X-rays are scattered from the foil and are imaged by a linear photodiode array to give line profile of the beam[189]. Because the x-rays are scattered rather than reflected, a Soller slit is used to give accurate mapping of each scattering point on the foil to a single diode in the array -see Figure Nevertheless, the measured profile must be deconvoluted from an instrumental function determined from the profile measured with a very small beam footprint on the foil. The limiting spatial resolution is determined by the spatial sampling of the projected beam footprint on the foil and can thus be improved by angling the foil at a more grazing angle to the beam. A beam position accuracy of 1 µm was claimed. The technique can be extended to 3-D imaging by tilting the foil in two planes and using a crossed-soller slit and diode array. A more recent paper[190] shows how the technique can give a fast output of the beam profile (still at in one dimension). The ultimate limit was 10 khz, determined by the readout speed of the electronics, though the actual measurements were performed at 2400 Hz. The obvious concerns for free electron laser use are: 1) ablation damage to the foil, 2) disruption to the beam through coherent diffraction if the foil is not perfectly featureless and 3) the limitation to hard x-rays to get high transmission through the foil. Another approach, tested on an undulator beamline at SPring-8, is described in Kudo et al. [191]. A 30 µm thick CVD diamond film was grown on a silicon substrate andthesilicon was etchedaway from acentralregion of10mmdiameter. Theexposed diamond has silicon doping from the substrate that causes it to photo-luminesce at 739 nm when exposed to an X-ray beam. The luminescence was imaged by a CCD camera giving a 2-D picture of the beam profile. The diamond film is almost transparent to hard X-rays (50% transmission at 3300 ev, 90% at 6200 ev, for a density of 3.5 g/cm 3 ) and so most of the beam passes through it to the experiment. The luminescence response to beam intensity was shown to be linear over at least four orders of magnitude. However, the luminescence is stimulated by a wide range of X-ray wavelengths and so the method is unable to distinguish between the on axis

142 8.7. Sampling techniques 127 X-ray beam Thin foil Scattered X-rays Soller slit Diode array Figure 8.10: The profiling system of van Silfhout, based on a Soller slit collimating the scattered X-rays from a thin foil. emission at the resonant wavelength and the lower energy radiation outside the central emission cone of the undulator, leading to an artificially broadened beam profile. However, this should not be an issue with a free electron laser beam. No specific data for spatial resolution is given, but this will be determined by the combination of the camera resolution and the beam footprint on the diamond. Bandwidth will be determined by the readout rate of the camera and the persistence of the luminescence in the diamond. Diamond has high thermal conductivity and the film, mounted in a water-cooled assembly, was able to withstand the full pink beam on BL46XU at Spring-8. Power loading is less of an issue with a free electron laser beam but there is a significant risk of ablation if the diamond is exposed to the full intensity of the fundamental. A further concern is that the CVD diamond is polycrystalline and thus there may be significant disruption to a coherent X-ray beam on passing through the film. An alternative approach to intensity sampling is to Bragg reflect part of the beam from a thin crystal onto a 2-D CCD detector whilst most of the beam intensity passes through the crystal. This also allows the beam to be fully imaged and so profile information to be extracted, Fajardo and Ferrer used a 500 µm thick beryllium crystal in a white beam from an undulator at the ESRF[192]. The crystal was set a 45 and so measured X-rays at 4.45 kev. The quality of the image is degraded by the effects of mosaic spread and the finite extinction depth of the crystal. This does not affect

143 Beam cross-section diagnostics centroiding resolution but does affect any profile measurement. The major disadvantage is the spectral dependence of the reflected and transmitted beams.varying the Bragg angle to work at different wavelengths would make a very complicated system. Furthermore, in the context of a narrow-bandwidth free electron laser source, the impact on the transmitted beam will be significant. The crystal acts as a band-cut filter and, because a significant fraction of the radiation could lie inside the crystal rocking curve width, the notch in the transmitted spectrum would be large. The mosaic spread of the crystal is also likely to cause strong diffractive disruption to the transmitted beam. Finally, the technique is only applicable to hard X-rays where adequate transmission through the crystal is possible. At lower photon energies, a diffraction grating can be used to split the beam in intensity (as discussed previously in chapter 5). This can be utilized in one of two ways; either the first-order diffracted beam is sent to the diagnostic and the zeroth order to the experiment or vice versa. For a beamline that requires a monochromator, it makes sense to use the zeroth order beam for the diagnostic. In such a case, it is necessary to ensure the zeroth order beam direction is fixed as the grating is turned to tune the wavelength, otherwise the diagnostic system will have to move considerably to follow it.in a normal fixed included angle monochromator, this can only be achieved by using additional steering mirror(s) to catch the zeroth order beam and redirect it to the diagnostic. Such a mechanism could be both large and complicated since translation as well as rotation of the steering mirrors is likely to be necessary. An alternative approach is possible with a variable included angle monochromator such as the SX700 mount when operated in collimated light. In this monochromator it is possible to operate in the so-called onblaze mode and this maintains a fixed angle between zeroth and first order beams. In this mode, when the angle between the first and zeroth order beams is ψ, the wavelength λ is related to the diffraction angle β by N n λ = 2 sin ( ψ 2 ) cos ( ψ 2 β ) (8.1) Whilst this mode also conveniently maximizes the first order efficiency when a blazed grating with a blaze angle of ψ/2 is used, there is a significant reduction in tuning range for a grating of a given line density and thus more gratings are required to cover a wide photon energy range. In the alternative approach when the zeroth order is sent to the experiment, the grating should ideally be kept at a fixed angle to minimize the reflections in the main beam path. The diffracted order will thus be reflected at a different angle as the free electron laser wavelength is tuned and the profile monitor will need to follow it. This will be easier than in the case where the grating is turned since the angular range over which the diffracted order moves will be smaller. Thus it should be possible to arrange the imaging detector to move on a rail to follow the beam. It must be remembered that the diffracted order will need to be imaged onto the detector. This is best achieved by using a varied-line-spacing grating that also allows aberrations to be corrected. This is basically the approach used in the diagnostic spectrometer at Flash[193], discussed elsewhere. When applied to spatial imaging,there are two important considerations when interpreting the measurement. Firstly, residual aberrations could still be present and secondly, the image will be blurred due to the dispersion of the pulse spectrum. A detailed design study would

144 8.8. Spot size 129 need to be performed to investigate whether this technique could give a useful pulse profile diagnostic. Another factor that should be remembered is that the position of the beam at the diagnostic will be dependent on the grating angle and thus the technique is not ideal for getting information on absolute positions and how the beam is moving. 8.8 Spot size From the users perspective, one of the critical factors determining the performance of a free electron laser is the size and quality of the focused beam spot. For many experiments, the requirement is for as small a focused spot as possible to maximize the flux density or fluence and to restrict interaction to a specific, targeted sample area.transverse intensity profiling is also critical when aligning the focusing optics to optimize the spot shape by minimizing any asymmetry and eliminating tails and flares. A precise measurement of the spot size is crucial to determining the absolute flux density, which must be known for some experiments. The most desirable solution for spot size determination would have the ability to directly image the spot with a suitable two-dimensional, high resolution, high repetition rate detector which is suitably robust to accept the unattenuated beam. However, extensive experience on synchrotron sources has demonstrated that the current generation of CCD and proportional gas-filled detectors can be permanently damaged by momentary exposure to the unattenuated X-ray beam of a relatively large (several millimeters) diameter. Whilst such devices should not be excluded from a survey of possible techniques it is reasonable to suggest that the majority of 2-D imaging systems will require significant attenuation and shielding to provide a usable service life on a free electron laser source. It should be noted that attenuating the beam using solid filters or foils has been demonstrated to affect the beam wavefront at Flash although the effect of using a gas attenuators is negligible 7. The remainder of this section is therefore subdivided into two sections covering those techniques that can be used with the unattenuated beam, and those for which significant attenuation will be required. Techniques useable with unattenuated beams Ablation crater analysis One of the most established methods of determining the beam cross section in conventional high power UV-Vis-IR lasers is by analysis of the laser ablation crater imprinted into a well characterized sample, predominantly PMMA (polymethyl methacrylate). PMMA is used extensively because of its well characterized ablation characteristics across a wide wavelength spectrum, its short heat diffusion length and the predominance of non-thermal processes when exposed to ultra-short laser pulses. The low ablation threshold of PMMA also allows characterization to be performed on less efficient or highly attenuated beamlines. Techniques exist to comprehensively reconstruct the beam profile from the ablative imprint[194]. The beam can be characterized at any point along the beamline or 7 P. Juranić et al. Desy internal presentation.

145 Beam cross-section diagnostics Open multiplier TOF GMD Faraday cup Diff. pumping Ions Ions ±2 cm FEL beam e - Faraday cup Figure 8.11: Setup for the ion yield saturation measurement at a beam focus. end station where it is possible to place a sample of PMMA. The material is readily available, inexpensive and can be easily shaped. It is particularly suitable for characterizing the beam profile in user-supplied sample holders and environmental chambers. Despite all these advantages, there are very significant practical barriers to using crater analysis beyond the initial commissioning stage. Measurements can only be taken of a single pulse (although some form of carousel or sample changer could theoretically be used for very low repetition rates). The technique is clearly disruptive to any experimental data collection and requires significant time to mount and remove the ablation sample. Although it may be possible to make a limited determination of the beam cross-section using in-situ optical microscopy, detailed analysis of the beam quality will be conducted offline. The measurements to determine the crater profile typically incorporate both optical and atomic force microscopy,so results are far from instantaneous. It is possible to envisage a certain degree of automation being employed if the number of routine measurements justified the investment. Even so, it is difficult to imagine the time between sample exposure and accurate beam cross section determination being reduced below the level of several hours. Photoionisation saturation of rare gases An advanced, non-disruptive technique for spot size minimization has been developed at Flash by A.A. Sorokin et al. [195]. This is based on the saturation effect of the photoionisation of rare gases. At lower irradiance levels there exists a linear relationship between the number of incident photons and the number of ions generated. However as the irradiance increases (e.g. due to the reduction of the spot size at the ideal focus position) the fraction of the atoms in the interaction region that are ionized approaches unity. The ion yield thus diminishes with respect to the number of incident photons as the interaction region and focus coincide. This saturation effect can be measured with an apertured time-of-flight (TOF) spectrometer mounted perpendicular to the beam direction (see section 7.3, see page 104), whilst measurement of the absolute number of photons per pulse is made using a gas monitor detector (the GMD presented in section 7.2, see page 100) Figure Careful selection of the target gas type and pressure relative to the energy of the photon beam is required to restrict the photoionisation process to one-photon single ionization[196].

146 8.9. Techniques requiring attenuated beams 131 The technique is not quantitative; rather the maximum level of saturation of the photoionisation signal indicates the optimum focus position. Further diagnostics are required to quantify the resultant beam size,although photoionisation saturation could be calibrated using a quantitative process (e.g. ablation crater analysis) for a given lateral position and gas pressure. One benefit of the technique is that it is nondisruptive, since both the TOF spectrometer and the GMD do not impinge directly on the incident photons.the system has currently been tested using macropulses of Flash free electron laser at a photon energy of 38 ev. 8.9 Techniques requiring attenuated beams Wire, knife-edge and slit scans For the majority of existing synchrotron-based micro-focus experiments, slit scanning methods are used to characterize the beam size and profile[197]. In general, diffraction or scattering effects from the scanning object are not taken into consideration when calculating the beam size. These techniques are covered in more detail in relation to general beam profiling in section 8.4. For synchrotron radiation sources, any thermal loading issues are overcome by implementing water cooling to the slit jaws or apertures. However,the fluence levels at the focus of a pulsed free electron laser source will accentuate the difficulties associated with ablation, for which significant attenuation will be the only solution. Photographic film This is included for the sake of completeness, and as a demonstration that a relatively low technology solution can prove extremely useful. Film was used extensively on second-generation synchrotrons e.g. SRS, Daresbury UK, to produce a permanent record of the size and shape of the focused X-ray beam. In this example the film used was Polaroid 55 large-format self-developing film which was chosen for its ease of use, speed, limited cost (at the time) and small grain size which led to comparatively high resolution images.its thinness also made it practical in an experimental set-up as it could be placed practically anywhere in the hard X-ray beam path without disruption to user equipment. One could suggest that photographic film is still viable for free electron laser applications since the grain size of high quality film stock can be as small as 0.5 µm, which is far smaller than the photo site spacing of even the best CCD sensors. Some form of pulse selection would be required to give single-pulse imaging and high levels of attenuation would be required to avoid ablation damage and over-exposure of the film. Since the film is by its nature disposable, damage would at least not be a catastrophe. In practical terms though, this is of little relevance since suitable film is now difficult to obtain in appropriate quantities and requires lengthy processing, digitization and subsequent image analysis. Polaroid self-developing film is no longer in production. For information, there is a closely related material which can also be used for beam size determination; namely self-developing X-ray dosimetry film 8. Similar products 8 E. g.

