UNIVERSITY OF CALIFORNIA. Los Angeles. Brookhaven National Laboratory Accelerator Test Facility. A thesis submitted in partial satisfaction

Transcription

1 UNIVERSITY OF CALIFORNIA Los Angeles Inverse Compton Scattering and Characterization of the Source at the Brookhaven National Laboratory Accelerator Test Facility A thesis submitted in partial satisfaction of the requirements for the degree Master of Science in Physics by Oliver Benjamin Williams 2009

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3 The thesis of Oliver Benjamin Williams is approved. Claudio Pellegrini Pietro Musumeci James Rosenzweig, Committee Chair University of California, Los Angeles 2009 ii

4 Dedication To my family. iii

5 Table of Contents List of Figures vi 1. Introduction History of Light Sources Inverse Compton Scattering Objectives 8 2. Theory and Simulation Introduction Derivation of Scattered Photon Energy Frequency Upshift Due to Relativistic Effects Emission Angle Normalized Laser Vector Potential and Undulator Equation Nonlinear Effects Simulation Details and 3D Effects Laser Bandwidth Laser Focus Electron Beam Energy Spread Electron Beam Angles Total Bandwidth Total Scattered Double Differential Spectrum (DDS) Peak Brightness Simulated ICS Source at ATF Angular Distribution Total X-ray Flux and Off-axis Photons Bandwidth from 3D Effects Time Profile Peak Brightness Diagnostic Foil K-edge Characteristics Obtaining the DDS Using Foil Bandwidth Measurement Using Foil Experiment The Accelerator Test Facility Electron Beamline High Power CO 2 Laser ICS Setup 51 iv

6 3.1.2 Alignment and Timing Procedure X-ray Diagnostics Data and Results Flux Measurements Angular Measurements DDS Measurements Central Photon Energy Calculated Bandwidth Peak Brightness (On-axis) Circular Polarization Conclusions 72 References 75 v

7 List of Figures Table 1: Electron and laser beam parameters at the ATF. 27 Table 2: Summary of ICS source parameters 39 Table 3: Detailed photon transmission for a 50 μm iron foil. 41 Figure 1: Schematic and photograph of Coolidge tube. 2 Figure 2: Examples of synchrotron facilities. 4 Figure 3: Photograph depicting the LCLS site. 5 Figure 4: Orthogonal interaction geometry for inverse Compton scattering. 7 Figure 5: Nonlinear inverse Compton experiment in the Neptune Laboratory at UCLA. 7 Figure 6: Relativistic electron (v c) and successive radiation wavefronts. 11 Figure 7: Example of the effect of intense laser fields on nonlinear red-shifting. 17 Figure 8: Simulated angular and intensity distribution of scattered photons produced by a 66 MeV electron beam colliding head-on with a linearly (x) polarized 10.6 μm laser pulse. 29 Figure 9: Spectral density vs. photon energy for various acceptance angles. 30 Figure 10: Laser-induced bandwidth. 32 Figure 11: Electron beam induced bandwidth effects. 33 Figure 12: Effect of electron angles on source bandwidth. 34 Figure 13: Effect of electron beam energy spread on source bandwidth. 34 Figure 14: Intensity (photons/mrad 2 /s) distribution of the x-ray pulse time profile. 36 Figure 15: A survey of light source facility peak brightness as a function of photon energy. 38 Figure 16: Transmission curves for various thin foils. 41 Figure 17: a) Angular intensity distribution of simulated ATF ICS source after passing through an iron foil. b) The same full angle ICS source spectrum before (top-blue) and after the foil. 42 Figure 18: Simulation of source total flux vs. electron beam energy after passing through the 50 μm iron foil. 45 Figure 19: (Left) ATF photoinjector and (right) linac synchronization diagram. 49 Figure 20: CO 2 laser room and table showing optical path and amplifier locations. 50 Figure 21: Diagram of the ICS interaction chamber. 51 Figure 22: Plot of laser transmission through a germanium crystal versus e-beam arrival time. 53 Figure 23: (Left) Amplification mechanism of microchannel plate detector. (Right) Detection efficiency of MCP. 56 Figure 24: Layout of the x-ray diagnostics section following the electron spectrometer. 57 Figure 25: Photograph of the x-ray diagnostics table at the end of beamline Figure 26: Image of source taken with MCP image intensifier for e-beam energy of 62 MeV. 60 Figure 27: Source images made for a 72 MeV e-beam after passing through various foils. 61 Figure 28: ICS source after passing through Fe-foil for e-beam energies of 64 MeV (top left), 65 MeV (top right), 66 MeV (bottom left), and 70 MeV (bottom right). 63 Figure 29: Plot of the lobe observation angle and corresponding e-beam energy. 64 Figure 30: Intensity lineouts for MeV from Figure Figure 31: Image of circularly polarized Compton x-rays after passing through the 50μm iron foil. 72 vi

8 Acknowledgements I would like to start by thanking my friend and advisor, Jamie Rosenzweig. He has always believed in my abilities and helped me when I forgot what it was to be a BMF. Many thanks also to my friend, Gil Travish, whom I could always go to for help in the lab or the name of a good restaurant. The many hours at the Neptune Lab could not have been more enjoyable, thanks to Sergei Tochitsky. We had many late nights in the control room, sometimes arguing, but usually laughing. Thanks to all the ATF guys, if it weren t for your expertise and willingness to work with me, I wouldn t have this thesis. To all the current and former PBPL ers, thank you for making the group such a fun and carefree place to learn and live. I never dreaded coming to work, and that s because of you guys. I m sure it will reign as the best research group in the world for years to come! Lastly, I want to thank my friends and (the few) enemies everywhere. You influenced who I am and what I believe. I will continue to learn and become a better person. I will become One. vii

9 ABSTRACT OF THE THESIS Inverse Compton Scattering and Characterization of the Source at the Brookhaven National Laboratory Accelerator Test Facility By Oliver Williams Master of Science in Physics University of California, Los Angeles, 2009 Professor James Rosenzweig, Chair An inverse Compton scattering source at the Accelerator Test Facility has been thoroughly simulated and characterized in preparation for future applications of this unique source of X-ray photons. Simulations were performed using a 3D time and frequency-domain code for various beam parameters achievable at ATF. Calculations show a total flux of 1x10 9 photons per shot is obtainable with photon energies ranging from 5 to 9 kev over the full divergence angle of 8 mrad. The spectral bandwidth is dominated by electron beam angles and energy spread. In experiment, iron and nickel foils were used as an energy diagnostic due to their viii

10 strongly absorbing K-edges near the design central photon energy. Measurements indicate 2x10 6 photons within a 1 mrad emission angle and 4.0±0.8% bandwidth. Simulation is relied upon for information on source size and pulse length and predicts 22 μm and ps, respectively, resulting in a peak brightness of 2.4x10 19 photons/mm 2 /mrad 2 (0.1% bandwidth). A circularly polarized laser resulted in a source energy and angular distribution indicative of circularly polarized x-rays. ix

11 1. Introduction 1.1 History of Light Sources The discovery of x-rays by Wilhelm Roentgen in 1895 [1] led to an enormous wealth of technology and fundamental knowledge of nature. Applications in biology and medicine have allowed for better diagnosis and treatment of disease and injury. The use of x-rays to study bulk crystal lattices, such as diamond, eventually led to protein crystallography and images of the DNA helix due to x-ray diffraction patterns [2, 3]. Industry has also benefited by using x-rays as an inspection tool for quality control of propeller blades and oil pipelines [4, 5], for example, while national security depends on x-rays for the scanning of cargo containers and trucks for nuclear materials and baggage inspection at airports. The constant demand for higher quality x-ray sources for research and applications has led to an array of increasingly advanced sources and the creation of a field of physics dedicated to new light sources. X-ray sources have come a long way since the Crookes (cold-cathode) x-ray tubes used by Roentgen. Beginning in the early 20 th century, a heated cathode was substituted and the Coolidge x-ray tube created, allowing for a longer lifetime and more reliable x-ray source [6]. Both models depended on the acceleration of electrons to energies close to that of the applied electric field, about kev. Today, these electrons are allowed to impact a metal target, creating a shower of x- rays with a continuous spectrum, extending to the incident electron energy from wellbelow, called bremsstrahlung. Some x-ray tubes consist of targets of specific 1

12 elements which radiate at particular x-ray wavelengths (K emission) and enhance the source spectrum near these spectral lines. The basic principles of this source are still employed at dental offices and hospitals around the world as well as small research facilities. But the inefficiency of this source, with its low flux, large divergence angle, and poor bandwidth pushed research towards a new paradigm of light sources: those based on accelerators. Figure 1: Schematic and photograph of Coolidge tube. Accelerator-based light sources have been in development since Lawrence Berkeley (and others) first invented the cyclotron in 1929 [7]. This worked similarly to x-ray tubes by accelerating charged particles with an applied electric field and allowing them to collide with solid targets, however, these circular accelerators allowed for the constant injection and acceleration of particles to higher energies. This resulted in rather high average power systems, necessary for use in radiation therapy, for example. Cyclotrons are limited, however, in the peak energy obtainable by the charged particles due to relativistic effects causing the particles to become out 2

13 of phase with the accelerating fields. A new accelerator which could synchronize the applied field to the arrival of the particles was created; the synchrotron. The synchrotron (and linear accelerator) uses radio-frequency (RF) waves in a resonant cavity to create an axial electric field which accelerates injected charged particles. The phase of these waves can be altered to allow for acceleration of relativistic charged particles. These devices are scalable to very large facilities, with the proton synchrotron-based Large Hadron Collider (LHC) boasting a circumference of ~27 km and circling under the borders of three countries. They were originally only used for high energy particle experiments, but were quickly realized as potential light sources when it was discovered that large amounts of light were produced when bending the relativistic particles (electrons) around the circle. This bending radiation, more commonly termed synchrotron radiation, was a parasitic product of going to higher and higher energies and drove for the development of synchrotron ring-dedicated light sources, where user beamlines were installed tangent to the ring and therefore in-line with the bending radiation. It was later realized that the strict ring geometry didn t need to be followed and multi-sided polygons could be used instead, where a periodic magnetic device, called an undulator (or wiggler), could be inserted in straight sections. These insertion devices greatly enhanced the photon flux and bandwidth over bending radiation due to the forced oscillation of particles passing through the magnetic field and created a very low angular divergence beam, a product of the highly relativistic electrons emitting the radiation [8, 9]. Because the x-ray pulse length is the same length as the 3