147 Beam cross-section diagnostics have been used on synchrotrons for beam profiling and have broadly similar advantages and drawbacks as self-developing photographic film. However, the resolution of dosimetry film (ca. 100 µm) is significantly worse than that for high quality photographic film and will be too low for many focused beam measurements on a free electron laser source. Gas-filled detectors Gas proportional detection systems for X-rays are commonly based on either wire grids[198] or, more recently, on metal strips lithographically printed onto either traditional circuit boards or glass substrates[199]. Existing large-field commercial detectors typically have pixel sizes of the order of tens of microns, although it should be possible to lithographically produce dedicated beam imaging detectors with smaller pixel sizes,and resolution could be further improved using pixel interpolation algorithms. However, although these detectors are sought after for their potential for measuring high global count rates and energy discrimination,they suffer from severe non-linearity due to space charge effects. Thus high count-rates that are very localized, as would be experienced with free electron laser beam imaging, would cause problems. Additionally, at high count rates there are also problems with rapid contamination of the gas and detector wires/elements,requiring very high gas flow rates and therefore high maintenance costs. These issues make them highly unsuitable for direct beam imaging purposes. Charge coupled device (CCD) Direct-detection CCD cameras for X-ray energies are commercially available with pixel sizes down to 8 x 8 µm 9. This is not sufficient for the strongest focusing that will be used on free electron laser, where spot sizes around 1 µm or less will achieved. Depending on the energy range to be covered, a selection can be made between back thinned, front illuminated and deep depletion CCD types. However, these sensors are specifically not designed for high flux density applications; saturation and damage occur at low irradiance. Significant effort has been channelled into developing radiation hard CCD cameras, the initial driver coming from improving the longevity of space-borne astronomical instruments and remote observation systems in the nuclear industry. Defects can be generated in the bulk silicon through exposure to radiation, and these defects can then become electrically active, leading to further space-charge, charge leakage and charge trapping issues in CCDs[200]. Three key approaches have been taken to minimize the degradation effects inccds; i) engineering solutions such as guard structures, voltage biasing and a reduction in the thickness of charge channels, ii) material developments such as reducing the contamination defects in silicon or replacement of silicon with alternative insulator materials and iii) alternative structures such as p-channel CCDs or charge injection devices (CIDs). CIDs individually address each pixel in the detector and do not suffer from leakage of stored charge from one pixel to another. Commercial nuclear inspection CID systems are available for X-rays, infrared and the ultra-violett with a stated pixel 9 See, for example,

148 8.10. Position and centroiding 133 size of 11.5 x 11.5 µm and a frame rate of up to 25 Hz 10. A Thermo Scientific CID camera has been employed as part of the transverse beam profiler for the IFMIF- EVEDA prototype deuteron accelerator[201]. As discussed in section 8.3, luminescent screens in conjunction with CCD cameras can be used for indirect detection. Using a scintillation screen, imaging of the X- ray beam from SRS dipole beamline 8.2 has been demonstrated using an attenuated Photonic Science CCD system. At the intensity levels experienced there,the main risk of damage was assumed to be thermal damage to the screen. For free electron laser the highest risk of damage will be ablation of the screen, and hence attenuation of the beam will be essential. Multichannel plate (MCP) A number of commercially available beam imaging systems exist based on fibrecoupled MCP technology 11 and a large range of conversion media exist to enable the imaging of neutron and electron beams in addition to IR, UV and X-ray radiation. However, these systems are of limited application to free electron laser beams since the inherent amplification due to the MCP is at odds with the requirement to strongly attenuate the beam. Solid State Detectors For many applications on existing synchrotron sources, silicon pixel detectors (often referred to as Monolithic Active Pixel Sensors, MAPS) or hybrid pixel detectors, typified by the PILATUS system[202], are seen as a significant emergent technology. They combine volume manufacture with small pixel sizes,large dynamic range, high count-rates and fast readout. However, in common with CCD-based systems the irreliance on silicon based lithographic plates makes them susceptible to radiation damage at modest beam intensities Position and centroiding Sampling techniques Beam centroiding is typically performed by sampling part of the beam, either spatially or in intensity. The basic objective in measuring the centroid is to measure the beam position and angle mainly for the purposes of beam stabilization through feedback control. Solid state photo-emission monitors Blade monitors are an example of spatial sampling and are widely used on synchrotrons. Mortazavi et al. [203] describe an early implementation at the NSLS (Brookhaven) giving a sensitivity of a few microns. Thin tungsten blades positioned edge-on to the beam intercept the periphery of the beam and the induced photocurrent is proportional to the amount of beam they intercept. If two identical blades are and

149 Beam cross-section diagnostics positioned either side of the beam, then the relative intensity they see is a measure of the beam position relative to the centre of the gap between the blades. These devices are thus centroid monitors giving beam position relative to the blade gap but there is an underlying assumption that the beam intensity profile is symmetric. Johnson and Oversluizen[204] also assert that the apparent deviation of the photon beam from the monitor centroid depends on the on the size of the [...] beam relative to the blade gap, though it is not clear why this should be if the detector and photon beam are symmetric (there are however problems created by stray light from adjacent magnets, q.v.). It is however clearly important that the blades be identical both physically and also in terms of photoelectric yield. The latter is a condition that is hard to ensure given that photoemission is a predominantly surface effect and so susceptible to contamination from the residual vacuum. Aging of the blades in a white synchrotron beam is likely and if the blades age differently then this would lead to long-term change in the null position of the beam relative to the gap. A similar approach uses two parallel horizontal wires or rods with a fixed gap[205]. The advantage of the blade approach is that blades are easier to cool than wires and less invasive than rods. Alkire et al. [206] report a relative accuracy of ±5 µm for their monitor which uses 1.5 mm diameter tungsten rods of 12 cm length and with a centre to centre spacing of 7.9 mm. Tungsten or molybdenum are often used as the blade material since their high melting point and hardness makes them resistant to the high powers produced by 3 rd generation synchrotron sources. However, when high-k undulators are used on high-energy synchrotrons the total power can be such that accidental exposure of such materials to the central part of the beam could be damaging. At the APS, CVD diamond was chosen since it has 10 times higher thermal conductivity than molybdenum, and lower thermal expansion allied to high strength and stiffness[207]. These monitors have sub-micron sensitivity. For initial tests, the diamond was coated with tungsten to give high photo-emissivity and electrical conductivity. Later, a 1 µm gold coating on 150 µm diamond blades was used[208]. This approach raises the prospect that it may be possible to coat the blades with a low-z material (e.g. carbon or beryllium) that would resist ablation from a free electron laser beam, which would otherwise be a major concern when using this type of monitor on a such a beam. An advantage of the blade type monitor is that extra blades can be added in various configurations such as a vertical cross[209], diagonal cross [210], etc. see Figure Thus, a single monitor allows bi-axial positional information to be calculated. Two such monitors longitudinally separated give beam angle information,though each should use a different blade arrangement to prevent the blades of the second monitor from lying in the shadow of the blades of the first monitor[207]. For the centroid measurement to give an absolute position and angle, the monitors must be accurately mapped to an external reference frame. However, if there is an asymmetry in the response of the blades (e.g. due to surface contamination) then, when the monitor is nulled, the beam centroid will not be centered on the gap. There is thus an error in the inferred absolute position relative to the external reference frame. Thus the absolute positional accuracy of a blade type monitor is not always easy to define. In the case of synchrotron light from dipoles, these detectors can be made effectively transparent to the X-ray beam by being designed to intercept only the UV light that has a much larger opening angle than the X-rays, which thus pass undisturbed through the blade gap (Figure 8.13). The same approach can also be used with undulator

150 8.10. Position and centroiding 135 (a) (b) (c) (d) Figure 8.12: Possible arrangements for bi-axial blade monitors. (a) simple vertical cross; (b) a diagonal cross allows better horizontal sensitivity when the horizontal opening angle changes considerably if an undulator is tuned from low to high K; (c) and (d) upstream and downstream arrangements used at the APS to prevent shadowing effects [40] (the tilted horizontal blades reduce the sensitivity to dipole radiation). UV X-rays Monitor blades Figure 8.13: Figure 9 -A blade monitor can be transparent at short wavelengths on a synchrotron source due to the reduction in opening angle as the wavelength decreases. sources since the emission outside the central cone is at a longer wavelength than the fundamental.however, free electron laser radiation does not have the same properties and so this approach cannot be used. There will be spontaneous radiation from the undulator, but this will be at a low intensity due to the low average current and may not be of sufficient intensity to measure. Furthermore, this approach has its drawbacks since the photons being detected are not the ones being used in the experiment and one must assume there is a unique and consistent spatial correlation between the spectral components in the beam. Whilst the range of wavelengths present in a synchrotron beam can be used to advantage as described above, it can lead to problems when using photo-emissive type monitors with insertion devices on synchrotron sources. The electron yield is much greater at VUV wavelengths and thus these monitors are disproportionately sensitive to the low-level long-wavelength radiation coming from the dipoles and steering magnets that surround the insertion device. Extreme lengths have been used to overcome this problem at the APS where the machine lattice has been modified to separate the insertion device light from the stray light in order to facilitate sub-micron level orbit

151 Beam cross-section diagnostics correction[211]. Galimberti et al. [212] describe a different approach that makes the beam position monitor only sensitive to the X-rays that are being used in the experiment. They have improved the blade monitor by adding electron energy analyzers to measure the blade signals. Thus they can select only the electrons emitted by the fundamental radiation and so isolate it from any low energy background and even electrons emitted by higher harmonics from the undulator. This is a much more sophisticated approach to that suggested by Warwick et al. [210] in which the blades are reverse-biased to prevent the low energy electrons leaving the surface. Whether such precautions would be needed on a free electron laser source would clearly depend on the nature of the electron beam transport, but it would be natural to assume the effect would be much reduced since the electron path is straight and the long undulator length should limit the acceptance aperture of radiation from other sources. In general, blade type monitors when used on undulator sources are sensitive to the undulator tuning due to the changing radiation pattern as the undulator K-value is changed. This makes position control to sub-micron levels difficult. A smart XBPM system (SBPM) has been developed at the APS in which the response of the XPBM is automatically characterized under all possible operating conditions of the undulator so that these effects can be automatically corrected for[208]. The effect of any change in beam footprint with wavelength must be considered carefully for free electron laser beams.this source approximates to a coherent Gaussian source and thus the divergence will be roughly proportional to wavelength. We can therefore expect a considerable change in beam footprint at the monitor as the wavelength of it tuned. This will certainly change the sensitivity and resolution of the monitor at different wavelengths and there is also the issue of the inferred position being dependent on beamsize. Possibly more important are the risk of ablation and the disruption to the beam. Providing the blades sit only in the wings of the beam, ablation and diffractive disruption to the downstream beam may not be an issue. But if the expands significantly, the blades will cut the beam at a position of greater intensity and so both the risk of ablation and diffractive disruption will increase. It may thus be necessary for a blade type monitor to have blades that move depending on the source s wavelength. In order to eliminate the sensitivity of a blade monitor to beam size, schemes using two triangular wedge swith a gap between them running at 45 to the horizontal have been developed[204] (see Figure 8.14(a)). The gap must be designed to intercept enough of the beam to get a decent signal with the smallest expected beamsize (i.e. at the shortest wavelength). This means that any significant increase in beam size will result in a significant loss in throughput. A variable gap will therefore be essential with a free electron laser source. Even then, this type of monitor will be more disruptive to the beam and be at greater risk of ablation then blade monitors and so is unlikely to be useful with a free electron laser source. A refinement of this scheme was reported by Mitsuhashi and tested at Spring-8[213]. Here, two wedge monitors are placed to just intercept the periphery of the beam, thus reducing the fraction of the beam intercepted and allowing bi-axial monitoring. Initially, the monitors were composed of triangular wedges but this design was found to be sensitive undulator gap. Thus a revised symmetrical scheme was developed and tested see Figure 8.14(b) and this reduced the sensitivity to the gap around ten times. Note the wedges are angled to the beam to reduce the power loading. The wedge type monitor can be extended to give bi-axial position detection by using a classic quadrant detector. These can be made using metal-foil photodiodes

152 8.10. Position and centroiding 137 Wedge plates Upper electrodes X-ray beam Signal out Lower electrodes (a) Figure 8.14: (a) The Wedge position monitor eliminates the sensitivity to beam footprint of the blade counterpart but is more invasive; (b) the symmetric design of Mitsuhashi et al. reduces the beam loss and has low sensitivity to undulator tuning. (b) but are also available commercially using semiconductor junction photodiodes[214]. One problem with using semi-conductor devices is that they tend to be insensitive at the edges and thus the amount of beam overlap needed to give a signal is increased to the detriment of the transmitted beam. Kenney et al. [215] describe how activeedge silicon detectors, which are active to within a few microns of the detector edge, can be used in various geometries for position, profile and intensity monitoring. For example, a quadrant detector with a small hole at the centre can be used to monitor the stability of a tightly focused beam. The beam is focused through the hole and only the periphery of the beam is stopped by the detector. The focus position is stabilized using feedback control based on the quadrant signals. An example device with 100 µm diameter hole is pictured whilst test were made on a simpler single element torus with 200 µm hole. This device showed excellent response uniformity to 12.5 kev X-rays. The effect of diffraction at the hole with a coherent free electron laser beam is a potential problem with this approach, as is the high risk of damaging the detector if the central part of the beam is inadvertently steered onto it. A significant disadvantage of the classic quadrant detector is that the fraction of the radiation transmitted, i.e. that which can pass through the hole in the middle, may not be large enough. Shu et al. at the APS[216, 217] have developed a quadrant detector that has a high transmission to hard X-rays. The detector is based on a 25 mm diameter CVD diamond disc of 150 µm thickness. This has a transmission of 78% at 10 kev. The quadrant pattern is formed with a 0.2 µm aluminum coating on the disc. In its simplest form, the photocurrent from the aluminum sectors is independently monitored and gives the positional information.the diamond in this scheme simply acts as a support for the aluminum electrodes that can withstand the intense synchrotron beam. A more sophisticated approach uses the photoconductive properties of insulatingtype (IIa) CVD diamond in which the diamond becomes conductive when exposed to the X-rays. The aluminium pattern is replicated on both sides of the diamond disc and a bias applied across the front and back electrodes Figure On exposure to X- rays, the diamond becomes conductive and a current flows. Since the conductivity is dependent on the absorbed X-ray power, the current is proportional to the intercepted X-ray intensity. Also,the sensitivity increases with photon energy and the detector

153 Beam cross-section diagnostics Diamond disc Output signals X-ray beam Bias Al quadrant electrodes Figure 8.15: Quadrant detector based on the photoconductivity of diamond. less sensitive to stray light from bending magnets etc. There are other ways of spatially sampling the beam such as using a pin-hole array[218] but these are significantly more invasive and ablation damage is highly likely. Solid state fluorescence monitors Measurement of the incident photon intensity on the monitor by recording the photoemission in some way is widely used because the electron yields are high and photoemission is the dominant de-excitation process until the Ga K-edge at 10 kev. Nevertheless, the radiative yield is appreciable above c. 5 kev and thus fluorescence presents an alternative detection route. Alkire et al. [219] describe a simple position monitor consisting of a 0.5 µm of Cr or Ti through which the beam (5 to 25 kev) passes with little attenuation. An array of four PIN photodiodes surround the beam axis in a vertical cross arrangement just upstream of the foil Figure The diodes record the fluorescence signal and give the same effect as the four blades of a normal bi-axial beam position monitor. The advantage is that the beam is measured over its full cross-section and so the true centre of intensity of the beam is measured. The measured position sensitivity was 1 2 µm. As with other techniques that involve passing the beam through a foil, the concerns with a free electron laser beam are ablation of the foil a diffractive disruption to the transmitted beam.