14 electron bunch, pulses are usually ~100 ps and require complicated, inefficient slicing techniques in order to obtain pulses short enough for demanding time-resolved, at the level of ps or below, studies [10]. For 50 years, synchrotron rings have been the primary source of high quality x-rays and thousands of user experiments have benefited from their light. However, their size and cost have stimulated for the development of more compact x-ray sources with competitive qualities. Figure 2: Examples of synchrotron facilities. (Left) Illustration of user beamlines utilizing bending radiation tangent to a synchrotron ring. (Right) Aerial view of a synchrotron radiation facility. Lasers, first developed around the same time (1960) as synchrotrons, offer exceptional characteristics in the form of extremely low angular divergence, coherence, high power, and the possibility to obtain ultra-short (sub-picosecond) pulses. The latter allows for the dynamic study of ultra-fast events where the laser functions as a strobe light, taking snapshots as an event occurs. Lasers are greatly limited, however, in the wavelength of light they can produce and cannot extend into 4

15 the realm of x-rays [11]. A facility called the Linac Coherent Light Source (LCLS) at the Stanford Linear Accelerator Center (SLAC) is near completion which would use a part of the existing linac and a very long undulator to create <100 femtosecond pulses of x-rays with laser-quality brightness and coherence. This x-ray free electron laser (FEL) project is expected to provide the x-rays necessary for new, groundbreaking discoveries of the ultra-small and ultra-fast, allowing for the imaging of molecular and even atomic motion, at or below the time resolution characteristic of this motion [12]. Such a project requires a huge amount of funding (~$500 million) and dedicated researchers to make it function and is certainly not compact or feasible for a hospital or university research. A smaller scale, less expensive x-ray source is still necessary. Figure 3: Photograph depicting the LCLS site. The size of the facility obviously makes it unrealistic for use at a hospital or small research institution, although it is expected to provide sub-100 fs, laser-quality x-rays. 5

16 1.2 Inverse Compton Scattering Inverse Compton scattering is (like Compton scattering) the interaction between an electron and photon, where energy/momentum is transferred from one to the other [13]. In the case of inverse Compton scattering, the electrons are relativistic and therefore much higher energy than the interacting photons. The fast initial state of the electron causes the scattered photon to be significantly frequency upshifted. This is a naturally occurring astrophysical process, where the interacting photon is often of the cosmic microwave background and is scattered to x-ray or gamma ray energies by relativistic charged particle cosmic rays. However, it can also be accomplished in a laboratory in order to produce high energy photons using relatively low energy electron beams. A high brightness electron beam is focused to a small spot size and scatters a focused high power laser pulse at the interaction point (IP). The scattering geometry is usually either with counter-propagating or orthogonally intersecting (figure below) beams. In application, scattered high energy photons propagate with the electron bunch and interact with an experimental sample after the electrons are dumped by a dipole magnet. The emission angle and source size are small, with a large number of photons scattered within a small bandwidth in each interaction. The pulse length is a product of the scattering geometry, and laser and electron beam parameters, with orthogonal scattering generally being capable of shorter pulses at the price of reduced flux [14, 15, 16]. The potential for synchrotron-quality x-rays in much shorter pulses (due to linac-based e-beams) and employing a small facility at a fraction of the cost of 6

17 a synchrotron, makes inverse Compton scattering extremely attractive across many scientific disciplines. Figure 4: Orthogonal interaction geometry for inverse Compton scattering. This geometry is used for short pulse x-rays due to the limited interaction time between the laser and electron beams. A counter-propagating geometry has substantially higher flux. dumped e-beam To x-ray detector e-beam x-rays focusing quadrupoles laser pulse Figure 5: Nonlinear inverse Compton experiment in the Neptune Laboratory at UCLA. The strongly focused laser and electron beam physically required an orthogonal interaction geometry and very compact interaction region due to the short focal length laser and electron optics [17]. 7

18 1.3 Objectives The calculation of expected ICS source parameters is non-trivial and involves accounting for beam focusing, energy spread and bandwidth, and the detailed motion of the electrons within the laser pulse. The wide array of source parameters makes optimization a challenge and user applications demand verification of x-ray qualities, so it is important that the source be well characterized before attempting any applications. Thus it is the intention of this thesis to characterize the ICS source at the Brookhaven National Laboratory Accelerator Test Facility (BNL ATF) for use in proof-of-principle application experiments. This involves verification of total flux, angular and energy distributions, effects of laser polarization, and conditions for producing sub-picosecond x-ray pulses. Theoretical calculations and simulation of design parameters will be matched against experimental results and conclusions made about the feasibility of using the ICS source at Brookhaven for imaging and high temporal resolution experiments. 8

19 2. Theory and Simulation 2.1 Introduction The interaction of an electron with an electromagnetic field is extensively covered in classic electrodynamic theory [18] and can also be treated using quantum electrodynamics [19]. For a relativistic electron additional corrections must be made resulting in a frequency upshift of the scattered electromagnetic field. However, the ICS system is composed of many electrons in the form of an electron beam and, analogously, the laser being treated as a photon beam. These electrons have a finite energy spread and emittance (phase space area) which define the beta function (how long the volumetric density can be maintained). Each electron has a chance of scattering with a photon, determined by both the Thomson cross-section and the electron-photon density around the interaction point. Three-dimensional effects such as the focusing of the beams, pulse and bunch length, and interaction angle also affect the resultant scattered photon parameters. To accurately predict the characteristics of an ICS source, numerical methods must be employed where the scattered photons for each electron are calculated and integrated over all angles and frequencies. However, there are basic equations which can be derived using analytical methods and function as useful tools in predicting scattered photon parameters. We shall first discuss these expressions and follow with a basic description of the equations used in the multiparticle simulations. Results of the simulations for various input beam parameters will be summarized and discussed. 9

20 2.2 Derivation of Scattered Photon Energy Frequency Upshift Due to Relativistic Effects One of the most appealing aspects of ICS sources is the possibility of producing high energy photons, even gamma rays, with relatively low energy electron beams. The physical mechanism of this frequency boost to the laser photons has been extensively studied in terms of undulator radiation at 3 rd generation synchrotron facilities [8, 9, 20]. It was postulated that inserting a periodic magnetic structure in the path of a relativistic electron beam circulating in a synchrotron ring could greatly enhance the amount of radiation produced by forcing many small amplitude oscillations. Additionally, Lorentz contraction of the approaching magnetic field and relativistic Doppler shift effects due to the small difference in relative velocity of relativistic electrons (v c) and emitted radiation (v = c), result in much shorter radiation wavelengths when observed in the laboratory frame. In the case of inverse Compton scattering, because the laser pulse interacting with the electron bunch is seen to be an alternating electromagnetic field, analogous to an undulator, but of much shorter wavelength than the undulator period, it is possible to obtain very short wavelength light using low energy electron beams [15]. 10

21 interaction angle between the laser and electron beam with Φ=180 o for countere - : v~c θ c=λf Figure 6: Relativistic electron (v c) and successive radiation wavefronts are close together, resulting in an apparent frequency upshift (relativistic Doppler shift), while off-axis observers see lower frequencies. We first consider the alternating period of the laser in the electron rest frame (following [21]). The electron sees a Lorentz contracted oscillation frequency, f, moving towards it, f ' c u (1) where c is the speed of light, γ is the unitless relativistic correction factor, E e /0.511, and λ u is the oscillation period of a fixed field structure, such as an undulator. Writing λ u in terms of the laser wavelength, λ L, and identifying it as a traveling wave propagating at an angle with respect to a relativistic electron beam yields, L u 1 cos (2) where β is the ratio of the electron velocity to the speed of light and Φ is the 11

22 propagating (head-on) beams. The frequency is further enhanced in the laboratory frame due to relativistic Doppler shifting and becomes observation angle (θ) dependent due to the relative velocity of the electrons to the emitted radiation. The frequency in the lab frame in terms of the rest frame (f ) can be expressed as, ' f f. (3) 1 cos Combining (1)-(3) gives us the expression for the expected scattered photon frequency dependent on interaction angle, laser wavelength, electron velocity, and observation angle: 1 c cos f (4) 1 cos L If we consider small observation angles off-axis, we can expand the cosθ term according to cosθ 1 - θ 2 /2 + and (4) can be approximated as, fl 1 cos f (5) 1 where the substitutions, f L = c/λ L and (1-β) 1/2γ 2 have also been made. Identifying the direct relation between frequency and photon energy and considering the common interaction angles of Φ = 90 o and 180 o, we have, for β 1, 2 2 EL E s for Φ = 90 o

23 2 4 EL E s for Φ = 180 o. (6) 1 2 As is evident above, the scattered photon energy, E s, for an ICS source differs from undulator radiation in that it picks up an extra factor of two for a counter-propagating laser. Because the effective undulator frequency for a laser photon is 10 4 times greater, this requires an electron beam 100 times less energetic than that found at a synchrotron facility [22]. It is important to note the (γθ) 2 factor in the denominator as this indicates red-shifting for off-axis photons and hence dictates the angular acceptance of the source assuming a small bandwidth is required and other parameters influencing bandwidth are minimal (discussed later) Emission Angle Additional effects on the radiation due to emission off-axis as the electrons traverse the oscillating field also need to be considered, but the angle into which this radiation is emitted must first be discussed for a better understanding of the process. Lorentz transformations of the angular radiation pattern from the electron rest frame to the lab frame greatly reduce the emission angle for relativistic particles, resulting in a searchlight or cone of radiation. As has been proven elsewhere [21], the angles into which this radiation is emitted can be expressed as, ' sin tan (7) cos ' 13