154 8.10. Position and centroiding 139 X-ray beam Foil Photo-diodes Figure 8.16: Photodiode array BPM used to collect fluorescence from a thin foil. Gas phase photo-ionisation monitors Split-plate ion chambers are examples of intensity sampling. This approach is more sophisticated than blade monitors as it samples the whole spatial extent of the beam and should thus give a more reliable measure of the beam centre of intensity if the beam is asymmetric or inhomogeneous. The beam passes through a gas at a low pressure between electrode plates with a high voltage bias between them, and the ion yield is recorded as a current from the plates. By splitting one of the plates diagonally (Figure 8.17), each half of the split plate receives a different signal depending on the beam position relative to the middle of the slit and the ion chamber records position parallel to the plane of the plates. The diagonal split improves the linearity of the monitor at the expense of sensitivity near the null position[220]. A split ion-chamber that can measure the vertical position of two partially overlapping beams simultaneously has been developed at the Cornell High Energy Synchrotron Source CHESS with a reported accuracy better than 10 µm and a bandwidth greater than100hzoveralinear rangeof5mm[221]. Theaccuracywas limitedmainly by drift in the analogue signal electronics and the ion chamber was actually able to resolve movements at the micron level. Differentiation of the two beams was achieved by designing the collecting field produced by the bias electrodes such that the col-

155 Beam cross-section diagnostics X-ray beam Wedge plates + Signal out Bias plate Figure 8.17: Arrangement of beam and plates for a split plate ion chamber. lecting electrodes collect only ions from the non-overlapping edges of the two beams. Thus, the ion path is short and this also improves linearity and bandwidth. Two make a bi-axial measurement, two ion-chambers are placed sequentially with their plate-pairs orthogonal. Schildkamp and Pradervand[222] describe a system tested at CHESS which achieved a resolution below 1 µm with a bandwidth of 1000 Hz. Important considerations when using ion chambers are: different gases may be needed to cover different photon energy ranges; the effect of saturation and recombination on the measured current; the transit time of the electrons and ions. A noble gas is preferred as it eliminates asymmetries that result when using polar molecules and lighter gases reduce the transit time of the ions to the plates and so help reduce the build up of space charge in the chamber. Whilst the ion chamber cannot be damaged by high intensities, the probability of recombination before the ions reach the plates increases in proportion to the beam intensity and the square of the distance travelled. If care is not taken, false position changes can be deduced as the beam intensity is changed. The upper limit on the detection bandwidth is set be the transit time of the ions to the plates; increasing the bandwidth requires reducing the plate gap and increasing the bias potential[223]. The other main limitation is the need for a gas. With a transversely coherent beam, it is not desirable to use windows to isolate the gas and so the chamber must be isolated by means of differential pumping. In the context of a free electron laser this is not such a major issue as gas attenuators will be a common feature and the significant

156 8.11. Wavefront measurements 141 advantage of the ionization chamber is that it can be considered non-invasive if the gas pressure is low enough. The ion chamber can thus be used as an on-line diagnostic giving pulse-by-pulse beam centroid position Wavefront measurements A wavefront is defined by the surface on which the radiation field has the same phase (assuming a monochromatic source). The direction of propagation of the radiation is perpendicular to this surface, hence measurements of the propagation direction can be used to find the wavefront this is the principle of the Hartmann sensor described below. A complete characterization of the radiation field at a particular wavelength requires a measurement of the magnitude and relative phase of the field. These results could then be input into simulations to deduce the radiation field at other locations in the beamline. Such measurements could in principle be made using a Hartmann-type wavefront sensor for a monochromatic source. For narrow-band sources such as free electron lasers, the wavefront sensor can be used to measure the tilt of the wavefront and ray tracing used to find the shape of the beam at other locations, assuming that diffraction effects are not important. The Hartmann sensor works by splitting the beam to be diagnosed into an array of mini-beams either by passing the beam through grid of holes (Hartmann plate) or an array of lenslets (Shack-Hartmann array) and comparing the resultant pinhole images or microlens focal positions on a 2D detector with those from a reference wavefront. Variations in the position of each resultant spot can then be used to determine the local slope in the wavefront. Let S xij denote the measured slope in the x-direction at the spot i,j on the detector, then S xij = dwij dx = λ dφ 2π dx (8.2) where W is the optical path difference and φ is the phase. A similar equation can be written for the y-direction. The field strength can be derived from the intensity of the spots. The actual wavefront W has to be reconstructed from the measured slopes there are two main methods of doing this, either by assuming the wavefront can be written as a low (normally second) order polynomial in the local co-ordinates (zonal method) or by expanding the wavefront in terms orthogonal functions, e.g. 2D Legendre polynomials (modal method)[224]. The modal reconstruction is useful in being able to identify the contribution of different aberrations to the wavefront shape. For X-rayapplications a Hartmann plate is used due to the lack of microlens arrays capable of focussing the beam. For IR and UV energies suitable microlens arrays are available, their commercial design and manufacture having been stimulated by common use in ophthalmology and corrective laser eye surgery. The use of wavefront measurements in commissioning a free electron laser beamline was demonstrated at Flash using a Hartmann sensor from Imagine Optics[225]. The sensor contained a Hartmann plate with a 51x51 pinhole array, each pinhole being a 110 µm square tilted 25 to aid close packing and prevent interference with adjacent holes. A direct CCD camera was used as the detector. The reference spherical wavefront was generated by inserting a pinhole into the beamline.

157 Beam cross-section diagnostics From the wavefront measurements on beamline 2 (BL2) 12, the depth of focus of the ellipsoidal mirror was calculated using ray tracing and a small astigmatism was found which was cured by remounting a switching mirror. The design focal spot size was still not obtained, but analysis of the wavefront measurements on BL2 and on the unfocussed BL3 showed that this was not due to any remaining aberrations but to the source being larger than expected during that phase of operation. The critical yaw angle of the toroidal mirror on BL1 was also set using the wavefront sensor. Based on this experience, an optimized wavefront measurement system, using a 320 µm hole pitch, has subsequently been designed in conjunction with the Laser Laboratorium Göttingen for use as an end-station diagnostic on Flash. At beamline 2 this wavefront sensor have been used to align a grazing incidence ellipsoidal mirror decreasing the wavefront distortion from 52.6 nm (peak-to-valley) and 9.2 nm (rms) to 12 nm and 2.6 nm respectively. This by correcting the mirror s pitch mrad and its yaw by mrad[226]. At BL1 the focal spot size and the position of the beam-waist (and its fluctuation on a shot to shot basis) have been found with the same sensor system[227]. At the Scss a Hartman wavefront sensor have been used to do single-shot measurements to characterize the spatial propertis of the Sase radiation[228] THz/IR techniques A major difficulty in IR and THz diagnostics is that of a suitable means of detection of the long wavelength radiation. The low quantum energy of IR and THz radiation means it is only able to stimulate vibrational and rotational modes in molecules and cannot directly cause ionisation. Therefore, measurement techniques that depend on the measurement of emitted electrons cannot be used in the IR and THz. There are two basic techniques for detecting IR and THz radiation that are well established and commercially available, namely: Thermal Photonic (quantum) The detectors can either be photovoltaic (an induced voltage drives a current in the detector circuit) or photoconductive (an induced resistivity change results in a voltage change in the detector circuit). In all cases, background radiation is the ultimate limiting factor and detectors may require (cryogenic) cooling and / or thermal shielding depending on the radiation levels and wavelengths to be measured and the required signal to noise ratio. Important factors to consider when selecting and IR detector are: Photo-sensitivity (Responsivity) The output voltage (or current) per watt of incident radiation power. Units: A / W or V / W. Noise equivalent power (NEP) The amount of incident radiation that gives a signal equal to the inherent noise level, i.e. that gives a signal to noise ratio of 1. Units: W / Hz. 12 For a layout of the Flash beamlines, see Ref. [104]

158 8.12. THz/IR techniques 143 Detectivity D The photo sensitivity per unit active area of the detector. The specific conditions under which the detectivity was measured are usually given as a function of: temperature (K) or radiation wavelength (µm), chopping frequency and bandwidth. Units: cm. Hz / W Spectral response How the output varies with incident wavelength. Response time How quickly the output rises and falls in response to an input pulse. Gating may be needed to measure individual pulses if the response is slow. Background Limited Infrared Photodetection (BLIP) The ultimate detection limit determined by fluctuations in the background radiation flux in the ideal case of zero noise generated in the detector and processing circuits. This is inversely proportional to the square root of the background radiation flux. Thermal detection Thermal detectors involve the measurement of a temperature dependent phenomenon such as: Temperature dependent resistance (bolometers), Thermoelectric effect (thermocouples and thermopiles), Thermal expansion (Golay cells), and Pyroelectric effect (thermally induced change in the surface charge of polarised crystals) Thermal detectors use the radiation as heat and thus the photo-sensitivity is independent of wavelength. Of course, as the wavelength increases, more photons are needed to give the same incident power. Therefore the quantum yield is inversely proportional to wavelength. Since the environment is a strong source of long wavelength radiation, achieving the required signal to noise at longer wavelengths becomes increasingly difficult. The spectral response of thermal detectors can be tailored by placing a window with a suitable transmission band over the detector. It is also highly desirable to use windows that, as far as possible, block the parts of the black body spectrum from the environment that are outside the output spectrum of the free electron laser source. Thermal detectors tend to have a slow response and are more suitable for timeaveraged measurements or measurements on continuous wave sources. For example, the response of pyroelectric detectors is at the millisecond level, though cryogenically cooled bolometers can respond much faster than this. The pyroelectric effect does not produce a permanent voltage on the crystal because the induced charge on the crystal surface dissipates through internal leakage and ions in the air. Thus, pyroelectric detectors produce a signal only when the temperature of the crystal changes and they only respond to pulsed sources. Use with a continuous wave source requires the input light to be chopped, giving a signal of opposite sign at each opening and closing of the chopper.

159 Beam cross-section diagnostics Photonic detection Photonic detectors are semiconductors with band-gaps that are narrow enough for the small energy quanta of IR photons to excite electrons across it. They are more sensitive and have a higher response bandwidth (i.e. are faster) than thermal detectors. Background thermal excitation will result in a significant dark output and some sort of cooling is normally required. Photonic detectors operate over specific wavelength ranges determined by the band-gap. The band-gap and response time also tend to vary with temperature, so cooling a detector to a level at which the intrinsic noise is low enough may shift its spectral response out of the required wavelength range. Most commercial photonic detectors work in the near to far-ir wavelength range from 0.75 to 15 µm (1.65 ev to 80 mev). Table 8.1 below 13 lists various photonic IR detectors. Detector Spectral response [µm] Temp [K] D [cm, Hz/W] Type PbS 1 to D (500,600,1) = 10 9 Intrinsic, Photoconductive PbSe 1.5 to D (500,600,1) = 10 8 InAs 2 to D (500,1200,1) = InSb 2 to D (500,1000,1) = Ge 0.8 to D (λp) = Intrinsic, Photovoltaic InGaAs 0.7 to D (λp) = InAs 1 to D (500,1200,1) = InSb 1 to D (500,1200,1) = HgCdTe 2 to D (500,1000,1) = Ge:Au 1 to D (500,900,1) = Extrinsic Ge:Hg 2 to D (500,900,1) = Ge:Cu 2 to D (500,900,1) = Ge:Zn 2 to D (500,900,1) = Si:Ga 1 to D (500,900,1) = Si:As 1 to D (500,900,1) = Table 8.1: List of photonic IR detectors and operating ranges A widely used photonic detector in existing IR-FEL facilities is the mercurycadmium-telluride or MCT detector. This is because the band-gap and hence longwavelength cut-off can be tailored by adjusting the relative proportions of CdTe and HgTe. The long wavelength limit of commercially available detectors is 24 µm taken from Hamamatsu Technical Information SD-12 Characteristics an use of infrared detectors InfraRed Associates Inc.,

160 8.12. THz/IR techniques 145 The website of the Felix IR Laser facility records that a Ge:Ga detector works from 10 to 200 µm 15. Liquid helium cooling is of course essential at such a long wavelength. New detectors The increasing exploitation of IR radiation on synchrotron radiation sources has stimulated development into new types of IR and THz detectors that aim to give Faster response Wider spectral response Higher quantum yield Lower noise Larger arrays Faster array read-out Higher spatial resolution Developing and future technologies include: Niobium nitride (NbN) superconducting bolometers (50 ps response time, size 0.1 x 1 µm) Transition Edge Superconducting (TES) detectors (a superconductor is held near the transition temperature and thus a small amount of added heat gives an exaggerated conductivity change, improving sensitivity and response time). Quantum Well Infrared Photodetectors (QWIPs) Zero-bias Schottky diodes Schottky diodes made at the Space Science Centre at Rutherford Appleton Laboratory have been tested on the ALICE accelerator at Daresbury. The fastest has a measured response time of 20 ns (1/e). They are able to distinguish (though not completely resolve) the individual THz pulses from the electron bunch train with 81 MHz repletion rate (12 ns period). IR and THz beam profiling Scanning The simplest way to generate a profile in one or two dimensions is to raster scan a detector element (thermal or photonic) through the beam. The spatial resolution is limited by the size of the detector or the defining slit in front of it. Diffraction at a defining slit will limit the resolution if the slit size is comparable to the wavelength. Because IR beams are relatively easy to manipulate, it is also possible to optically raster the beam over the fixed detector. This is likely to be faster than moving the detector since the optical raster will use angular shifts of a lens or mirror whilst the detector raster will use linear motions of the detector. 15 Felix IR Laser facility:

161 Beam cross-section diagnostics Scanning a linear array detector is more efficient, though the spatial sampling of the scan in the direction along the array is fixed by the array spacing. The array must also be matched to the beam size, whilst a single element scan can used on an arbitrary beam size. imaging Infrared imaging is of course widespread. Even a standard CCD based digital camera can image in the near infrared, whilst security applications have driven a huge development of sub-optical imaging systems. Here we will therefore consider the more challenging area of longer wavelength imaging and imaging which is tailored to the nature of free electron laser sources. It is conceivable that any of the basic types of single element IR detector can be built into an imaging array, either 1-dimensional or 2-dimensional. The specific technical questions that need to be addressed are: The size of the detector elements The spacing of the detector elements The read-out time Sensitivity and spectral response Achieving high spatial resolution requires small and closely spaced detector elements, but this can lead to problems with sensitivity at long wavelengths since the low quantum efficiency means the signal generated in each element is too small to detect. For example, a commercial pyroelectric array detector was found to be unable to detect the THz output of the quantum cascade laser at Leeds University, UK. Consideration must also be given to diffractive effects at these long wavelengths. Diffraction at defining apertures could lead to a decrease the spatial resolution. Does a sensor element that is smaller than the wavelength of the radiation accurately record the incident intensity? Beam splitters The detectors described in here are opaque to the beam and thus cannot be used as part of a noninvasive detector. However, it is relatively easy to split an IR and THz beam in amplitude such that only a small part of it passes to the detector and the rest passes to the experiment 16. The most suitable techniques for IR and THz are: Plates and pellicles can be made of various materials depending on the transmission band required. Pellicles can be coated to enhance the reflectivity at the expense of transmission. Wire grids these are polarising beam splitters, suitable for the longest wavelengths only (determined by the wire spacing). 16 See chapter 5 (see page 73).

162 8.12. THz/IR techniques 147 Wavefront sensing The Shack-Hartmann sensor is a standard instrument for measuring wavefronts in the optical and IR region. Commercial instruments tend to be limited to operation in the near-ir ( 2 µm wavelength), probably because of the types of IR sensitive array detectors that are available with sufficient pixel count, density and sensitivity. CCD cameras would seem to be the standard detector, giving megapixel array size with spacing in the 20 µm range. High pixel count and small spatial separation is required to allow accurate centroid determination of a large number of micro-beams, both of which are necessary for accurate wavefront reconstruction. Extending operation to the far-infrared would require, for example, an MCT array detector. It is not clear that an MCT array with sufficient pixel count and density is technically feasible, let alone cost effective. Alternatively, and for operation in the THz region, the array would have to be made of thermal detectors. As mentioned before, pyroelectric array detectors are commercially available. These currently have rather low pixel counts compared with CCD cameras and a detailed technical assessment would have to be made to decide on the minimum pixel count that would be required. This assessment would also need to consider the effects of the much stronger diffraction and the Hartmann plate of micro-lens array. Electro-Optical Imaging Electro-optical sampling of THz radiation uses the Pockels effect in electro-optic crystals. A THz pulse acts like a transient bias that induces a transient polarisation in the crystal. The polarisation induces a birefringence in the crystal that is probed by a synchronous optical laser beam, the probe beam undergoing a polarisation change as it passes through the crystal. Wu et al.[229] describe how to exploit the EO effect to produce a 2-dimensional image of the THz beam cross-section, see Figure The THz beam was focused at a ZnTe EO crystal and was overlapped with a co-propagating optical laser beam. The optical field probes the spatial distribution of the electric field in the crystal that the THz radiation induces. Crossed-polarisers either side of the EO crystal convert the resulting polarisation modulation of the optical beam as it passes through the crystal into an intensity modulation that is recorded by a CCD camera, which thus gives a 2-dimensional intensity image of the THz beam. This technique can be directly applied to determining the focus size of THz beams. Obviously, a very fast optical laser that is synchronised to the THz pulse is also required. The Pockels effect is very fast and imaging rate is limited by the camera. Gating of the camera should allow single pulse measurement provided there is enough modulation in the optical beam to produce a measurable signal at the camera. Measurement of unfocussed beams is likely to be limited by the photon density of the THz and optical probe beams, since the optical beam must spatially overlap the THz beam for a complete 2-D image to be recorded in one shot. The available size of EO crystals will be another factor limiting the largest beam footprint that can be measured. These limitations could be overcome by using an optical system such as a telescope to compress the beam diameter without modifying the wavefront.

163 Beam cross-section diagnostics THz beam Pellicle ZnTe crystal Analyser CCD Camera Probe beam Polariser Figure 8.18: Layout of the EO imaging system of Wu Summary The ideal or universal diagnostic for a free electron laser source would be able to: Give a full spatial image of the photon beam. Do this for every pulse produced. Not change the photon pulse in any significant manner. Operate over a wide spectral range (at least sufficient to cover the full output range of the source) At the moment, such a universal diagnostic is not possible. Techniques that give full spatial profiles tend to be slow and invasive Faster techniques often only give information such as beam centroid Non-invasive techniques are too insensitive to measure a single pulse Operating wavelength range is strongly limited by the detection technique employed For radiation with wavelengths from the VUV to X-rays, there is a considerable range of diagnostics employed on synchrotron radiation sources that could be developed for use on free electron laser sources. Many of these techniques involve transferring the spatial information to electrons that are detected and analysed to extract the spatial information. Imaging detection is often achieved by converting the electrons to visible photons with the aid of luminescent screens. For harder X-rays, fluorescence is the dominant process and detection of the fluorescent photons, probably indirectly by conversion to visible photons, is a better approach. For the IR and THz, these approaches cannot be used and the choice of detection method is much more limited. Photonic detectors are fast and efficient but are mainly limited to detecting in the near to far infrared, up to 24 µm with HgCdTe (though 200 µm is possible with Ge:Ga). Thermal detectors must be used at frequencies below a few THz and these tend to be slow. However, output at these extremely long wavelengths is not generally in the realm of free electron laser sources. Electro-optical techniques are probably a better solution for the very long wavelengths. It is thus inevitable that a range of diagnostics and detectors will be employed depending on the information required and the use to which it is to be put, for example:

164 8.13. Summary 149 Centroiding techniques for pulse by pulse beam position monitoring and feedback Invasive imaging for optimising the source and photon transport during commissioning Fast imaging arrays or wavefront sensors situated behind gas-phase experiments The use of beam splitters to separate a part of the beam for the more sophisticated diagnostics whilst the bulk of the beam is passed to the experiment are also likely to be a common feature of the photon transport systems due to the lack of truly noninvasive diagnostics. These splitters can be removed from the beam path for maximum throughput and/ or if the diagnostic is not required. Ideally, the beam splitters should divide the beam in amplitude so the diagnostic beam has the same beam profile as the measured beam (but at lower intensity). This should be straightforward in the IR and THz, but more challenging in the VUV and Soft Xray, where knife-edged mirrors that divide the wavefront are the easiest splitter to implement. Multilayer and slotted-mirror type beam splitters would be required to give amplitude beam division. Despite the considerable challenges that must be faced when making good spatial diagnostics for free electron laser beams, there are a wide range of techniques that can be employed. A judicious combination of techniques will allow the required information to be measured.

165 Beam cross-section diagnostics Summary Cross-section diagnostics measures the transverse intensity distribution of the beam. For both optimization, commissioning of experiments and instruments it is important to know where the beam is and how large it is. Measuring the focus size can be done either via ablation crater analysis (the size of a hole in a thin film), by the saturation of an ionization process in a gas or by using a wave-front sensor. Techniques developed for synchrotron sources may not be immediately used at free electron lasers or not at all. Examples of invasive techniques are: Direct imaging Wire grids Scanning wires, slits, knife-edges, pin-holes. All have the drawback that they are not single shot. Non-invasive techniques can be used while other experiments are running. Rest gas ionization Photo dissociation Synchrotron light Compton scattering A combination of techniques is needed, in practice, to diagnose the beam: Centroiding techniques for pulse by pulse beam position monitoring Invasive imaging for optimizing and commisioning Fast imaging devices or wavefront sensors situated behind gas-phase experiments. In the THz range photodiodes in the infrared or thermal detectors for longer wavelengths can be used. The latter only for averaging measurements. Beamsplitters offers the possibility to use invasive diagnostics in parallel to other experiments.

166 9. Pulse length, profile and jitter The material presented here in this chapter is partly adapted from Survey of diagnostics techniques for measuring the temporal properties of ultra-short photon pulses by M. A. Bowler, A. J. Gleeson and M. D. Roper. Iruvx WP7, 2009 by A. Lindblad. 9.1 Introduction In chapter 8 methods to discern the transverse extent of a photon-beam were discussed. Here we will review methods as to determine the length and profile of a pulse; the jitter between the pulses is also an important temporal parameter which is necessary to measure. A key measure of the performance of a freeelectron laser is the temporal properties of the photon-beam. The pulse length is required for the integral pulse power at the experiment; the pulse profile determines the quality of the pulse in terms of length and height of, and deviation from, the ideal pedestal shape in Figure 9.1 (i.e. deviation from the transform limit for the spectral content of the pulse) this is also related to the jitter, since if the pulse shape lacks repeating structure the centroid will be shifted on a pulse to pulse basis which is equivalent to a shift in relative occurrence times; the pulse jitter is a random fluctuation in the arrival time of a pulse, by necessity this needs to be correlated to another timing event. For δt t Figure 9.1: Ideal pulses have square profiles of length δt, occurring with frequency t 1 ; the pulse shape can be significantly deviated from the ideal square and occur within a frequency envelope defined by a time-jitter. pump-probe experiments this is obviously a crucial parameter. The profile and timing of a free electron laser pulse is certainly going to change on a pulse by pulse basis by an amount that will cause difficulty to at least some experiments. This is especially true for Sase operation because the pulses are generated from random noise. Therefore, there is a general need for the temporal diagnostics to be permanently on-line so that the profile and timing of every pulse can be measured. Such a diagnostic should obviously impose a negligible change on the pulse 151

167 Pulse length, profile and jitter being measured. The diagnostic thus needs to be either effectively transparent to the pulse, or at the very least interrupt only a small part and pass the major part of the pulse undisturbed to the experiment. Hence, there is a very demanding specification on an ideal pulse timing diagnostic apparatus: Measure all pulses at the repetition rate of the machine, i.e. in the khz and MHz regimes. Meaure the intensity profiles of the pulses with a temporal resolution of about 1 femtosecond carrying in mind that this resolution needs to be maintained over pulse lengths that can have a duration of hundreds of femtoseconds. Measure the arrival time of the pulse with a resolution in the femtosecond domain. Be transparent to the pulse, or sample a minuscule part of the pulse. Work in a spectral range from the VUV to the hard X-rays. A diagnostic tool that fulfils all of the above demands can not be found. Below we will survey the techniques available in the VUV and X-ray regime together with their limitations vis-à-vis the ideal outlined above. Many of the techniques that are currently being used and developed are based around cross-correlation with an external optical laser (a high-power IR Ti:Sapphire) and can give both pulse length and pulse jitter (relative to the optical laser). These techniques have started out as multi-shot measurements since they initially required scanning the IR pulse delay. But there is a lot of activity in developing the techniques for single-shot use and in improving the temporal resolution to the femtosecond level (see page 153). Electro-optical sampling also uses cross-correlation with an optical laser and is used mainly for electron bunch measurements but can also be used for measuring the lengths of THz pulses directly (see page 155). An alternative approach to pulse length measurement is auto-correlation, (see page 155). Simple intensity autocorrelation only gives a pulse length and not the profile. However, more sophisticated autocorrelation techniques have been developed in the visible and UV that can give the full pulse profile of pulses as short as a few femtoseconds. There is some possibility to extend these techniques to shorter wavelengths, though the limit here is not clear. Reflectivity modulation of a semiconductor by a free electron laser pulse has been used to give single shot measurements with a temporal resolution of 40 fs. Streak cameras are a well established technology for measuring pulses with picosecond lengths and they are being developed to achieve resolutions of a few hundred femtoseconds. Streak cameras can give single pulse measurements but only at limited repetition rates. Recently an elegant way of achieving few femtoseconds resolution in the timedomain was demonstrated at Flash by Tavella and co-workers. Their technique utilized the terahertz radiation generated in the undulator, which is then phasecorrelated to the X-ray pulse. The optical laser system of the facility can then be diagnosed together with he terahertz radiation without disturbing the X-ray pulse[230].