24 where θ is in the lab frame and θ is in the electron rest frame. For relativistic electrons, β 1 and γ >> 1, and for even large angles, θ, we have a tightly confined cone of radiation in the direction of electron propagation with half angle expressed as, 1 rad. (8) 2 For applications in other scientific disciplines this is an important aspect of the radiation. Directionality and low angular divergence make this a very desirable source in comparison to x-ray tubes and bremstrahlung sources where radiation is emitted in nearly 4π steradians Normalized Laser Vector Potential and Undulator Equation The narrow emission angle characteristic of this radiation also introduces possibilities of interference effects and narrow bandwidths, but is limited by the excursion angle the electron makes off-axis as it propagates through a laser field or undulator. Emission at large angles compared to 1/2γ will tend to pollute the on-axis spectrum as red-shifted photons observed off their emission axis will lie within the central radiation cone. Additionally, for high fields, the average axial velocity (and hence relativistic factor, γ) will be reduced due to non-negligible excursion off the propagation axis. The name given to describe the magnitude of the deflection in an undulator is the magnetic deflection parameter or the undulator parameter, and analogously for lasers, the normalized laser vector potential. These are expressed respectively as: 14

25 ebu K and, 2mc a L eel (9) 2mc with B and E being the magnetic and electric field magnitudes of the undulator and laser, e the charge of an electron, and m the electron mass. A practical equation in terms of the laser intensity, I, for the calculation of the normalized laser vector potential is given below. It is worth noting the dependence of a L on λ L, as this is important in designing an optimal ICS source. a L I[ W / cm ] [ cm] (10) L Following Attwood, we can write the effective axial value of the relativistic factor in terms of a L, *. (11) 2 1 a L 2 If we now substitute γ * for γ in (6) and simplify, we can see the red-shifting effects on the radiation due to a L, 2 4 EL E s. (12) 2 a 1 L 2 2 Equation 12 is the key analytical expression for calculating scattered photon energy and will be used in conjunction with numerical simulations for experimental analysis. When pertaining to undulators (using K and only having the factor of 2γ 2 instead of 15

26 4γ 2 ), it is commonly referred to as the undulator equation, which we will also call it here. Throughout the remainder of the paper it will be assumed (as in eqn. 12) that we are working in a head-on collision geometry, that is, Φ=180 o. The orthogonal collision (Φ=90 o ) has the benefit of being capable of producing very short radiation pulses due to the availability of ultra-short lasers (10 s of femtoseconds) and small spot sizes. But because the electron and laser beam are interacting for such a short period, photon flux is greatly reduced, in addition to there being increased bandwidth effects from the many laser angles (i.e. wave numbers) being seen by the electrons at the focus. Accordingly, it is now customary for ICS sources to be designed using a head-on collision due to the benefit of increased flux and decreased bandwidth. Additional characteristics of 180 o scattering will be discussed in following subsections Nonlinear Effects It is worth briefly mentioning the effects of high a L, resultant of long laser wavelengths and high intensities. As mentioned above, large excursions off-axis reduce the average axial velocity of the beam as well as induce oscillations in the velocity. These oscillations give rise to harmonic motion which result in integer upshifts of the fundamental energy, going like ne s (n = 1, 2, 3, ), as well as different angular distributions for even and odd harmonics and red-shifting according to equation 12 (see figure below). This non-linear harmonic generation becomes nonnegligible for a L 1 and is characterized by an increase in radiated power and a broad 16

27 shift to higher frequencies [23, 24, 25]. For a L >> 1, a super-continuum of harmonics can form, allowing flexibility in wavelength tuning [22] and an extension to previously unobtainable photon energies. This type of radiation is often referred to as wiggler radiation, where the name wiggler is specifically given to undulators of high K. Because the non-linear motion and harmonic creation is not particularly desirable for beamlines absent of monochromators and requiring small bandwidths, ICS sources are generally designed with a L < 1. The calculations required for this process are also much more difficult and computation times are greatly increased, so we will only discuss linear inverse Compton scattering. Figure 7: Example of the effect of intense laser fields on nonlinear red-shifting. This was done for an electron beam energy of 64 MeV. 17

28 2.3 Simulation Details and 3D Effects The theory of inverse Compton scattering has been thoroughly studied and documented [23, 24] but a three dimensional (3D) time and frequency-domain code is necessary in order to fully determine the temporal, spatial, and spectral distributions of the scattered photon spectra. Collaborators [26] have developed such a code for arbitrary laser-electron interaction geometries. It is capable of producing transverse and longitudinal (temporal) intensity distributions including increased bandwidth effects due to: energy spread of the electron beam, finite laser bandwidth, electron beam angles due to focusing and emittance, and a spread in perpendicular k-vector components of the laser seen by the electrons at the focus. Because of the complexity of calculating all bandwidth increases due to the above effects, a generalization of the computation being performed in the code will be discussed and the reader is referred to the literature [26] for more detailed information. Thomson scattered photons are produced when an electron (bunch) collides with a photon (laser). In the case where the laser photon energy is much less than the electron rest mass, that is E L << MeV, the scattered photon energy is nearly that of the incident photon, E s E L. This is called the Thomson limit and is almost always the situation at an inverse Compton facility. Because the electron recoil due to the photon momentum is negligible, one can assume ballistic motion of the electrons through the laser field, an essential criterion for the 3D code discussed. The number 18

29 19 of photons scattered in the electron rest frame, s N, is the integral of the product of the electron-photon densities with the Thomson cross section, σ, dt d t n t n c N e s r r r 3 ), ( ), (. (13) Because the total number of scattered photons is Lorentz invariant and is therefore independent of the electron relativistic factor, we can express it in terms of the electron four-current, J μ = ecn e (1, β), and the photon four-flux, Φ μ = cn γ (1, ck/ω) (note the dropped prime due to Lorentz invariance), dt d t n t n c k c x d J ce N e e s r r r 3 4 ), ( ), ( ) 1 ( (14) If we consider the rate of scattered photons from a single electron, n e (r, t) = δ[r e (t)], and evaluate the integral at r e (t), the position of the electron at time t, we have, ] ), ( [ ) 1 ( t t n c k c dt dn e e s r (15) This can now be expressed as the rate of scattered photons per unit frequency into a given solid angle, )] ( [ ) ( ), ( ) (1 g d d t F d d d t n c k c dt d d dn s s e e s s L r (16) L F represents the incident photon flux seen by the electron, ω s is the frequency of the scattered photon, dζ/dω is the differential Thomson cross-section, and g(θ) is the relativistic Doppler upshift of the photon, which is dependent on θ, both the angle

30 between direction of observation and electron direction, as well as electron and incident photon directions. The form of dζ/dω is dependent on the scattering geometry and laser polarization and the reader is referred to the literature for the exact equations. Equation 16 is the main expression used for the single particle 3D simulation and it is important to note certain assumptions which are made in order for the calculations to remain valid. As stated earlier, it is assumed the scattering is in the Thomson limit where there is negligible recoil of the electrons while interacting with a photon. This assures ballistic motion of the electron bunch through the laser pulse within the interaction region. A very high laser field can also cause non-negligible motion of the electrons through the laser pulse, hence changing the initial parameters and subsequently giving erroneous results of the scattered photons. It would require intensive computations to correctly model electron motion in the laser field and the resultant radiation. Therefore, we are restricted to working in the linear scattering regime, where a L << 1. While the physics for a single electron interacting with a photon have been discussed, in reality, the system is composed of billions of electrons in a bunch all with a certain energy and trajectory as they pass through the interaction region, described by their energy spread, emittance, and divergence at a focus. The finite pulse length of the laser introduces its own inherent energy spread (bandwidth) and, while passing through a focus, has various perpendicular k-vectors that are seen by the electrons at different times during the interaction. These 3D qualities of the two 20

31 beams impart additional bandwidth to the scattered photons which must be accounted for when designing and optimizing an ICS source Laser Bandwidth Because of the finite pulse length and corresponding inherent bandwidth of the laser, the electrons see a range of photon energies as they scatter the laser photons. As this occurs in the electron rest frame and is then Lorentz boosted into the lab frame, there is a direct relationship between the incident and scattered photons, BW pulse s o s o. (17) It is foreseen that this could be a problem with CPA Ti:Sapphire laser systems where terawatt power levels are achieved from ~100 fs pulses and 2-3% bandwidth is not uncommon. The bandwidth imparted from lasers by this mechanism should be considered when designing an ICS source Laser Focus If a plane wave approximation for the laser at the focus is made, then there is zero spread in the perpendicular k-vectors and no additional bandwidth effects exist. This may be a reasonable approximation considering other sources of bandwidth, such as electron beam emittance and laser bandwidth, but breaks down in the case of a very strong laser focus or ultra-low emittance beams. In the case of the 180 o interaction, the bandwidth increase due to the laser focus in terms of waist size, w o, is, 21

32 BW focus 2 1 s o 4, (18) s wo and the Rayleigh range is given by, Z R w. (19) M 2 o 2 o M 2 is a measurement of how diffraction limited the laser is; here we take M 2 = 1, corresponding to an ideal Gaussian mode. To demonstrate how small of an effect the laser focus plays on bandwidth for a head-on collision, let us consider a Ti:Sapphire laser (λ o = 800 nm). In order to see an increase in bandwidth by 1%, one must focus the laser down to a waist of w o 1.3 μm and Z R = 6 μm, a difficult feat requiring a very high quality laser, optics, and excellent alignment. This makes the plane wave approximation a reasonable assumption and simplifies the calculations made in the simulation. As a practical design note, if one wishes to maximize the total scattered photon flux, it is desirable to match beam sizes and the corresponding Rayleigh range to the laser pulse length in order to allow all the photons in the laser pulse to interact with the electron bunch. These parameters are of course limited by nonlinear effects corresponding to high a L which will also tend to increase bandwidth due to redshifting and electron excursion angles greater than the emission angle. These nonlinear sources of bandwidth will not be quantified here, however, due to the assumption made earlier that a L << 1. 22

33 2.3.3 Electron Beam Energy Spread The intrinsic energy spread picked up by the electron bunch during acceleration due to RF phase curvature, thermal emittance, wakefields, and space charge forces is manifested in the scattered photons by the variation in the Lorentz correction factor, γ. Because the scattered photon energy scales like γ 2, the bandwidth is twice the electron beam energy spread, s 2 BW energy, (20) s where s is the average scattered photon energy and is the average Lorentz correction factor. This contribution can be relatively small given the high brightness electron beams being employed for ICS sources where the rms energy spread is typically on the order of 0.1%, unless pulse compression is performed. This technique, which requires that one impart an energy chirp on the beam and then employ a magnetic chicane to rearrange the electron time-ordering, brings the expected level of energy spread encountered to ~1% Electron Beam Angles A fairly large source of bandwidth for ICS-produced photons, which is not so easily ameliorated, is the electron beam convergence/divergence (due to emittance and beam focus) at the interaction point. Because the scattered photons are emitted in the direction of the electrons, the central axis of the photons, and thus observed x-ray spectra, tend to vary depending on the divergence angle of the electron at the time of 23

34 scattering. It is thus a mixing of central emission angles from the individual electrons, which results in a polluting of the average central radiation spectrum. The rms divergence of the electron bunch at the interaction point is expressed as ' e, x x x, (21) 2 e, x where ε x is the rms geometric emittance in x of the electron bunch, ε n,x = γε x is the normalized rms emittance, σ e,x is the beam size, and Δξ x is the 1/e 2 divergence of the electron beam. The on-axis spectral broadening for a 180 o interaction can be written in terms of the 1/e 2 divergence as, BW divergence 2 s s x y n e, x. (22) Total Bandwidth The last expression in Eq. 22 assumes the emittance and beam sizes are equal in both x and y. These four sources of bandwidth due to 3D effects of the colliding beams can be combined into one expression to give the total bandwidth of the scattered photons: BW tot BW BW BW BW. (23) 2 pulse 2 focus 2 energy 2 divergence Total Scattered Double Differential Spectrum (DDS) To conclude the description of multiparticle effects on the scattered photon distribution, we must discuss how the code incorporates an electron bunch in the 24

35 calculations. While Eq. 16 is for a single electron scattering a flux of laser photons, we can apply it to the multiparticle case by summing over all the electrons in the bunch such that the total scattered photon double differential spectrum (DDS) is, dn,,, t q dns x, y,,, s, t e e dd dt T s ddsdt e s, (24) where the charge of the macroparticle is denoted by q e, and and represent the angle formed by the transverse position of the detector and distance from the interaction point. Because the distance between the detector and the source is usually at least one meter, the source size (typically < 100 μm) has a negligible effect on the angular spectrum seen at the detector. The code also possesses the ability to accept input electron distributions from particle dynamics codes such as PARMELA, to allow more systematic treatment of expected experimental conditions Peak Brightness The ability to deliver high flux, low bandwidth photons over a small angle and in a short period of time is often the judging criteria for the effectiveness of a source. This is generally termed, peak brilliance or peak brightness, where peak refers to the photons delivered during one pulse. In contrast, average brightness is dependent on the repetition rate of the source, determined by trains of microbunches and duty factor. We limit our discussion to peak brightness, which is usually expressed in terms of a 0.1% bandwidth and is written as, 25

36 B peak NT (0.1%) (% BW ) [photons/s/mm 2 /mrad 2 (0.1% BW)], (25) s acc s tot where N T is the total scattered photon flux within an acceptance angle, θ acc, ζ s is the source size (typically the transverse electron bunch size at the IP, which is smaller than the laser intensity profile), and η s is the source pulse length (approximately the electron bunch length for a head-on collision; η s η e + η L /4γ 2 ). A reduced brightness from bandwidth due to 3D effects and acceptance angle is included in (25) by supposing only a fraction of the total photons scattered are within the 0.1% bandwidth. After having now established the fundamentals of the ICS process, our attention will be turned to simulation-generated numbers for scattered photons given the existing accelerator and high power laser at the ATF. 2.4 Simulated ICS Source at ATF As discussed earlier, the Accelerator Test Facility at BNL offers a unique opportunity to investigate the physics of inverse Compton scattering. The existence of a magnetic compressor chicane and high brightness electron beam of moderate energy allow for the possibility of sub-picosecond, narrow bandwidth x-rays while the sub-terawatt CO 2 laser system provides a very high flux of incident laser photons, resulting in high brightness, single-shot x-ray yields. In this section, various scattered photon characteristics for electron and laser parameters used in the experiment will be covered: 26

37 1) Angular distribution 2) Total x-ray flux and off-axis photons 3) Bandwidth from 3D effects 4) Time profile Following a thorough characterization of the source by simulation, a novel method for analyzing the spectral content of measured x-rays is discussed and the feasibility for its use in experiment is modeled. Below are listed default beam parameters for the simulated interaction. Various values were changed to observe the effect on the source characteristics and these will be noted in the relevant sections. e-beam Parameter Value Laser Beam Parameter Value Energy [E e ] 66 MeV Pulse Energy 2 J Charge [q e ] 300 pc Wavelength/E L 10.6 μm/0.117 ev Spot size, rms [σ xy ] 30 μm Waist size, rms [w o ] 60 μm Nrml emttnce, rms [ε n,xy ] 2 mm-mrad Pulse length, FWHM [τ L ] 6 ps Bnch lngth, FWHM [τ e ] 4 ps Laser undltr paramtr [a L ] 0.38 Energy spread [Δγ/γ] 0.5% Laser bandwidth [Δω o /ω o ] ~0.6% Table 1: Electron and laser beam parameters at the ATF. 27

38 The a L here is calculated by the numerical code and assumes a Gaussian temporal distribution of the laser pulse. Because the electrons don t experience the full 2 J of laser energy in 6 ps, the effective a L is smaller than what would be calculated by (10), a L =0.69. This value of the undulator parameter (a L =0.38) is still fairly large and its effects may not be negligible in the experiment assuming these laser parameters are met. The opportunity for error between simulation and experiment due to this will be systematically determined and discussed in the experimental section Angular Distribution The figure below shows the intensity and angular distribution of the scattered photons ~2 meters downstream of the interaction point. This plot does not assume any absorption effects passing through windows and air, or quantum efficiency of the detector. 28

39 Figure 8: Simulated angular and intensity distribution of scattered photons produced by a 66 MeV electron beam colliding head-on with a linearly (x) polarized 10.6 μm laser pulse. X and Y axes are given in mrad while the color map indicates intensity by total photon count. The elliptical distribution is indicative of a linearly polarized laser in x. The entire emission angle is shown here, where photons are detectable out to a full angle of 10 mrad along x and 12 mrad in y. As discussed earlier, the characteristic FWHM full angle perpendicular to the plane of polarization (major elliptical axis) goes like 1/γ, which is ~8 mrad. The FWHM full angle in the plne of polarization (minor elliptical axis), goes like 0.635/γ, corresponding to ~5 mrad for a 66 MeV (γ=129) electron beam. Given the intensity distribution of the above figure, the simulation does correctly give these values for FWHM intensities. 29

40 2.4.2 Total X-ray Flux and Off-axis Photons The total integrated x-ray flux over all angles and energies is calculated to be ~1.1x10 9 photons for the given beam parameters. It is important to note that this is essentially 100% BW, where all the red-shifted photons off-axis are being summed over. Looking only on-axis within a 1 mrad full angle, there are ~2x10 7 photons. This aspect is commonly overlooked when quoting total flux for ICS sources, yet is relevant information for many user applications as it provides the possibility for obtaining a partially coherent, near-monochromatic source by using only a pinhole, assuming the bandwidth from 3D effects is small. The contribution to bandwidth from off-axis photons is ~0.4% within 1 mrad (0.5 mrad half angle). A plot of spectral density (photons/ev) for various acceptance angles is shown below and highlights this characteristic of ICS. Figure 9: Spectral density vs. photon energy for various acceptance angles: 0.5 mrad (red) to 10.0 mrad (gray). It is clear that as the acceptance angle is increased, more red-shifted photons 30

41 are included in the integrated spectrum and the effective bandwidth is greatly increased. It should be noted that this plot was generated for the case of an energy spread of Δγ/γ=1.0% and γ=127 (65 MeV) Bandwidth from 3D Effects This section will focus only on bandwidth incurred due to the physical aspects of the colliding beams, so we will limit our analysis to photons within a 1 mrad acceptance angle on-axis. As discussed earlier, the major sources of bandwidth for ICS photons tend to be from finite angles in the electron beam and laser bandwidth. The latter is especially true for very short pulse, high power lasers such as tabletop CPA Ti:S systems, where <150 fs pulses are common and can start having nonnegligible effects on the scattered photon bandwidth. For long pulse and wavelength, high energy lasers like CO 2, laser bandwidth plays a smaller role and there is more dependence on the quality of the electron beam. Plotted below is the source bandwidth assuming negligible effects from the electron beam (i.e. ε=0 and Δγ/γ=0). This demonstrates that for parameters at BNL the laser focus and pulse length (bandwidth) play a minor role in bandwidth contribution, compared to the electron beam. Including the laser focus only very slightly increases the spread and adds a small red shift. 31