168 9.2. Cross-correlation techniques Cross-correlation techniques Cross-correlation techniques are currently the most widely used techniques at XUV wavelengths as they give pulse length and jitter information. A wide range of techniques based on the photo-ionisation of gases are being developed as they have the potential to be transparent to the photon beam. With a known reference laser pulse, cross-correlation between this and a X-ray pulse can be used to measure the relative jitter of the free electron laser pulse with respect to the laser pulse; in some circumstances said measurement can be used to estimate the length of the X-ray pulse. The pondermotive energy is given by U p(t) = e 2 E 2 a(t)cos(ω l t+φ) where E a is the amplitude of the laser field, ω l the laser frequency and φ the phase respectively[231]. In most experimental configurations, the presence of side-bands would be the dominant effect, but this can be suppressed by measuring the photo-electrons ejected in a direction perpendicular to the polarisation axis of the laser radiation, allowing the shift due to the ponderomotive energy to be observed. The intensity of the side-bands is proportional to magnitude of the photoelectron wave-vector[232] k = 1 2m( ωfel I p) Deconvolution of the side-band intensity as a function of delay is obviously not a single shot measurement. In order to determine the pulse length, the jitter between the two pulses and the X-ray pulse length must be small enough not to dominate the cross-correlation curve. Such a technique can be successfully applied to measure the pulse length of soft X-ray radiation generated by HHG where the jitter between the generating infrared pulse and the resulting HHG radiation is very small. In the case of radiation from a Sase free electron laser, the cross-correlation curve will most likely to be dominated by the jitter between the pulses, and can in fact be used to measure the distribution of the jitter. It may be possible that this technique could be used for seeded free electron lasers where the pulses will be more stable and the jitter smaller. An example of being able to estimate the time delay from a single shot measurement is given in Radcliffe et al. [232], where they used 13.8 nm pulses from Flash of about 20 fs long to ionise Xe and measured the sideband intensity in the presence of 120 fs pulses from a Ti:Sapphire laser. This case is favourable for the formation of side-bands due to the relatively large photo-electron wave-vector and up to four high energy side-bands were obtained. From theoretical simulations of the side-band intensity, the number of side-bands gives a measure of the laser field intensity during the FEL pulse, and hence the overlap of the pulses. In this experiment, a precision of better than 50 fs was achieved for the relative delay, but note that the sign of the relative delay cannot be obtained. The cross-correlation curve has a FWHM of about 600±50 fs, which is dominated by the jitter, and gives the FWHM of the jitter distribution of 590 fs. It should be possible to determine the sign of the jitter by using a chirped laser pulse (as also suggested in the XFEL TDR [89] for the Auger electron measurements mentioned below) but this idea has yet to be tested.

169 Pulse length, profile and jitter Ifthis work were tobe extendedtoveryshort X-rayspulses, thenit would be found thatthespectralwidthofthex-raypulsewouldsmear outtheside-bands. This canbe overcome by observing the photo-electron spectra for electrons ejected at right angles to the polarisation of the laser. In this case, as noted above, sideband formation is suppressed, and one can measure the red-shift in the energy of the electrons due to the ponderomotive force exerted by the laser field. This has been done successfully using an HHG source of SXR (90 ev) photons co-focussed with the generating 770 nm laser pulses [231]. A delay scan yielded an X-ray pulse width of the order of 2 fs FWHM; again, extending this to free electron lasers would require the relative jitter to be of a similar size to the pulse width. For a seeded free electron laser, this may be possible if the X-ray pulse timing is dictated by the laser seed. A significant disadvantage of these techniques is the need to co-propagate the FEL and IR pulses to a common focus. For on-line use, this requires a permanent extra focus to be included in the beam transport system, which is not always convenient or desirable. A perpendicular geometry would be more flexible - this has been used in the configuration adapted by Cunovic et al. [233] where they have used the second method of obtaining the pulse length by mapping the temporal co-ordinate of the pulse to spatial co-ordinates. In the proof of principle experiment, outlined below, 32 nm radiation from Flash was used to photo-ionize Kr in the presence of a pulse from a Ti:Sapphire laser. In principle this is a single shot technique, but for this first experiment the data were too noisy and had to be summed over several shots. The unfocussed free electron laser beam, of FWHM 7 mm, entered the experimental chamber containing low pressure Kr through an aperture 500 µm wide. The FEL beam was crossed at right angles with a focussed beam from a short pulse Ti:Sapphire laser. The widthof thex-raybeam inthechamber is equivalentto1.7 ps, muchlonger than the laser pulse length of 150 fs, and one has to assume that the intensity variation over the width of the central part of the X-ray beam accepted by the aperture is not great. Hence as the laser beam traverses the pulse, the intensity of the side bands in the photo-electron spectra will map out the intensity of the free electron laser beam as a function of time. The interaction region is imaged by an electron lens system containing a retarding grid which only allows the passage of electrons whose energy has been upshifted by the laser beam. A line will be formed in the 2D electron detector, corresponding to the different emission time of electrons, which in turn yields information about the intensity variation of the X-ray pulse. In order to be able to use this technique for single shot measurement, the signal would need to be increased by about two orders of magnitude from that obtained in [233]. This could be achieved by increasing the target gas density in conjunction with the free electron laser pulse energy, but there is a limit to the increase before space charge effects become important. In the measurement reported in [233] the total pulse energy was 2-15 µj before the entrance aperture to the chamber. If photoelectrons with higher energies were produced, the signal would also be increased as the side-band production increases with increasing energy as noted above. For use as an online diagnostic, the experimental set-up would need to be redesigned without the entrance aperture as this will disrupt the beam through edge diffraction effects. There does not seem to be an intrinsic need for aperturing the beam on entry to the experimental chamber. An alternative to detecting electrons from direct ionisation is to use electrons generated by Auger decay of an inner shell hole. The energy of the electrons can also be modified by the presence of a strong laser field, creating side-bands. An advantage

170 9.3. Electro-optic techniques 155 of using Auger electrons is that their energy spectrum is fixed and does not depend on the energy width of the exciting X-ray pulse, and the Auger decay times are short compared with the typical duration of free electron laser pulses. If the laser pulse were chirped so that the side bands are broadened, then some measure of the X-ray pulse length can be obtained as well as the jitter e.g. in the European X-Fel technical design report it is said that a linear chirp of 1 ev in a laser pulse of width of 300 fs would lead to a broadening of 0.25 ev of the sideband for an 80 fs X-ray pulse[89]. 9.3 Electro-optic techniques The electro-optic technique uses birefringence induced in an electro-optic crystal by the electric field of THz pulses or electron pulses. The amount of birefringence depends on the electric field and is probed by monitoring the change of polarization of a short optical laser pulse. The limitation to the THz regime for direct photon pulse measurements is due the availability of crystals with a suitable electro-optic response function. For electron bunches, the electro-optic detection method makes use of the fact that the local electric field of a highly relativistic electron bunch moving in a straight line is almost entirely concentrated perpendicular to its direction of motion. The limitations to temporal resolution are discussed in Berden et al. [234] and include the EO material selection, crystal thickness, wavelength dependence and beam probe displacement. Philips et al. [235] have demonstrated measurement of electron bunch lengths of 118 fs FWHM using a 35 fs probe laser at the Flash facility. The method can be used to monitor the relative timing of an external laser with the electron bunch, and using this information to improve the resolution of crosscorrelation data. A proof-of-principle experiment has been carried out at Flash by Azima et al. [236] where they have measured the relative arrival time of the electron bunchand thelaser pulseat theentrance tothefree electron laser as well as measuring the side-band formation in the photo-electron spectra from Xe in the presence of the laser field. A plot of side-band intensity against the delay between the laser and the free electron laser has a rms width of 410 fs which is mainly due to jitter in the free electron laser pulse. When the electro-optical data are used to correct for the jitter, the rms width of the curve is reduced to 100 fs. They call this technique TEO timing by electro-optic sampling. 9.4 Autocorrelation techniques The advent of ultra-short (< 100 fs) optical pulses from lasers has driven a significant amount of development into measuring the temporal profile of such pulses. Since there are no detectors with a fast enough temporal response to directly measure the intensity profile of pulses with lengths shorter than a few hundred femtoseconds, the approach taken has been to probe the pulse with another short photon pulse. Of course, this leads to the immediate problem of producing a suitably short probe pulse. In autocorrelation measurements, the probe is created by splitting the original pulse into two (or in some cases more) parts that are each a replica of the original and one part is used to probe the other. Since the pulse being measured is its own reference, autocorrelation is thus used to study shape of pulses rather than timing jitter (though

171 Pulse length, profile and jitter a technique such as Spider (q.v.) can be used to derive the time correlation function of a train of pulses). Intensity autocorrelation When optical lasers producing ultra-short pulses were first developed, the instrument that was most likely to be employed to measure the pulses was a simple intensity autocorrelator. This was not because the autocorrelator was especially good at this job, but rather because autocorrelation was about the only technique that could be used to measure pulses with durations below 100 fs since the fastest alternative instruments, such as streak cameras, were limited to temporal resolutions of several hundred femtoseconds at best and more generally picoseconds. A second-order intensity autocorrelator is relatively easy to produce. The key components are a beam splitter to divide the beam into two (in principle identical) replicas of the input pulse, a means of altering the path length travelled by one of the replicas so as to vary the relative temporal delay between them in precise increments, and a means of recombining them so that they overlap spatially. There must also be some means of measuring the temporal overlap as a function of the delay. Typically, this is achieved by spatially overlapping the two beams in some instantaneouslyresponding, non-linear medium so that a signal is produced that is proportional to the overlap intensity I(t)I(t τ). A detector records the intensity of this signal, after separating it by some means from the transmitted replica pulses. Since the detector will inevitably have a response that is very slow compared with the ultra-short pulse length, it automatically performs a time integration of the signal. The signal as afunction of the relative temporal delay τ is thus the autocorrelation function of the temporal intensity profile of the original pulse. A(τ) = dti(t)i(t τ) (9.1) Because the phase information is lost in this measurement, the Fourier transform of the autocorrelation function is just the power spectrum of the original pulse. Autocorrelation thus gives the pulse length but not the pulse profile. Indeed, one has to assume a pulse profile even to extract a pulse length. The autocorrelation also tends to smear out any structure (such as satellite pulses) and in general any number of pulse shapes can give the same autocorrelation function. Thus, changing the assumed pulse profile can give significant changes to the extracted pulse length. In general, autocorrelation measurements are prone to systematic errors (for example caused by misalignment) since the only constraints on the trace are that it should have a maximum at zero relative delay, be zero at delays much larger than the pulse width, and be symmetric with respect to zero delay. In fact, the autocorrelation of complicated pulses always tends to a sharp spike sitting on a smooth pedestal 1. In the visible and UV regions the non-linear medium is usually a second harmonic generation (SHG) crystal which has a second-order non-linearity in its electric susceptibility and produces light at twice the frequency of the input light and with and intensity that is proportional to the product of the intensities of the two input pulses. 1 See, for instance, autocorrelation.htm

172 9.4. Autocorrelation techniques 157 The SHG signal thus rises quadratically with intensity of the original pulse. The SHG signal is generally detected through a spectrometer to isolate it from the fundamental light. The short wavelength limit for SHG production is determined by the transmission of the non-linear crystals. The crystal must be transparent at half the wavelength of the incident light for the SHG signal to be detectable. Petrov et al. [237] have demonstrated autocorrelation measurements to 250 nm (5 ev) using SrB 4O 7 (SBO), which is transparent to 125 nm. A further limitation of SHG is the finite bandwidth over which the crystal will function. It is important that the SHG signal be phasematched to the original pulses since otherwise there can be a spectral filtering effect that can significantly distort the autocorrelation function[238]. For very short pulses, this means the crystals have to be very thin. The crystals also need to be thin to limit dispersion that will change the pulse being measured. To overcome some of the limitations of SHG from crystals, Dai et al. [239] have demonstrated using SHG from metal surfaces. This will work from the far-infrared to the plasma frequency of the metal being used (e.g. about 10 ev for gold). Autocorrelation measurements have also been demonstrated using two-photon absorption inside a semiconductor-based photon detector [240]. The advantage here is that the non-linear medium and detector are combined and so the experimental set-up is simplified. However, a detector with a bandgap that is between the photon energy and twice the photon energy is required and so different materials will be required for different wavelengths. Extending the technique to the XUV is also unlikely to be possible. Worth noting is that Liu et al. [241, 242] have shown that autocorrelation can give the full pulse profile if the pulse is split into three beams. In this triple-optical autocorrelation for direct pulse shape measurement (Toad), the delay between all the pulses must be varied and the beams are focused into a third-harmonic generation (THG) crystal. Thus, although the technique requires only time-domain measurements, the extension to wavelengths shorter than the optical will be significantly more challenging than extending two-beam autocorrelation. Making a two-beam autocorrelator that works at VUV and shorter wavelengths is challenging but not impossible. A successful instrument has been built for Flash by BESSY[137] and a simpler system has been made by the University of Hamburg[243] (cross-correlators between X-ray and optical pulses have also been achieved[244]). A significant challenge is achieving the initial beam splitting. Amplitude division whilst preserving the quality of the original pulse-front is probably impossible at VUV to SXR wavelengths. In the BESSY instrument, the beam is divided spatially (i.e. wavefront division) using a knife-edged mirror and one must thus assume that the temporal profile of the beam is the same over the beam cross-section. Diffraction effects from the wavefront division are a concern but are said to be minor in the focal plane[137]. A second knife-edged mirror after the delay line is used to overlap the two beams by angling one of them slightly with respect to the other. The delay of one beam with respect to the other is achieved through an optical delay line using translating mirrors. The relative delay range available is -3/+25 ps and is limited by the overall mechanical design and the size of the delay line mirrors, since the beam moves along these as the delay is varied. The mechanical specifications (e.g. mirror quality, angular precision, translation accuracy and overall stability) are very challenging for short wavelength operation. The shortest wavelength that can be measured is determined by the reflectivity of the mirrors since there are four mirrors per beam path. Making the instrument