42 Figure 10: Laser-induced bandwidth. Electron beam emittance and energy spread are set to zero for this simulation in order to more accurately resolve bandwidth effects from the laser. The finite laser pulse length (6 ps) increases the source bandwidth by ~0.3%, while not including the plane-wave approximation only negligibly increases the bandwidth. The Gaussian bandwidth distribution is indicative of the corresponding Gaussian temporal (frequency) distribution of the laser. It is obvious from the preceding figure that the source bandwidth for this particular set of beam parameters is dominated by the electron beam qualities. Illustrated below is the effects of beam angles and energy spread of the electrons on the source bandwidth. Beam angles are 50% (ε =1 mm-mrad and ζ =60 μm) and 200% (ε =4 mm-mrad and ζ =15 μm) that of default while energy spread is set at realistic levels above and below (1% and 0.1%). It is seen that for the default parameters, the bandwidth due to energy spread is close to that due to beam angles, evident by the faint low energy tail. When the energy spread is reduced to 0.1%, the 32

43 tail becomes very obvious and the bandwidth is dominated by beam angles. Decreasing the emittance or increasing the spot size relaxes the beam angles (eqns. 21 and 22) and the energy spread of the electron beam starts to take over, shown by the Gaussian distribution, loss of the low energy tail, and extension to higher energies. An increase in beam angles results in red-shifting and a larger tail. Figure 11: Electron beam induced bandwidth effects. A plane-wave approximation has been assumed in the simulation due to source bandwidth being primarily influenced by qualities of the electron beam. 33

44 Figure 12: Effect of electron angles on source bandwidth. Figure 13: Effect of electron beam energy spread on source bandwidth. 34

45 The large increase in low energy photons for the cases of higher emittance and tighter focused electron beam, are expected due to an increase in electron angles at the interaction point. More electrons are emitting radiation at angles off-axis of the direction of propagation (for both electrons and radiation). The radiation emitted at angles by individual electrons has the same characteristic Lorentz contracted cone, where they peak in photon energy on-axis but are red-shifted off-axis. The redshifted parts of these cones blend in with the cones of radiation emitted by electrons with small or no angles, red-shifting the entire observed spectrum and creating the long, low energy tails. It is also true, however, that the high energy photons that were on-axis for the large angle, radiation-emitting electrons now lie in the off-axis, redshifted regions of the clean spectrum. Thus, the bandwidth over all angles increases and cannot be remedied by angular selection, such as with a pinhole. This shows the importance of high brightness electron beams of very low emittance and modest focusing schemes in creating a small bandwidth ICS source. Increasing the beam size results in smaller angles and a decrease in bandwidth, but also reduces the flux. The comparison between default and 0.1%spread shows the strong influence that the energy spread of the electron beam has on the bandwidth when the beam angles are relatively small; the shape of the distribution is almost completely dominated by the energy spread and the characteristic low-energy tail from beam angle effects is no longer resolvable. Looking at the spectral density for the default beam parameters, 50% of the total photons lie within a bandwidth of ~2.0%. This increases to ~3.0% in the case of 35

46 Δγ/γ = 1.0% (compressed beam energy spread). Due to the step size used in the simulation, there is an inherent error of ±0.4% bandwidth. These numbers agree closely with the bandwidth calculated using eqns The bandwidth could be reduced further by improving the energy spread and selecting only a slice of the electron beam by masking it transversely in a dispersive section of the beamline (the F-line at BNL ATF). While this would reduce the total flux, it would decrease the bandwidth proportionally more, increasing the peak brightness Time Profile As was covered in an earlier section, the electron bunch length primarily determines the x-ray pulse length for a head-on interaction, and this is verified through simulation in the figure below. Figure 14: Intensity (photons/mrad 2 /s) distribution of the x-ray pulse time profile. Compression of the electron bunch from 4 ps to 300 fs results in equally short x-ray pulses and greater 36

47 intensity. It should be noted that bunch compression using a magnetic chicane, as is done in the experiment, increases the electron beam energy spread and therefore also the bandwidth Peak Brightness Using eqn. 25, we can now calculate the source peak brightness. The source size was found to be ζ source = 22 μm (in both x and y) and because we are restricting the accepted angle to θ acc = 1 mrad, the flux is actually N T = 2x10 7 photons. For the τ s = 4 ps pulse (BW~2.0%) the resulting peak brightness is B peak = 4.1x10 19 photons/s/mm 2 /mrad 2 (in 0.1% BW). This is increased by almost an order of magnitude, to B peak = 3.6x10 20, when considering the τ s =300 fs pulse and corresponding bandwidth increase (BW~3.0%). Shown below is a plot of various light source facilities with their peak brightness as a function of photon energy, followed by a summary table of the simulated source characteristics. The ICS source at BNL ATF approximately covers the shaded region in the plot, making it comparable to the APS 6-8 GeV wiggler radiation sections. 37

48 Figure 15: A survey of light source facility peak brightness as a function of photon energy. The simulated ICS source (BNL ATF) lies approximately in the shaded region, where the brightness rivals that of the APS wiggler sections. The ICS source is also capable of pulses a few hundred femtoseconds long, much shorter than that of synchrotrons and without the need to employ inefficient pulse slicing techniques. ICS Source Parameter Total flux (N T ) Photon energy (E s ) Value 1x10 9 (2x10 7 ) photons 7.8 kev Bandwidth (0.5N T ) (BW tot ) 2.0/3.0% Pulse length (τ s ) Source size (σ s ) Acceptance angle (θ acc ) 4 ps/300 fs 22 μm 8 mrad (1 mrad) 38

49 Peak brightness (B peak ) B peak =4.1x10 19 /3.6x10 20 ph/s/mm 2 /mrad 2 in 0.1%BW Table 2: Summary of ICS source parameters as simulated using the 3D frequency-domain code and assuming beam parameters of the ATF (Table 1). The reduced total flux down to 2x10 7 photons is due to an acceptance angle of 1 mrad, which is what is used in the calculation of B peak for both τ s =4 ps and 300 fs. 2.5 Diagnostic Foil Now that the source characteristics have been determined through simulation, we need a method of verifying the parameters in experiment, particularly the spectral and angular distribution. However, checking our experimental diagnostic through simulation will provide a platform for more thorough analysis of data. Spectrometers designed for analyzing soft x-rays in the 4-10 kev range are not inexpensive. They can cost thousands of dollars and require known sources for calibration. We wanted to develop a method of analyzing the spectral content of our source without spending this kind of money, yet still have the confidence to make a claim on the central frequency and bandwidth. This required a process which was highly photon energy dependent and which itself had a very small bandwidth, so as to be able to resolve bandwidths less than 1% (< 80 ev). Nature provides us with such a process in the form of photoelectric absorption at an elemental K-edge. 39

50 2.5.1 K-edge Characteristics When a photon has an energy just above the binding energy of an elements K- shell electrons, a resonant absorption occurs where the probability for a photon being absorbed is very high. Photons with energies below the K-edge have a much smaller chance of being absorbed [27]. Choosing a thin foil of a specific thickness and material can greatly attenuate photons above the K-edge and act as an effective lowpass filter. This transition can occur over a very narrow energy range of less than 1 ev (BW<0.01%), providing the energy resolution necessary to analyze the ICS source. As shown earlier, the beam parameters at the ATF allow for x-rays with energies up to 9 kev. A comfortable operating energy for the electron beam is around 66 MeV, which produces ~ 7.8 kev photons. This is in the area above the iron K-edge, with its absorption edge at kev. There are other elements with K- edges close to an energy obtainable by our beam parameters: titanium (4.966 kev), vanadium (5.465 kev), chromium (5.989 kev), manganese (6.539 kev), cobalt (7.709 kev), and nickel (8.333 kev) [28]. However, if we are analyzing the source by passing it through a thin foil, we need an element which can be easily (and cheaply) made into a foil. Of the elements above, titanium, iron and nickel are the best choices. Foils made from these elements are relatively cheap and are quite robust and easy to handle, making them desirable for use in experiment [29]. Plotted below are transmission curves for iron and nickel foils [30], with silver also plotted 40

51 for comparison (as it has no K-edge near our photon energy). The table shows how quickly the transition occurs in the case of the 50 μm iron foil. Figure 16: Transmission curves for various thin foils. Elements with a strongly absorbing K- edge (iron and nickel, above) can act as low pass filters by only allowing transmission of photons with energies below the K-edge. Photon Energy (ev) Transmission x x x x x x x 10-7 Table 3: Detailed photon transmission for a 50 μm iron foil. There is a drop in transmission by 10-6 within a 0.2 ev interval. This aspect makes for a high resolution energy diagnostic (better than 0.01%). 41

52 2.5.2 Obtaining the DDS Using Foil These properties demonstrate how a foil with a K-edge near the source energy can be used as a very effective low-pass filter. If we now consider that the photon energy of the ICS source has the same dependence on angle as the undulator radiation (eqn. 6), that is photons are red-shifted when observed further off-axis, then if the source is tuned to be above the K-edge of a foil, all photons on-axis should be absorbed and those lying off-axis will transmit. This will create a hole in the transverse profile of the source. As the central energy of the source increases, a larger hole will start to appear as more red-shifted photons off-axis begin to have energies higher than the K-edge and are thus attenuated. Plotted below is an example of the simulated transverse profile and the resultant spectrum of the source after passing through a foil with a K-edge near the central energy. Figure 17: a) Angular intensity distribution of simulated ATF ICS source after passing through a 50 μm iron foil. On-axis photons above the K-edge are absorbed while red-shifted photons observed off-axis lie below the K-edge and are transmitted, forming lobes perpendicular to the 42

53 laser polarization. Analysis of the image shows photons at the intensity maximum (lobes) have an energy of ~7 kev. b) The same full angle ICS source spectrum before (top-blue) and after the foil. The absorption curve of the foil is clearly evident in the resultant transmitted spectrum with the sharp absorption line at 7.1 kev. Using this highly energy dependent diagnostic we can visualize the DDS of the ICS source; giving a spectral mapping of the photons over the emission angle. A void of photons indicates an angle-energy correlation with these photons (within the null) being above the K-edge. However, we can also see from simulation that hot spots, or lobes, appear in the image after passing through the foil. No such nonuniformity exists in simulation for the intensity profile prior to passing through the foil. As was covered earlier and shown in figure, for a linearly polarized laser the angular distribution is elliptical with the major axis being perpendicular to the polarization vector. The existence of these hot spots must indicate a position in angle where there are photons just below the K-edge (E s <7.1 kev) and are thus maximally transmitted. Accordingly, the distance between these lobes should increase/decrease if beam parameters are altered such that the central energy is changed, e.g. increasing/decreasing the electron beam energy. Substituting a foil with a higher K- edge (e.g. iron to nickel) would result in an image similar to lowering the central energy, decreasing the lobe separation as more on-axis photons are transmitted Bandwidth Measurement Using Foil Because the foil K-edge has practically zero bandwidth compared to the ICS source, it can be used in conjunction with a flux diagnostic to determine the relative 43

54 bandwidth of the x-rays. In theory, a monochromatic source with a pinhole on axis (to remove red-shifted off axis photons) will be almost completely attenuated after passing through a foil with a K-edge below the central photon energy. The electron beam energy can be tuned such that the central energy is less than the K-edge and all photons are transmitted. Now if this source is considered to have finite bandwidth, one can project this bandwidth using a flux diagnostic and incrementally scanning the electron beam energy such that the central photon energy goes from below to above the foil K-edge. The measured transmitted flux will drop off quickly for low bandwidths, while for larger bandwidths, the interval of scanned electron beam energy will be greater and the transmitted flux curve will be less steep. This process is demonstrated in the figure below, where only the e-beam energy spread has been changed to affect the source bandwidth. 44

55 Figure 18: Simulation of source total flux vs. electron beam energy after passing through the 50 μm iron foil. The shape of the source spectral distribution affects the transmission curves above. There are more high energy photons in the distribution for larger energy spreads (see previous figures). These photons are then absorbed first as they lie above the K-edge for lower central energies. This is especially evident in the above plot for 2.0% energy spread, where a significant number of photons are absorbed before E s =7.11 kev. Because the beam energy is being scanned along the foil transmission curve, the narrower the bandwidth the faster the transmission increases as more photons lie around the central energy, which is getting closer to the K-edge. The flux strongly decreases for narrower bandwidths when passing over the K-edge and the e-beam energy range (source central energy scan) necessary to attenuate most photons is smaller. A completely monochromatic source would have a scanned flux curve (above) matching that of the foil transmission curve. Under the same criteria used to determine the bandwidth, we are interested in the region about the spectral peak where 50% of the photons exist. This is where the flux curve (above) starts to fall sharply due to the majority of photons lying above the K-edge, thus it is here attention should be paid in extrapolating the bandwidth. The slope of the line tangent to the steepest part of the flux curve can be related to the bandwidth of the source. Assuming a perfectly monochromatic source with a central energy just below the K-edge (i.e. E s 7.11 kev), the measured flux after the foil will 45

56 be 2.8x10 6 photons (see figure, T=0.13). This is the assumed initial flux as all photons experience this attenuation before being strongly absorbed by the K-edge. Applying the 50% criteria for photons along the tangent, this number becomes 1.4x10 6 photons. If multiplied by the inverse of the slope (photons/mev) -1 the result is the scanning range (in MeV) of the electron beam energy necessary to attenuate 1.4x10 6 photons, or 50% of the original flux. The span of central photon energies covered by this e-beam energy range is the bandwidth of the source. For the default parameters (0.5% spread), the slope is 1.65x10 6 photons/mev. This inverse multiplied by 1.4x10 6 photons yields a beam energy range of ΔE e =0.85 MeV. Evaluating the corresponding photon energies about the K-edge (e.g. 63 MeV to MeV) and taking their difference yields ΔE s 190 ev, or BW tot =2.7%. Applying the same method to 1.0% spread yields a slope of 1.19x10 6 photons/mev, corresponding to ΔE s 270 ev or BW tot =3.7%. These values for bandwidth are both slightly higher than what was determined earlier (2.0% and 3.0%, respectively) by 0.7%. The initial total flux for all three cases is the same, but it increases as the e-beam energy is raised and the emission cone is narrowed (by ~16% from 61 to 66 MeV). The resultant increase in measured flux after passing through the foil is negligible (2% over the entire range, or 0.8% near the K-edge, MeV). The inclusion of red shifted, off-axis photons slightly contributes to an increased bandwidth. A change in energy of ΔE e =5 MeV results in Δθ rad =0.64 mrad, or a half angle of Δθ obs =0.32 mrad. Inserting this into equation 12 gives a red shift of 11 ev, amounting to an increased bandwidth of ~0.2% at this central photon energy. 46

57 Error in bandwidth (±0.2%) also exists due to the step size used in the simulation. The combination of these uncertainties results in a calculated bandwidth very close to that found by direct analysis of the source spectrum before the foil. This demonstrates the feasibility of using a K-edge foil as a bandwidth diagnostic. Additionally, the ends of the plot also contain relevant information. The tails of the measured flux curve are related to the tails of the spectral distribution. Because these tails don t usually contain more than 50% of the photons, we are not concerned with them in calculating the bandwidth, although they are useful in determining the shape of the spectrum. The use of a thin foil as an energy diagnostic has been shown through simulation to be a very simple, yet effective tool in unfolding the angular spectrum and bandwidth of an ICS source. However, there are many parameters which must be met in experiment in order to actually produce a source with the characteristics described in this chapter. We will next discuss the ATF facility and the experiment in detail and compare measurements with simulation. 3. Experiment 3.1 The Accelerator Test Facility The Brookhaven National Laboratory Accelerator Test Facility (BNL ATF) is a program dedicated to proof-of-principle experiments conducted by in-house researchers as well as users from other institutions. The existence of a 70 MeV high 47

58 brightness electron linac and TW-class CO 2 laser system allows for unique opportunities to study the interaction of electron beams with very high intensity laser pulses and laser-induced plasma wakes. It is this aspect which makes ATF a natural candidate for studying inverse Compton scattering. There have been many experiments done prior at ATF investigating inverse Compton scattering. First photons were made in 1999 with a much lower laser power (600 MW) than what is currently available. Studies of the effect of laser/e-beam timing and overlap at the interaction point (IP) were conducted with the conclusion that these were both critical parameters in the optimization of photon flux [31]. After extensive laser upgrades, a peak laser power of ~100 GW and a tight laser focus (w o = 30 μm) allowed for a very intense laser field at the IP and the study of nonlinear effects of ICS. As a result, in 2005 the second harmonic was observed for the first time with a record number of photons in a single shot produced for ICS (~ 2x10 7 ) [25] and the prospects for ICS as an inexpensive, table-top x-ray source experimentally demonstrated Electron Beamline The electron beamline at ATF consists of a 1.6 cell photoinjector with a cavity frequency of GHz. Photoelectrons are produced by a frequency quadrupled Nd:YAG laser (λ=1064 nm to λ 4 =266 nm) with a 10 ps pulse length striking a magnesium photocathode at the back of the (photoelectron) gun. A high power S- band klystron delivers MW s of RF power to the gun which fills with a 100 MV/m 48

59 longitudinal electric field and accelerates the 4 ps, 300 pc (up to 2 nc) electron bunch to a few MeV. Subsequent acceleration by linacs and careful transport down the magnetic lattice of the beamline results in a MeV beam at the IP capable of being focused down to 20 μm [32]. Pictured below is an example of the photoinjector used and a schematic of the RF-laser timing system. Figure 19: (Left) ATF photoinjector and (right) linac synchronization diagram High Power CO 2 Laser The CO 2 laser pulse is sliced by a pulse split from the photocathode driver, so allows for nanosecond synchronization between the laser and electron bunch. Using pulse slicing via a semiconductor switch and Kerr cell, 6 ps pulses with up to 6 J each can be produced, resulting in peak laser powers as high as 1 TW [32]. This high energy, high power system stresses the cavity optics and discharge capacitors in the final amplifier and allows for a pulse repetition rate of only 0.03 Hz (1 shot every 30 49

60 seconds). The 10.6 μm laser pulse is transported to the experimental hall via 3 dielectric or copper mirrors and enters the interaction chamber through a lowabsorbing salt (KCl) window. It is then focused by a 90 o off-axis parabolic (OAP) mirror and interacts with the counter-propagating electron beam at its waist. A schematic of the laser system is shown below. Figure 20: CO 2 laser room and table showing optical path and amplifier locations. The laser exits to the experimental hall behind radiation shielding, where the electron beamlines reside. Good focusing of both the laser and electron beams is required to optimize flux and reduce bandwidth effects. Astigmatic focusing of the laser due to the 90 o OAP must be minimized in order to produce the design laser field at the IP. After the laser is relieved from the chamber by a second mirror and salt window, the waist at 50

61 the IP is optically reconstructed and imaged onto an IR-sensitive, pyroelectric camera in order to optimize focusing before making high power shots. 3.2 ICS Setup Figure 21: Diagram of the ICS interaction chamber Alignment and Timing Procedure As has been demonstrated by ATF in previous experiments, precision alignment between electron and laser beam at the IP is critical for maximum photon flux [ ]. Because the axis of the electron beam is dictated by the magnetic axis (and therefore, mainly physical axis) of the focusing quadrupoles, a HeNe laser 51

62 representing this axis is first established. This alignment HeNe starts far upstream and is aligned past the interaction chamber, traveling through 2 mm holes in the parabolic mirrors for passing the electron beam and scattered x-rays. This e-beam HeNe is counter-propagating with the CO 2 laser and acts as a reference vector for the required e-beam position on monitors all along the beamline. A remotely insertable alignment probe is located at the center of the interaction chamber and includes a phosphor screen, 150 μm pinhole, and germanium wafer (for synchronization, discussed later). The pinhole is aligned to the e-beam HeNe and thus determines the interaction point. After the pinhole position has been set, the CO 2 laser must be focused and transported through the pinhole. Watching the transported beam on the pyrocam following the re-imaging optics allows for fine tuning of the laser vector through the pinhole. This alignment procedure assures that, assuming the e-beam is also transported through the pinhole, the laser and electron beam will overlap transversely. However, due to the short pulse lengths of both the laser and electron bunch (6 ps and 4 ps, respectively), it is not guaranteed the beams will see each other in time without synchronization of picosecond resolution. While signals from strip line monitors and fast photo diodes allow for subnanosecond timing, other methods must be employed in order to have synchronization at the few picosecond level. This is the purpose of the Ge-wafer. When the electron beam hits the wafer, a semiconductor plasma is formed [33]. This plasma is reflective to the 10.6 μm laser light and almost fully attenuates the 52