173 Pulse length, profile and jitter relatively compact prevents the use of extremely grazing angles of incidence; the fixed path arm uses 3 grazing whilst the variable path arm uses 6 grazing and therefore the intensity of the two pulses is not the same. With carbon coatings, good reflectivity is possible from 30 to 200 ev. Different coatings (e.g. nickel) could be used to extend this range to higher photon energies. A mechanically much simpler instrument has been developed at Synchrotron Soleil for use as a VUV Fourier Transform interferometer[245]. This also uses wavefront division to split the beam but in this design two roof-mirrors are used so that the optical assembly for each beam path is monolithic. However, this means there are two 90 deflections in each path and so the longest operating wavelength is in the VUV. Autocorrelation measurements on pulses from an HHG source using another splitmirror approach have been reported by Tzallas et al. [246]. In their work, a focusing wavefront divider is made by splitting a spherical mirror into two halves. A translation of one half-mirror along the surface normal gives a relative delay between the parts of the beam reflected from each half whilst the mirror also focuses the split beams to a common position in the detection medium. Two-photon ionized He gas is used as the non-linear medium and the He ion yield measured by a time-of-flight spectrometer. Stigmatic imaging with a spherical mirror requires the system to operate at nearnormal incidence. The upper photon energy is thus limited if a simple metallic coating is used. Multilayer coatings could be used to allow operation at shorter wavelengths, though the operating bandwidth would be quite narrow for a given multilayer. The final challenge in the XUV autocorrelator is a means of measuring the autocorrelation signal. In the measurements reported in [247] using the BESSY/Flash instrument, the temporal coherence was deduced from the fringe visibility of the spatial interference pattern as a function of relative delay. In these measurements, the mutual coherence function, which is closely related to the auto-correlation function, is measured. The mutual coherence function is defined by[248]: Γ 12(τ) = u 1(t+τ)u 2(t)dt where u i:s are the field values at the two slits. An alternative detection technique that gives a second-order signal like SHG is two-photon ionisation [ ]. The strength of the two-photon ionisation signal produced when one photon is contributed from each beam is clearly proportional the temporal intensity overlap of the two beams. The wavelength range over which such schemes will work depends on the ionisation potential of the gas. For first ionisation potentials, this ranges from ev for helium to 4.5 to 9 ev for toluene. Two-photon single-ionisation above 24 ev is unlikely to be practical due to the need to discriminate against single-photon ionisation events which will give an increasingly strong background of first order signal as the photon energy increases. Nakajima and Nikolopoulos [252, 253] have made a theoretical study of using twophoton doubleionisation of helium, which would cover the range 40 to 54 ev. This scheme could be extended to shorter wavelengths by using heavier elements (Li, Be, B etc) and their higher ionisation stages [254]. Nevertheless, continuous coverage of a wide photon energy range will not be possible with ionisation based techniques. In summary, autocorrelation is a feasible pulse length measuring technique in the VUV and XUV, though only the pulse length is measured and the technique is usually

174 9.4. Autocorrelation techniques 159 multi-shot, though adaption to single shot should be possible (see for example the description of single shot Frog in section 3.2.1). The pulse length extraction is also not particularly robust due to the need to assume a pulse profile and the susceptibility to systematic errors. Autocorrelators do not give information of pulse timing (jitter). The mechanical demands of the instrument are high but can be surmounted. Finding a suitable non-linear detection technique to measure the auto-correlation signal is even more demanding and unlikely to give continuous wavelength coverage. Autocorrelators are invasive in that they modify the beam passing through them, but they can be designed so that they can be inserted into or removed from the beam path without affecting the operation of downstream optical elements. Autocorrelation techniques for complete pulse characterization Complete characterisation of the pulse intensity profile requires the measurement of both the spectral and phase information so that the electric field can be computed as a function of time. There are three distinct approaches to this that have been used in the visible and near-visible spectral regions, viz. spectrographic, tomographic and interferometric. In all cases, filtering of the pulses is required. It is the practical realization of some of these filters that make extending the techniques to shorter wavelengths so difficult. The two classes of filter that are important in current pulse length analysis techniques are time-stationary filters (in which the time of incidence of the input pulse does not affect the output) and frequency stationary filters (where the output is not changed by arbitrary shifts in frequency of the input). Frequency-stationary filters are time non-stationary. These filters can be further classified as amplitude-only or phase-only i.e. they modulate only the amplitude or only the phase of the input. Finally, the filter may have a linear or non-linear response (with frequency or time as appropriate). A non-dispersive delay line is a simple filter that adds the same time delay to all the frequency components in the pulse. A delay line is thus a linear spectral phase modulator, since a linear (with frequency) shift in the spectral phase is equivalent to a time shift. A spectrometer is an example of spectral amplitude filter. These are both time-stationary filters. Both these types of filter are relatively easy to implement across a wide range of wavelengths, though some thought must be given to the frequency response function (e.g. bandwidth, resolution) of practical devices. The simplest time-non-stationary filters are a time-gate and a frequency shifter. A time gate is a time-nonstationary amplitude filter and is used to take time slices of a pulse. A linear temporal phase modulator gives a linear variation of phase with time, which is the same as a translation or shift of the frequency axis, and thus gives a spectral shift or shear to the pulse. Time-non-stationary filters are more difficult to implement, especially for ultra-short pulses. Spectrographic techniques are probably the most widely used pulse profiling techniques. They work by measuring a two-dimensional representation of the one- dimensional field, i.e. they are phase-space measurements. This is the critical step since it allows a generally unambiguous retrieval of the phase information in a way that is not possible with a one-dimensional measurement. The only ambiguities are the absolute phase and absolute arrival time.

175 Pulse length, profile and jitter Frequency Resolved Optical Gating (FROG) An example of a spectrographic technique is Frog or Frequency-Resolved Optical Gating. This uses a sequential spectral filter and a time-gate, in either order, followed by an intensity detector. Depending on the order of the filters, the recorded signal is a measure either of the spectrum of a series of time slices or a measure of the time of arrival of a series of spectral slices. The technique is thus operating in the timefrequency domain (phase-space) and is both temporally and spectrally resolved. The technique is not limited to just autocorrelation measurements (i.e. it will work with external gate pulses), but in all practical applications the pulse is used to analyse itself in manner that is an extension of intensity autocorrelation. input-pulse Beam-splitter Probe, E(t) Non-linear medium Gate, E(t τ) τ Spectrometer Figure 9.2: The basic layout of a Frog experiment; τ marks the variable time-delay between the probe and gate pulses. In the first description of Frog by Kane and Trebino [255], a replica of the pulse to be measured is used as the time gate. Thus, the initial pulse is split into two pulses (gate g(t) and probe E(t)) and the gate pulse has a variable temporal delay applied to it see Figure 9.2. The two pulses are focused and overlapped spatially in an instantaneous non-linear medium (in this case, self-diffraction due to the electronic Kerr effect in glass is the non-linear process). The diffracted light is then passed to a spectrometer and a complete spectrum recorded, i.e. the spectrogram: 2 S E(ω,τ) = E(t)g(t τ)e iωt dt The spectrogram is recorded for a range of relative delays of the probe and gate that is sufficiently wide to give zero temporal overlap of the gate as it is shifted from before to after the probe pulse. Frog is thus essentially a spectrally resolved autocorrelation (as seen from the similarity of the equation above and Equation 9.1).

176 9.4. Autocorrelation techniques 161 If self-diffraction is used as the non-linear effect the signal pulse is given by E S(t,τ) [E(t)] 2 E (t τ), which yields I frog(ω,τ) = [E(t)] 2 E (t τ)e iωt dt It does not matter (i.e. it does not degrade the temporal resolution) that the gate has the same time-width as thepulse beingmeasured, though ashorter pulse would be preferable. However, the gate pulse should not be too short as an infinitely short gate yields only intensity information, (whilst a CW gate would yield only the spectrum). The use of the pulse to gate itself does however complicate the inversion process since one cannot input any knowledge of the gate pulse into the analysis. Anotherpointtonoteis that, ifthefrog measurement recordsan equalnumbern temporal slices and spectral slices, then N 2 measurements are made in total. But the analysis will yield only N intensity and N phase values, i.e. 2N derived values. There is thus a lot of data redundancy in the measurement, though this does contribute to making the data inversion give unambiguous results. In fact, the unambiguous nature of Frog is a one of its most important features (and is quite contrary to simple autocorrelation). Although the technique as described above is multi-shot due to the need to scan the time delay, the technique can be adapted for single shot measurements [255, 256]. This is achieved by focusing the pulses to lines in a common plane and crossing the lines at an angle. The position along either of the line foci is now a linear function of relative delay between the two pulses. If the line foci are orthogonal to the dispersion plane of the spectrometer, then an imaging spectrometer with 2-D detector will be able to record spectrum in one plane simultaneously with delay in the orthogonal plane. Thus the spectrum can be recorded as a function of delay and frequency in one shot. The length of the line foci and relative angle will determine the range of delays that is recorded, which must be sufficient to give zero overlap of the pulses at each end for the Frog measurement to be successful. The size of the delay step is determined by the spatial resolution of the spectrometer detector. The experimental configuration as described in [255] is quite simple since both the delay line and spectrometer are straightforward. Though the technique has the disadvantage of being invasive, it would seem to be extensible to wavelengths shorter than the visible and UV. The key limitations are the need to find a suitable beam splitter, and in particular the need for a non-linear process to mix the two beams and give a signal proportional to the combined intensity. As with autocorrelation, two-photon ionisation would be possible non-linear process, at least at lower photon energies. Norin et al. [257] used two-photo ionisation from Xenon to study the chirp of the 5th harmonic (15.5 ev) radiation produced by HHG in a method that is described as similar to Frog. The HHG is produced from xenon from frequency doubled IR radiation (Ti:Sapph)whilsttheprobepulseissplitofffrom themainirbeam. Amagnetic bottle spectrometer is used to collect the photoelectron spectrum as a function of probe beam delay. The intensity of the sideband corresponding to the absorption of one 15.5 ev and one IR photon is measured as a function of relative delay. This allowed the extraction of the linear chirp in the HHG pulse and its length, but not the actual pulse shape. 2

177 Pulse length, profile and jitter Sekikawa et al. [258] were able to fully characterize the 5th harmonic pulse of a Ti:Sapphire laser using twophoton ionisation in Frog (TPI Frog). This is because they show that the TPI spectrum is equivalent to the spectrally resolved SHG used in conventional Frog. They also claim the technique is scaleable to XUV and SXR pulses through the detection of two-photon absorption from the K-shell to a free state in boron. Frog is probably the most widely used technique for measuring the pulse profile of ultra-short optical pulses. There are a number of different geometries for measuring Frog as described by Trebino et al. [256]. They are summarized briefly below. Polarization-gate FROG (PG FROG) The basic layout of PG Frog is shown in Figure 9.3. The input pulse is split into two equal replicas. One replica (the probe) is sent through crossed polarisers and the other (the gate) through a half-wave plate to give a ±45 linear polarisation with respect to the first. The two replicas are then spatially overlapped in a material with a fast third-order susceptibility such as fused silica. The gate pulse induces birefringence in the silica through the electronic Kerr effect and so the silica acts as a wave plate and rotates the polarisation of the probe beam slightly which allows some light to be transmitted through a polarisation analyser. Because this occurs only when the gate pulse is present in the silica, the transmitted intensity as a function of relative delay is an autocorrelation measurement of the pulse. Spectrally resolving the transmitted light thus gives the Frog measurement. input-pulse Beam-splitter Polariser Probe, E(t) Fused Silica λ 2 -plate Gate, E(t τ) Filter τ Photodetector Polariser Figure 9.3: The basic layout of PG Frog. The biggest advantage of PG Frog is that there are no ambiguities on inversion so that the pulse characterisation is complete in all cases. Another advantage is that the non-linear process is automatically phase matched so alignment is easy. The main disadvantage is that the polarisers must be of high quality; an extinction coefficient

178 9.4. Autocorrelation techniques 163 of better than 10 5 is recommended. This makes the polarisers expensive and more importantly fairly thick, which can introduce dispersion to the pulse and so change the pulse being measured, a particular problem for the shortest of pulses. Also, because a third-order non-linearity is used, the sensitivity of the technique is reduced. The fact that PG Frog polarises the beam is the biggest impediment to extending the technique to wavelengths shorter than the UV. Polarisers and half-wave plates with the required performance are impossible to make for the XUV and X-ray regimes. Achieving a large phase shift in this spectral range is only possible using anomalous dispersion near an absorption edge and so polarisers would be limited to narrow spectral ranges. Even then, absorption is strong and the performance would not meet the exacting requirements for PG Frog. Finally, a third-order non-linear process would be needed to extract the Frog signal. There seems little possibility of extending PG FROG to wavelengths shorter than 250 nm (5 ev). Self-diffraction FROG (SD FROG) Self-diffraction Frog is the technique as originally described by Kane and Trebino[255] see Figure 9.2. As with PG Frog, the electronic Kerr effect is used as a third-order non-linear process. In SD Frog however, the intensity oscillations of the interfering beams induce a refractive-index grating in the silica and this diffracts each of the beams in a different direction. The first order diffraction of one of the beams is spectrally resolved to make the Frog measurement. The advantage of SD Frog therefore, is that the beams can have the same polarisation and polarisers are not required. Application to beyond the UV is therefore potentially more straightforward than with PG Frog. However, a third-order non-linear process is still required. Self-diffraction is not actually ideal even in the visible since it is not a phase-matched process. The non-linear medium must therefore be kept thin (< 200 µm) and the angle between the beams small (< 2 ) in order to minimize the phase mismatch. Since the phase-mismatch is wavelength dependent, the problem is of particular concern when measuring the shortest pulses. SD Frog is thus best suited to pulses of length > 100 fs. Transient-grating FROG (TG FROG) Transient grating Frog overcomes the phase-matching problem of SD Frog by splitting the beam into three parts. Two of the beams are overlapped in space and with fixed (ideally zero) relative delay in the optical Kerr medium to create the refractive index grating. The third pulse is diffracted from the induced grating and the diffracted beam spectrally resolved as the delay relative to the other two pulses is varied. TG Frog thus has the phase-matching of PG Frog without the need for polarisers. Operation into the deep UV is thus possible. Operation at shorter wavelengths still requires an equivalent third-order non-linear process. Producing three beams by wavefront division will also be quite challenging. Second-harmonic-generation FROG (SHG FROG) SHG Frog differs from the three techniques described above by using a secondorder non-linear process. This gives a significant advantage in terms of sensitivity

179 Pulse length, profile and jitter as second-order processes are inherently more efficient than third-order ones. The probe and gate beams are overlapped spatially in an SHG crystal and a signal at twice their frequency is produced with intensity that is proportional to the product of the individual intensities. The SHG signal is spectrally resolved as function of the relative pulse delay. Since each frequency in the original pulse is up-converted by the crystal, the SHG spectrum is directly correlated to the original pulse spectrum. It is thus important to ensure that the crystal works over a wide enough bandwidth to up-convert the entire bandwidth of the original pulse. Failure to record the entire pulse bandwidth will prevent the Frog inversion from working. Since the crystal bandwidth is inversely proportional to crystal thickness, short pulses require very thin crystals, e.g. for measuring 100 fs pulse at 800 nm, the maximum crystal thickness should be 300 µm for KDP (potassium dihydrogen phosphate) and 100 µm for BBO (β-barium borate). Of course, operation at VUV to X-ray wavelengths will require the crystal to be replaced by another non-linear medium in any case. The options for this are discussed in Section 9.4. SHG Frog has the most potential to be extended to operation at wavelengths shorter than the visible/uv part of the spectrum. A final point that should be noted with SHG Frog is that it is ambiguous with respect to the direction of time since SHG Frog traces are always symmetric with delay. Thus it is not possible to tell if a pulse with a satellite has the satellite before or after the main pulse. Third-harmonic-generation FROG (THG FROG) THG Frog is very similar to SHG Frog except that third-harmonic generation is used as the non-linear process. The advantage of this is that the third-order nonlinear process removes the time-direction ambiguity inherent in SHG Frog (except in the particular case of a Gaussian pulse profile with a purely linear chirp). A potentially important variation of THG Frog is where surface third-harmonic generation is used (STHG)[259]. Not only is STHG a relatively efficient process (compared to other third-order processes) but by interacting only at the surface the phase-matching bandwidth is very large. This is of particular value when measuring pulses of only a few fs in duration which require SHG crystals of only a few tens of µm in thickness. Table 9.1: Different FROG Schemes Type E sig(t,τ) SHG E(t)E(t τ) Pol. Gate E(t) E(t τ) 2 Self. diff. E(t) 2 E(t τ) THG E(t) 2 E(t τ)

180 9.5. SPIDER Spectral Phase Interferometry for Direct Electric-field Reconstruction An example of an interferometric pulse profiling technique is Spectral Phase Interferometry for Direct Electric-field Reconstruction or Spider[260]. The concept of the technique is to have a linear spectral phase filter in parallel with a linear temporal phase filter. These are followed by a spectral amplitude filter before an intensity detector. The input pulse is divided into two replicas and one replica passes through each of the phase filters before being recombined and passing through the amplitude filter before reaching the detector. If the linear temporal phase filter is adjusted from null, then one of the replicas is given a spectral shift relative to the other. On recombining the pulses they interfere spectrally (beat) and the apparatus becomes a spectral shearing interferometer. The spectral interferogram is recorded on the detector as the spectral amplitude filter is tuned over the bandwidth of the pulse, i.e. the spectrometer resolves the frequency mixed signal. This information together with knowledge of the applied spectral shear is sufficient to reconstruct the electric field of the pulse through direct inversion. The linear spectral phase filter can be used to introduce a temporal delay between the two replica pulses. This additional degree of freedom allows the correlation of pulses in a train of non-identical pulses to be calculated[260], but otherwise can, in principle, be set to an arbitrary value. In practice however, the time delay is important as it adds an extra phase to the frequency spectrum of one pulse replica relative to the other and this is used to ensure several fringes per independent frequency component. This makes an unambiguous reading of the spectral phases from the spectral interferogram possible (because the ac and dc terms of the Fourier transform are well separated) and thus ensures that the inversion can successfully recover the electric field. In terms of the practical implementation of Spider, the all-important temporal phase filter is the hardest to implement. The spectral phase filter is just a nondispersive delay line and the spectral amplitude filter is a spectrometer with sufficient bandwidth and resolution to record the pulse bandwidth and resolve the spectral interference fringes. Because the final measurement is spectral, Spider can be applied to single pulses (assuming there is enough signal to noise to extract the interferogram accurately). Returning to the temporal phase filter, it is necessary to achieve an appropriate amount of spectral shear. In[260], the use of electro-optic phase modulator(eopm) is considered to give insufficient spectral shear. Therefore, a method using up-conversion of the two replica pulses is described. A broadband non-linear material is required and each of the replica pulses is up-converted through mixing with a quasi-continuous wave of different centre frequency. The up-converted pulses are thus centred at a different frequency and the required spectral shift is achieved. In [261], up-conversion is again used, but the two replica pulses are temporally displaced and mixed with a strongly chirped pulse in the non-linear material. The temporal delay results in mixing with a different frequency range of the chirped pulse and again the spectral shift is achieved. The fringe separation in the interferogram is now inversely proportional to the temporal separation. Note that the spectral phase filter (delay line) of the original concept is now linked tothe role of the temporal phase filter and cannot thus be adjusted independently. Indeed, the temporal delay and spectral shear are linked through the chirp of the pulse used to drive the upconversion.

181 Pulse length, profile and jitter The spectral and temporal shifts must be chosen to suit the length of the input pulse and the spectrometer resolution, and this places constraints on the length of pulses that can be measured. The most important factor is to ensure that the delay is small enough to ensure the fringes can be resolved whilst not so small that the inversion process cannot unambiguously determine the phases. It is thus apparent that extending the Spider technique to shorter (XUV, SXR) wavelengths is dependent on a satisfactory method of achieving the required spectral shear. (We will assume that splitting the beam by means of a knife-edged mirror will prove to be satisfactory since true amplitude division is likely to be impossible). The use of non-linear materials is prevented by strong absorption. Another approach that has been suggested for the XUV is to use two-colour, two-photon atomic ionisation to transfer the frequency spectrum of the photon to the photoelectron energy spectrum[262]. This however brings additional problems since an electron spectrometer is now needed to resolve the photoelectron spectrum, which contains the interferogram. Matching the fringe spacing and interferogram bandwidth to the performance of available electron spectrometers will place limits on the range of pulses that can be analysed. For example, an electron spectrometer with a challenging high resolution of 1 mev can only probe a temporal range of 660 fs from the uncertainty relation. In [263], Smirnova et al. describe an approach for measuring fast processes with photon pulses that are long relative to the process. The approach is to spectrally shear, by dressing with a weak IR field, a correlated two-electron spectrum of photoionisation and Auger electrons created when an XUV pulse interacts with the sample. The spectrally shifted electron spectrum interferes with the original spectrum and the phase is mapped to an amplitude modulation in the spectral intensity and thus can be measured. The technique is thus Spider with electrons. The relevance here is that there is no reason in principal why the same approach cannot be used to measure the field of the X-ray pulse since the spectral content of the pulse will be encoded into the electron spectrum. The key requirement for the technique is that very tight synchronisation (sub-fs) between the XUV pulse profile and the phase of the IR pulse is required. The technique will also be flux intensive since the correlated two-electron spectrum must be measured, but given sufficient photons per pulse a single shot measurement can be made. In summary, the extension of optical techniques like Frog and Spider to the XUV and shorter wavelengths looks challenging. Progress in this area has no doubt been limited by the lack of sources giving ultra-short pulses in this spectral range, and one might therefore reasonably expect more progress in the future. The advantage of these techniques is that they give the exact pulse profile by calculating the electric field and thus provide complete information. But the techniques are also invasive. The input pulse must be divided and manipulated and as such they are not the obvious choice for a pulse-by pulse diagnostic even when single pulse characterisation is possible. 9.6 Reflectivity modulation Maltezopoulos et al. [264] describe how the free electron laser beam incident at a glancing angle on the surface of a GaAs substrate modifies the reflectivity of the GaAs to visible light in proportion to the intensity of the X-rays. Thus, a visible laser (frequency doubled from near-infrared 800 nm) is used to simultaneously illuminate the area of the GaAs illuminated by the X-ray pulse and the reflected visible light

182 9.7. Streak cameras 167 imaged onto a CCD. The intensity distribution and position of the visible image give the free electron laser pulse profile and timing. The technique is inherently pulse-by-pulse, and does not use co-propagation, but is not transparent. Also, the visible light must overlap the entire area of illumination from the free electron laser and so some sort of focus of the X-rays may be required. The technique is thus not an on-line diagnostic but could be used for checking the beam at the experimental end-station (where there is likely to be a focus anyway). Alternatively, since this technique does not require such high beam intensities as the cross-correlation methods described in Section 9.3, it may be possible to split off a small part of the FEL beam and use that to monitor the arrival time of the pulse. In any case, the temporal resolution is limited by the length of the visible pulse and the space-to-time correlation of the visible imaging system. The work presented gives a resolution of about 40 fs rms. Gahl et al. [244] suggest that the key limitation to the temporal resolution is the visible probe pulse length, of the order fs in this example. They also suggest that the time required for the GaAs surface to recover to its original level of reflectivity could be of the order of hundreds of picoseconds, but this would only be a limit in multi-shot measurements at repetition rates in the GHz region. A further consideration is the potential for radiation damage of the GaAs surface. Maltezopoulos et al. [264] used an optimised beam fluence of 13 ± 5 mj/cm 2 rms for their measurements, commenting that permanent damage was observed at an unstated higher fluence, thus requiring the GaAs surface to be renewed. Conversely, measurements at a lower average fluence led to very weak contrast in the images, making temporal determination unreliable. A related technique has been recently proposed by Krejcik [265]. In his scheme, the X-rays strike a magnetised film and cause a change in the magnetisation which is probed using MOKE (Magneto- Optical Kerr Effect). An IR laser illuminates the magnetic film and undergoes a small relative polarisation rotation ( 1 ) in the part that is reflected from the area the X-rays illuminated. The polarisation of the reflected IR beam is analysed and mapped over the beam profile. Thus, a time to space mapping of the arrival time of the X-ray pulse is achieved. The advantage of the MOKE analysis is that the magnetisation change is extremely rapid and so there is no issue with the response time of the process reducing the temporal resolution achieved. The disadvantage is that the magnetic material needs a resonance at a magnetically active orbital at the X-ray wavelength of interest. Thus the technique is not applicable to arbitrary wavelengths. 9.7 Streak cameras Streak cameras work on similar principles to oscilloscopes and cathode-ray tubes and work by mapping time to a spatial coordinate in the detector. The incident photon beam is focused onto a slit and then passes through a photocathode. The photoemitted electrons are drawn between two parallel plates that are also parallel to the slit. A high-speed sweep voltage, synchronised to the pulse arrival, is applied across the plates. This gives an angular deflection of the electrons that is directly related to their time of arrival and thus to the duration of the pulse. The deflected electrons are then multiplied with a micro-channel plate (MCP) before impacting on a phosphor screen. The streak pattern on the screen is imaged by a CCD or other suitable

183 Pulse length, profile and jitter detector, using a light intensifier tube if required. The advantages of streak cameras are the applicability across a wide wavelength range (X-rays to near-ir, although not with a single camera), single-shot time resolution in the picosecond range for off-theshelf systems, and the ability to work at high repetition rate, albeit with reduced temporal resolution. They can also provide information on intensity and position in addition to the temporal information in a single measurement. Historically, the resolution of streak cameras has been restricted to several picoseconds in single-shot mode. In multiple-shot averaging systems, the use of a synchronised sine-wave sweep voltage adversely affects temporal resolution by making these systems highly susceptible to source jitter. However, there have been recent improvements in off the shelf systems and the fastest commercially available streak cameras claim a time resolution of <300 fs for single-shot measurements and 500 fs for multiple shots [266] although it is unclear at what wavelengths these speeds are attainable. Although the multi-shot system can operate at MHz repetition rates, the single-shot system is limited to operating below 100 Hz due to limited sweep voltage cycling. Several fundamental limitations of the systems are now being addressed. In order to limit the affects of source arrival jitter, photoconductive switches are being utilised in conjunction with a beamsplitter to accurately trigger the voltage sweep. Bonté et al. [267] employ photoswitches supplied by Fastlite[268], whilst the camera under development at the Advanced Light Source (ALS) uses in-house photoconductive GaAs switches. Feng et al. [269] at the ALS state that one of the most significant fundamental limitations to the temporal resolution is set by the energy spread in the electrons from the photocathode. By adding a four-dipole, timeof- flight dispersion corrector they have simulated 50 fs resolution. The current best temporal resolution achieved by the ALS system is 233 fs using 266 nm UV light [269]. Researchers led by J. Larsson at MAX-lab are developing ultrafast streak camera systems where the standard CCD detector is replaced with a smart camera [270]. This combines the CCD detector with an on-chip processor that undertakes signal processing prior to readout, reducing the amount of data output and thereby improving the potential readout speed. The development system is currently capable of 4000 frames/second and has demonstrated a resolution of better than 300 fs at X-ray wavelengths in multi-shot experiments. In a separate development at the Thomas Jefferson National Accelerator Facility (J-Lab), tests have been made with an ultrafast streak camera in which the voltage sweep plates are replaced with a dedicated RF frequency deflection system, although the temporal resolution is currently in the several picosecond range Summary In this chapter we have surveyed the techniques that have been employed or could be developed to measure the temporal properties sub-picosecond pulses at VUV/XUV and shorter wavelengths. The ability to measure pulse length, pulse profile and pulse timing are critical to the success of many experiments on free electron laser sources. Because such sources show significant shot-to-shot fluctuations in the pulse proper- 2 A. Margaryan, J-Lab seminar June 28, June28.pdf