63 Ratio of transmitted to reference signal [a.u.] transmitted signal. If the electron beam arrives after the laser, then there is no effect and the laser transmits normally. This allows one to watch the transmitted intensity and scan a laser delay arm towards later arriving pulses, witnessing where exactly the e-beam starts to arrive before the laser and creates the reflecting plasma, thus being synchronized in time at a certain point in space (the pinhole) [34]. Because the plasma recombination time is ~7 ns, this scan must start with an early arriving laser pulse. Below is an example of data taken at the Neptune Laboratory for this synchronization method micron transmission vs. e-beam arrival Time [ps] Figure 22: Plot of laser transmission through a germanium crystal versus e-beam arrival time. The sharp drop in transmission is indicative of electrons impacting the crystal and creating a plasma opaque to the laser photons. 53

64 Once synchronization has been determined, the probe is removed and high power laser shots can be made for x-ray production. After an ICS interaction, both the electron beam and x-rays travel together through a hole in the focusing mirror. The e-beam is then dumped by a dipole spectrometer into a Faraday cup or phosphor screen where the charge or energy of the interacted electrons is measured. The x-rays continue to propagate through a 250 μm beryllium window, separating the beamline vacuum from air. It is after this Be-window where x-ray diagnostics are placed to analyze the ICS-produced photons X-ray Diagnostics Standard CCD cameras and photodiodes are inadequate imaging and flux diagnostics for x-rays. Typically, the equipment is much more expensive, yet necessary for accurate characterization of an x-ray source. For this experiment, an inhouse silicon diode detector, previously calibrated on an NSLS beamline, was used to measure the total x-ray flux while a commercially available microchannel plate (MCP) image intensifier imaged the transverse profile of the scattered photons. The silicon diode detector works on the principle that when a photon of sufficient energy strikes the silicon detector surface, electron-hole pairs are created and charge accumulates [35]. This charge is interpreted by electronics and displayed on an oscilloscope as a voltage signal. Depending on the circuit elements used (i.e. capacitors), different sensitivities can be achieved and a relation between voltage and total deposited energy (in ev) reveals the absolute photon flux. The detector was 54

65 operated in two modes (standard and sensitive) and had different calibrations for each. The standard mode used a 2200 pf capacitor in the circuit and was calibrated to 5.9x10 7 ev/mv. The sensitive mode (no capacitor) was used when looking at only the on-axis photons passing through the pinhole and was calibrated to 8.2x10 6 ev/mv [36]. A voltage readout from the scope and the assumption of a central energy for a single photon yields the total flux on the detector. The detector is mounted on a motorized translation stage to allow removal prior to imaging on the MCP and has a sensitive diameter of 25 mm. The MCP image intensifier is a high voltage device, operating in a similar fashion to a photomultiplier tube. It consists of a lead-glass wafer in which micronsized channels are made at predetermined angles and spacings which affect the overall detection efficiency. Photons of sufficient energy (few ev) striking the inner walls of the channels create photoelectrons which are then accelerated by a kv electric field. These now energetic electrons continue striking the inner surface of the walls, creating more electrons which are subsequently accelerated. This avalanche effect allows for very high gains to be achieved and is suitable for high and low flux applications. After leaving the channel, the electrons are then accelerated onto a fiber-optically coupled phosphor screen which is imaged using a standard CCD camera. Because the MCP is essentially an electron multiplier, it requires a moderate vacuum environment (at least <10-3 torr) to function efficiently and maintain its design lifetime. A schematic of the gain mechanism and plot of the detection efficiency is shown below. It can be seen that for our photon energy (wavelength ~1 55

66 Angstrom), the detector response is nearly linear with an efficiency of a few %. This is the ability to detect the initial photon by creating a photoelectron. For our chevron (two-wafer) MCP, a maximum of 2.4 kv can be applied, while a maximum of 6 kv can be applied to the phosphor screen. This amounts to a variable gain of up to ~2x10 7 over the 40 mm detection diameter [37]. Figure 23: (Left) Amplification mechanism of microchannel plate detector. (Right) Detection efficiency of MCP; for our wavelength (~1 Angstrom) we have a few % efficiency. The various diagnostic foils (50 μm iron, nickel, and 20 μm silver) are mounted on remotely controlled mechanical flippers with a clear aperture of 20 mm. This allows us to switch between K-edges and the control foil (silver) to verify the strong absorption dependence on central photon energy. These are immediately followed by a 1.3 mm pinhole mounted on a 2-axis motion system. The diameter and longitudinal position (z=1.3 m from IP) of the pinhole determines a 1 mrad acceptance angle. The precision motion system remotely allows for exact placement of the pinhole about the central axis of the source. 56

67 Because the motion devices needed enough area to operate and were not built for a vacuum environment, they resided in air following the electron spectrometer. It was therefore necessary to reestablish vacuum for the MCP using another section of beam pipe and 250 μm Be-window. This slightly decreased the photon flux seen on the MCP and increased the propagation distance of the x-rays to 1.93 meters. Given the source opening angle (~8 mrad), this distance was sufficient to observe the full transverse profile on the 40 mm detection area of the MCP. A schematic layout of the x-ray diagnostics table is shown below. Figure 24: Layout of the x-ray diagnostics section following the electron spectrometer. 57

68 250 μm Be-window Insertable Ni, Fe, and Ag foils MCP image intensifier (CCD camera not pictured) 1 mrad pinhole on remote 2-axis control Remotely insertable Si-diode detector 250 μm Be-window Figure 25: Photograph of the x-ray diagnostics table at the end of beamline Data and Results 4.1 Flux Measurements After performing the alignment and timing procedure described above, first shots were taken at 62 MeV and flux measured with the Si-diode detector to verify ICS photons were actually being created. The signal was maximized by fine tuning beam synchronization using the CO 2 delay arm and rastering the e-beam across the laser waist to find the optimal transverse position. The measured signal after optimizing was ~2.0 V, corresponding to a total deposited energy of ~1.2x10 11 ev. Assuming a central photon energy of 7 kev, this results in ~2x10 7 photons. This is 50 times less than predicted by simulation. However, simulation is summing photons 58

69 over all energies and angles and is not accounting for attenuation through the Bewindow and ~0.3 m of air. The laser beam waist is also slightly astigmatic and larger (w o 70 μm) than the design w o =60 μm, resulting in reduced flux (~9x10 8 photons) compared to simulated parameters. If attenuation through the window and air (T~0.5 at 7 kev) is accounted for, the flux becomes to ~4x10 7 photons. The 2 mm hole in the OAP (focal length =25 cm) could also be a source of losses as it only passes a 1ζ FWHM x-ray beam size. This also assumes the electron beam vector (dictating the x- ray vector) is exactly on axis of the hole and there is no clipping. 4.2 Angular Measurements Once the signal was maximized given our experimental beam parameters, the Si-diode was removed so the source could be imaged by the MCP. Gain settings of the MCP are dependent on the flux hitting the detector and, in addition to the camera, determine the dynamic range of the image. Shown below is the image taken for no foil and 62 MeV at voltage (gain) settings of phosphor screen=4.3 kv and MCP=1.4 kv. The expected ellipticity for a linearly polarized laser is evident. The tilt is due to y-polarization of the laser at a small angle with respect to the vertical (perpendicular floor surface). Given the detector distance and image size, an opening angle of 8.2 mrad (major axis) is calculated, in very close agreement with theory. 59

70 Figure 26: Image of source taken with MCP image intensifier for e-beam energy of 62 MeV. 4.3 DDS Measurements Central Photon Energy Because the central photon energy is expected to be <7.1 kev for this e-beam energy, there is no expected energy-angle correlation in the image after passing through the iron foil. This was verified as the only resultant effect of the foil on the source was the preferential attenuation of lower energy, off-axis photons, as is expected given the transmission curve of the iron foil below the K-edge. The energy of the e-beam was then increased to 72 MeV to guarantee the central photon energy was above the iron K-edge (and even the nickel K-edge of 8.33 kev). Images were taken for iron, nickel, and silver foils at this energy and are shown below for gain settings of phosphor=4.4 kv and MCP=1.6 kv. 60

71 Figure 27: Source images made for a 72 MeV e-beam after passing through iron (left-slightly saturated), nickel (right), and silver foils. The larger null and lobe separation between iron and nickel is indicative of different K-edges and demonstrates the energy-angle correlation of the ICS source. The apparent removal of the ellipticity after the silver foil is due to greater attenuation of those off-axis photons along the major axis. The iron foil image indicates the central photon energy for this e-beam energy lies well above the iron K-edge, attenuating even far off-axis photons and only transmitting strongly red-shifted photons below the K-edge. The nickel foil, with a K-edge ~1.2 kev higher than iron, transmits fewer off-axis photons, resulting in a decreased lobe separation and smaller on-axis null. The nickel foil image actually shows evidence of the finite bandwidth of the source due to the leakage of photons 61

72 on the null. For control, the silver foil was inserted instead and the resultant image shows no dependence on angle other than the same preferential attenuation of off-axis photons as for the case (E e =62 MeV) with central energy below the iron K-edge. Now that the effect has been confirmed, attention is drawn to the validity of equation 12 in its ability to predict a red-shifted photon energy for a given observation angle. The electron beam energy was scanned from 64 to 72 MeV and the resultant source image taken after passing through the iron foil. The source can be seen to go from a central energy below the K-edge (indicated by lack of null) to well above the K-edge at 72 MeV. The increased lobe separation as the beam energy is raised is evidence of a changing central energy. Images of this scan are shown below for chosen e-beam energies. 62