184 9.8. Summary 169 ties, we ideally need to be able to measure each and every pulse that is used in the experiment. The temporal diagnostics techniques thus need to be automatic, reliable, noninvasive and capable of handling large amounts of data. And yet a key point to note is that many of the techniques are currently at the level of experiments in themselves. This is not unexpected since sources of ultra-short pulses at VUV and shorter wavelengths are a relatively new phenomenon, and it is only through availability of such sources that the diagnostic techniques can be developed. In the early days of ultra-short optical wavelength pulses, the principal diagnostic was the relatively uninformative autocorrelator, and yet sophisticated diagnostics that fully characterize the pulse profile can now be bought off the shelf. We should not however be complacent that developments to shorter wavelengths will rapidly follow the availability of the sources. Certainly, basic second-order autocorrelation as been successfully demonstrated into the soft X-ray, but this gives only information about the pulse length, and even then assumptions have to be made about the pulse profile. At optical wavelengths, autocorrelation was extended through the addition of spectral analysis (e.g. FROG) and this allowed complete pulse profile retrieval. But a key requirement in autocorrelation techniques is a non-linear process that can mix the two pulses and produce a signal that is proportional to the autocorrelation function. Here we are limited not only by the availability of suitable physical processes but also by detectors since the non-linear signal may be accompanied by a strong background that is hard to discriminate from the signal of interest. This is particularly true when the physical process produces electrons rather than light, as will generally be the case at short wavelengths where ionization is a dominant process. Two-photon ionization is the most widely cited physical process that might fulfill the requirements and auto-correlation measurements have been successfully performed into the XUV. The wavelength range over which two-photon ionisation will work is limited by the ionisation potentials of available gases and so different gases are needed to cover different wavelength ranges. Furthermore, once the energy of a single photon is above the gas IP, then the large background of single-photon ionisation events is likely to swamp the two-photon signal. Thus two-photon ionisation is only viable at photon energies between half of and the full IP of the gas. Two-photon double ionisation may then be the way forward into the soft X-ray, but at the moment such schemes are untested. A fundamental limitation of autocorrelation techniques is that they cannot provide information about the timing of the pulse since it is measured against itself. Thus, there has been a lot of development in crosscorrelation techniques in which the free electron laser pulse is measured against a known pulse from an IR laser. As well as pulse length information, we can gain information on timing jitter relative to the laser, which is often very convenient, for example when the laser is also used in pumpprobe experiments. A significant amount of work has been undertaken in this area and many possible approaches to cross-correlation have been demonstrated or at least suggested. A well-established approach is to measure the intensity and/or number of sidebands that appear on the photo-ionisation spectrum of a gas as the infrared laser falls in and out of temporal overlap with the free electron laser pulse. This requires the infrared laser and X-ray pulse to be spatially overlapped in the ionisation chamber, and thus has some implications for the optical layout of the beamline. Nevertheless,

185 Pulse length, profile and jitter the gas absorbs so little that the X-ray pulse is unaltered and the diagnostic meets our requirement for being non-invasive. In the first implementations of this sort of crosscorrelator, complete pulse characterisation required measurement over a succession of free electron laser pulses with differing infrared pulse delays. The pulse profile measure was thus an average profile and not shot-by-shot. This limitation can be overcome by converting the temporal information to spatial information and recording the photo-electron spectrum with an imaging detector. Proof of principle experiments have been done but more development is needed to improve sensitivity and temporal resolution. There are other approaches to cross-correlation that have been proposed, using for example Auger electrons and chirped infrared pulses. This is an active area of research at the moment. The common theme is detection through the ionisation of gases, thus all these schemes rely on electron detectors, which adds significantly to the complexity of the measurement. A different approach to cross-correlation is that of reflectivity modulation. Although this is an invasive measurement, it is more sensitive than gas based measurements and so not all the beam is needed. Thus, a small part of the beam can be split off and sent to the cross-correlator whilst the rest of the beam is passed to the experiment. Since the technique is relatively simple and is inherently pulse resolved (but limited to the external laser repetition rate), it is quite attractive. Some work is needed to improve the temporal resolution however. Streak cameras are a long established instrument for measuring short pulses. However, current instruments are too limited in terms of temporal resolution and repetition rate. There are a number of active development programs aimed at addressing these points and it seems likely that temporal resolution of 100 fs will be possible whilst the use of smart detectors will give operation to several khz. Electro-optical techniques are not useful for directly measuring the profile of the free electron laser pulses since they only function at THz frequencies. But they can be usefully employed for monitoring the timing of the electron bunch relative to an external laser. This is likely to give important information on the overall timing of the X-ray pulses.

186 9.8. Summary 171 Summary Pulse length and jitter can be diagnosed with cross-correlation techniques. They rely on encoding the electrons emanating from a photoionization of a gas spectrally with energy from a known laser pulse. The main photoionization peaks will then get side-bands (also called satellites) whose intensity is proportional to the delay between the laser photon pulse and that of the free electron laser. With a chirped laser pulse (the photon-energy varies over the pulse) the pulse length may also be extracted from such a measurement. Autocorrelation techniques uses the pulse itself, the pulse length is deduced from splitting the pulse and recombining it after the two parts of the pulse have traversed different optical paths. The correlation between different parts of the pulse can then be measured. Although the technique is single shot a pulse shape has to be assumed to extract the length of the pulse. More advanced autocorrelation techniques Frog and Spider can also deduce the pulse shape. Reflectivity modulation of a GaAs surface induced by an optical laser can be used to extract the pulse length since the free electron laser beam modifies the reflectivity of the surface. The position and intensity of the visible reflected light can then be recorded on a pulse-by-pulse basis but not in a manner transparent to the experiments. The resolution limit is quoted to the 40 fs rms currently. Modulation of other processes have also been suggested, such as the Magneto-optical Kerr effect. Streak cameras work on similar principles to oscilloscopes and cathode-ray tubes and work by mapping time to a spatial coordinate in the detector. The incident photon beam is focused onto a slit and then passes through a photocathode. The photo-emitted electrons are drawn between two parallel plates that are also parallel to the slit. A high-speed sweep voltage, synchronised to the pulse arrival, is applied across the plates. This gives an angular deflection of the electrons that is directly related to their time of arrival and thus to the duration of the pulse. The deflected electrons are then multiplied with a micro-channel plate before impacting on a phosphor screen. Current time-resolution for streak cameras are about 300 fs.

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188 10. Free electron laser experiments Written by: A. Lindblad A free electron laser provide a tunable pulsed (transversely) coherent photon beam with unprecedented brilliance. The beam can thus be focussed to small spots where a very high X-ray photon density can be acquired. The properties outlined, enable a number of experiments that are, more or less, unique. The large number of photons per pulse (often tens of billions or more) allow time-resolved imaging and spectroscopies where combinations of the free electron laser beam and laser beams make pump and probe experiments more advanced. The high degree of coherence make single-shot imaging of nano-structures possible. The high X-ray photon density enable the study of non-linear processes in the X-ray regime, as well as the ability to study processes with low cross-sections or with low target density (e.g. imaging of single unsupported nanostructures/molecules). In this chapter some of the experiments carried out at free electron laser will be highlighted our treatment here will not by any means be all encompassing but is rather intended to give an introduction to which kinds of experiments successfully exploits the unique properties of this kind of X-ray source. One may condense the experimental efforts into: imaging and measuring atoms and atomic processes on the nanometer and femtosecond scales. Adding that the development is towards Ångström and attosecond time-scales The holy grails of free electron laser experiments Molecular movies The short pulse length of free electron laser sources makes it possible, either via splitting or sub-pulse structure, to get a X-ray pump - X-ray probe experiment. With the addition of external lasers X-ray pump, UV/Vis Laser-probe or UV/Vis-pump X-ray probe is made possible. All of this in the femtosecond regime. This, potentially, makes it possible to follow a photo-excited process like a movie, but with a femtosecond frame-rate. 173

189 Free electron laser experiments Single-molecule/nanostructure imaging Real-space imaging of nanostructures and ultimately single-molecules can be realized by the reconstruction of the image via a recorded image in momentum space obtained from X-ray scattering from the object. Single-shot spectroscopy/imaging Single-shot experiments are made possible by the large number of photons available that can get focussed down to a very small point owing to the beam quality. Since the pulses are short and intense the data for imaging and spectroscopy can be acquired before the sample explodes. This is also a cornerstone for the success of time-resolved measurements as outlined above. In the following some examples from each field will be given. Both planned and already performed experiments are presented as to show what is done today and where different groups and facilities intends to head in the near future Time-resolved spectroscopies Core-level photo-electron spectroscopies give information about the chemical state of the constituting atoms (being in free molecules or atoms, molecules or atoms on surfaces or in solids). By using photon-pulses time-resolved spectroscopies can be performed. At synchrotrons and HHG laser sources the number of photons per pulse is verylowcomparedtothoseatafreeelectronlaser (atleast generally)whichiswhythis kind of experiments needs to be performed at X-ray free electron laser facilites[271]. Many fundamental properties of matter can be studied with this type of spectroscopy, e.g. magnetization dynamics, reflectivity changes and molecular dissociation dynamics. UV/Vis pump-x-ray probe spectroscopy With an ordinary laser synchronized (with a known time-delay) to the free electron laser X-rays it is possible to study the development of the core level photo-electron spectrum. At Flash, the Ge 3d photoemission from a n-doped Ge crystal have been studied in this manner[272]. Time-resolved pump-probe experiments at the Lcls[273]: N 2 molecule studied with 1.05 kev X-rays (10 11 photons/pulse) with a Wiley-McLaren ion time-of-flight spectrometer. The counting rate was about 3 Hz. Comparing to the 30 Hz repetition rate of the X-ray source focussed on 3 µm 2 and molecules/cm 3. Time resolved core level photo-electron spectroscopy(as described also in Ref.[274]) studied of atoms and molecules (in gases, clusters, liquids and solids) combined with lasers will be an important investigative tool at free electron laser to study how the chemical state of an atom can change with time depending on how its neigbours are excited. Velocity map imaging have been used sucessfully for characterization of the overlap between free electron laser X-rays and 800 nm optical laser for instance using hydrogen[275] as the target. X-ray/X-ray Auto-correlation spectroscopy at the X-Fel have been discussed by Grübel[276].

190 10.3. Imaging and Crystallography 175 Sample Free electron laser beam Ce:YAG screen Grating Figure 10.1: Possible set-up for a single shot Nexafs measurement (adapted from Ref. [278]). Nexafs X-ray absorption near an ionization threshold (Nexafs) allow for the mapping of unoccupied states in a sample the absorption intensity is recorded as a function of photon-energy. The absorption may be studied with any decay product from the excitation, e.g. ions, electrons, photons. A possible way of doing Nexafs in a single-shot fashion is depicted in Figure 10.1 a grating acts as a beamsplitter which continuously disperse the X-ray pulse over a sample, thus the need for sweeping the photon-energy is eliminated and a single-shot measurement made possible[277, 278] Imaging and Crystallography The high fluence of free electron laser beams allow imaging of micro- and nanoparticles via X-ray scattering on a shot-to-shot basis. A problem that needs to be circumvented is the radiation damage and subsequent explosion of the particles upon the multi-ionization this problem becomes more and more substantial with decreasing particles size. For a 50 femtosecond long pulse the resolution limit have been estimated to 0.2 nm because of the blurring caused by the Coulumb-explosion of the sample[279]. A demonstration of single nano-sized particle X-ray diffractive imaging have been performed by Bogan and co-workers[280] where an ærodynamic lens provided nanoparticles from an electrospray source. A part of their set-up is shown in Figure There is clearly a strive towards imaging ever smaller objects[281] and ultimately single molecules, both in free form and in their natural environment, i.e. in water or

191 Free electron laser experiments Figure 10.2: A prototypical single particle X-ray diffractive imaging (after Ref. [280]). in cells[282]. Recently a virus particle was imaged using overlays of recorded patterns from single particles which shows that even if the object explodes because of the deposited X-ray energy it survives long enough to be imaged[283]. The imaging activities at Flash have recently been reviewed[284], as well as the specific strives towards coherent diffractive imaging [50]. At the Lcls there is an endstation dedicated to coherent X-ray imaging[285]: the (CXI) instrument[286]. At Fermi@Elettra the first operational beamline is intended for coherent scattering experiments. As free electron laser promise to deliver X-rays of sufficient quality to allow singleparticle/single-molecule imaging and that phase-retrieval algorithms become ever more sophisticated this area of research attracts a lot of effort. With phase-retrieval information (lost in the imaging process) this will ultimately allow for single-particle tomographic measurements of nano-particles, proteins and parts of cells. Figure 10.3 depicts X-ray scattering through a randomly ordered sample (powder diffraction). If the beam is incoherent and wide (Debeye-Scherrer scattering) the scattering angle is proportional to the mean distance between the scattering centers in the samples. If the beam is small and sufficiently coherent one still obtains information about the mean distances in the film via the scattering angle but on the detector a speckle interference pattern occur instead of diffuse rings. The speckles angular extent is inversely proportional to the beam width. By overlaying the X-ray scattering images from two time-delayed pulses Günther and co-workers have recently demonstrated that sequential imaging with femtosecond resolution is indeed possible to obtain for nanometer sized objects[287]. This is a significant step towards time-resolved imaging of objects at the atomic scale Non-linear X-ray science Photoionization Withveryhigh irradiance levels (towards W/cm 2 )at 93eV photonenergy, Xe 21+ have been observed in ion-time of flight spectra this corresponds to the absorption

192 10.4. Non-linear X-ray science 177 λ/d d λ/a a Figure 10.3: X-ray diffraction using diffuse and coherent beams. of about 57 photons for that atom (or 5 kev absorbed X-ray energy)[288]. This amount of energy deposited in a single atom allow the study for many processes of fundamental nature. With shorter pulses in the attosecond regime (the atomic unit of time being 24 as) processes may even be possible to study on the same time-scale as the electron s travel-time around the nucleus. Sequential ionization of atomic argon have been studied at the Scss free electron laser. They find evidence of a sequential electron emission from the absorbing atoms during the pulse duration[289], access to even shorter pulses would naturally benefit the study of this kind of physical phenomena. A summary of the findings on different rare gases is provided in Ref [98]. In this reference a survey of different possible experimental set-ups is also provided. Multiphoton ionization of atomic clusters have also been studied in this regard (see, e.g. Ref. [290]) since this allows for a detailed study of the Coulomb explosion from the interaction of nano-particles with free electron laser light. Recently Fang and colleagues have reported on an experiment where double corehole ionization in nitrogen molecules[291] is demonstrated. This type of experiment give insight in how fast photons are absorbed during the pulse since the single coreionized species have a lifetime in the low femtosecond regime. An experiment involving X-ray emission following two-photon absorption have also been suggested by Sun and coworkers[292].