73 Figure 28: ICS source after passing through Fe-foil for e-beam energies of 64 MeV (top left), 65 MeV (top right), 66 MeV (bottom left), and 70 MeV (bottom right). Due to the DDS of the source and strong K-edge absorption, areas of the image where intensities are high will be at observation angles where the central energy is red-shifted to 7.1 kev, resulting in maximum transmission of the photons. Performing the same scan in simulation shows a dominance of ~6.9 kev photons at the peak lobe intensity, regardless of e-beam energy. Plotted below is the experimentally measured observation angle (above figures) versus e-beam energy compared with that found from simulation and equation 12, assuming a photon energy of 6.9 kev. 63

74 Figure 29: Plot of the lobe observation angle and corresponding e-beam energy. Simulation indicates a maximum of ~6.9 kev photons at the lobe peak intensities. The photon energy was kept constant and e-beam energy adjusted for a given angle to produce the plots from the undulator equation (eqn. 12). Simulation was red-shifted by an appropriate amount (~290 ev) to fit measured data and corresponds to a L =0.29. The lobe positions generated through simulation fit the measured data quite well after introducing a laser vector potential-induced red-shift of ~290 ev, assuming a L =0.29 in equation 12. According to parameters within our control, this represents the necessity for a higher e-beam energy, ΔE e =1.3 MeV, in order to regain the same lobe separation.. Because the simulation does not include this effect in its calculations and we expect a L =0.38 for our laser design parameters, it is not unreasonable to suppose that the discrepancy with measurement is this red-shift. Slightly astigmatic laser focusing and a larger laser waist at the IP are probable explanations for the decrease in a L from design. 64

75 4.3.2 Calculated Bandwidth The existence of bandwidth in the simulation could explain the difference with that of the plot generated from the undulator equation. It takes a higher e-beam energy to compensate for photons on the lower-edge of the spectrum, before the formation of any lobes can be resolved. Once the bandwidth is accounted for, lobe separation increases quickly until the e-beam (source) is at an energy where the observation angle is large enough to not be affected by bandwidth and the curve starts to follow that predicted by the undulator equation (for a monochromatic source). The energy offset of the zero-null point between simulation and a monochromatic source is close to the bandwidth found using the transmitted flux through the foil. The energy difference above is ΔE e =0.93 MeV (ΔE s =205 ev), corresponding to BW tot =2.8%, where the flux method gave 2.7%. In simulation, there is also a redshift of ~60 ev on top of the bandwidth increase due to the finite angles in the beam, which shifts the zero-null e-beam energy to higher values in comparison with the undulator equation. Subtracting out this red-shift yields a zero-null difference, and thus bandwidth, of ~2.0%, the same as the directly evaluated bandwidth of the simulated spectrum. Plotted below are intensity lineouts along the major axis of images taken near the zero-null point (64-66 MeV, above). Because the MCP has a linear response, such that a region with twice as many incident photons will have twice the intensity 65

76 (for an unsaturated image and constant gain setting), it is accurate to assume that a null with 50% the intensity of the lobes contains 50% of the photon count found at the lobes. The angular distribution below the K-edge indicates higher flux on-axis, therefore there are less than 50% of the original on-axis photons for our assumption. These lost photons are being absorbed because they have energies above the K-edge and the remaining ones have energies below (resulting in transmitted intensity). A value for the intensity on-axis which is much less (<50%) than the lobes is an indication that for this e-beam energy, the majority of photons are being absorbed and therefore lie above the K-edge. For example, in order to create a 1 mrad (full angle) null with a monochromatic source, the interval of e-beam energy one would have to change by to go from the zero-null point to the 1 mrad hole is ΔE e =0.12 MeV (~0.2%), only enough to compensate for off-axis red-shifting. In experiment, one must also compensate for the source bandwidth by increasing the e-beam energy such that the spread of lower energy photons leaking through the foil are raised above the K-edge and absorbed. This provides a method for claiming a bandwidth using the recorded images. The increase in e-beam energy required to go from zero-null (intensity=i max ) to a 1 mrad null with I 0.5I max is effectively the bandwidth 66

77 67

78 Figure 30: Intensity lineouts for MeV from Figure 27. The increase in null size is evidence for the near total attenuation of source photons when the central energy is raised above the iron K-edge. For the image taken at 65 MeV, the approximate width of the null (at 0.5I max =400 a.u.) is 7 pixels or 0.76±0.11 mrad (using 210 μm/pixel and 1.93 m detector distance). This means that over almost 1 mrad, more than 50% of the original (below K-edge) photons are now above the K-edge due to the increase in e- beam energy of 1 MeV, from 64 MeV (zero null). This 1 MeV increase represents a central energy increase of ~220 ev, or 3.0% bandwidth. At 66 MeV, the width of the null (I=400) is ~20 pixels or 2.18±0.11 mrad. At this energy, the bandwidth is fully compensated for and there are a negligible number of photons leaking through the foil over 1 mrad. This 2 MeV shift represents an increase in central energy of ~450 ev, or 6.2% bandwidth (although this is more than twice the accepted angle of 1 68

79 mrad). This is equivalent to almost the entirety of the 1 mrad (default) spectral distribution lying above the K-edge. Because of the direct relation between angle and photon energy, the limiting angular resolution can be expressed as a limiting energy resolution; ±0.11 mrad = ±60 ev, or 0.8% error in bandwidth. If we assume that 65.3 MeV (assume 30% increase of energy increment=30% increase in angle) is necessary in order to create a 1 mrad null, then we can say the total increase in e-beam energy required to compensate for the bandwidth is ~1.3 MeV, corresponding to ~290 ev or 4.0±0.8% bandwidth. This is more than what is predicted by direct analysis of the spectrum (2.0%) and by the flux transmission method (2.7%). However, as was mentioned earlier, the effects of nonlinear motion (due to a L >0) on the spectral distribution is not accommodated for in simulation. If we consider analytically, using (12), the contribution to bandwidth from this effect is the same as the amount red-shifted. Because the excursion angle for the electrons is θ NL ~a L /γ, there are ICS emission cones being radiated at different angles as the electrons and laser interact, similar to the bandwidth produced by divergence angles in the electron bunch. This allows the red-shift to be thought of as a contributing bandwidth in itself and is therefore additive with any previously calculated bandwidth to produce a new total bandwidth, BW TOT expressed as, BW TOT 2 tot 2 NL BW BW, (26) where BW NL is the bandwidth due to nonlinear electron motion and red-shifting by the high laser field. As was previously discussed, there is a red-shift of ~290 ev for 69

80 a L =0.29, corresponding to BW NL =4.0% and for BW tot = 2.0%, we have BW TOT =4.5% as predicted by simulation and equation 12. If the bandwidth is dominated by the nonlinear motion in the laser field, then it is no surprise that the (supposed) energy required to offset the red-shift (as done for simulation) is the same as that needed to compensate for bandwidth, as they are produced by the same mechanism. 4.4 Peak Brightness (On-axis) After the images above were taken, the 1 mrad pinhole was inserted on the source axis and all foils removed prior to taking flux measurements with the Si-diode in the sensitive detection mode. At 66 MeV, the measured flux was ~1x10 6 photons. Assuming attenuation losses in air and the Be-window, this becomes 2x10 6, still an order of magnitude less than the 2x10 7 photons predicted by simulation. For the experimentally measured flux and bandwidth and assuming the other original source parameters, the calculated peak brightness for the ATF ICS source is B peak = 2.0x10 18 photons/s/mm 2 /mrad 2 (in 0.1% BW). Following this measurement, the electron beam was sent through the magnetic chicane compressor with an increased energy spread of 1.0% in order to achieve a bunch length of 300 fs, resulting in an x-ray pulse of equal length. The measured flux with the inserted pinhole was the same, ~2x10 6 photons before attenuation, therefore the only different parameter is the bandwidth increase due to the larger energy spread e-beam. No energy scan or images were taken for the compressed beam scenario so the increase in bandwidth is calculated analytically and results in BW TOT =5.0%, a 70

81 relatively small increase due to dominance by BW NL. The peak brightness for this sub-ps x-ray pulse is calculated to be B peak = 2.4x10 19 photons/s/mm 2 /mrad 2 (in 0.1% BW). 4.5 Circular Polarization The laser polarization was switched to circular during another run and qualitative measurements made. The flux was not noticeably different and no bandwidth scans were taken, although the source was imaged and the effects of the iron foil observed. The ellipticity from the linear laser polarization was lost, as expected if the radiating electron bunch is treated as the superposition of x and y radiating dipoles. The asymmetry in the energy-angle correlation has also disappeared and results in the formation of a ring, instead of lobes, after the source passes through the foil at a central energy higher than the K-edge. This is due to a smaller magnitude of axial deflection by the electrons in the laser field along a given polarization vector. Therefore, there is no increased propagation distance, and hence red-shift, between the transverse axes. The result is that the spectral and intensity distributions are the same for x and y. Shown below is an example of the source images taken after passing through the iron foil for a circularly polarized incident laser. 71

82 Figure 31: Image of circularly polarized Compton x-rays after passing through the 50μm iron foil. There is evidence of clipping on the left side of the image, most likely due to the 2 mm hole in the laser mirror. Due to laser power jitter, the flux measured on the Si-diode varied. This, with a low repetition rate, made the flux dependent bandwidth measurement (figure 18) very difficult as it required a scan of the electron beam energy and a large data sample to accurately determine the bandwidth via this method. Therefore, it was opted to abandon taking these measurements due to time constraints. However, Poynting and photon energy of the source was stable, important for application experiments. 5. Conclusions This thesis investigated the physics and feasibility of an inverse Compton scattering light source through simulation and experiment. Specifically, delivered 72