Electron Sourcery. P. Musumeci UCLA Department of Physics and Astronomy. SSSEPB SLAC, July th 2013

Transcription

1 Electron Sourcery P. Musumeci UCLA Department of Physics and Astronomy SSSEPB SLAC, July th 2013

2 Acknowledgements Material from these lectures has been liberally taken from talks/papers/lectures/proceedings/notes from a large number of people which I thank and acknowledge here J. B. Rosenzweig D. Dowell X. J. Wang C. Brau J. Luiten F. Sannibale D. Filippetto B. Carlsten W. Graves P. Piot J. Schmerge K. Jensen P. Hommelhoff C. Pellegrini M. Ferrario R. Li B. Reed M. Krasilnikov F. Stephan S. Schrieber C. Vicario L. Cultrera I. Bazarov

3 Course objective Lecture 2: Generation of electron beams: physics of photocathodes, photoinjectors, alternative sources using ultra cold gases or plasmas, fundamental limits on beams phase space density. Disclaimer. Extremely wide topic. Hard to cover exhaustively in a full semester class. Impossible in 3 hours. The declared goal of the class is to increase breadth more than depth So concepts, figures, tables and references are preferred over equations and derivations

4 Outline/Syllabus Electron source applications Electron source figures of merit Cathode physics Photoemission. Thermal emittance and quantum efficiency Child Lamguir law and space charge limits Maximum achievable brightness Photoinjector gun types Beam Dynamics in RF guns Longitudinal equation of motion Transverse RF effects: rf focusing and emittance. Space charge effects Cylindrical beams Emittance oscillations Scaling laws Blow out regime, pancakes and cigars Magneto Optical Trap based ultracold sources Nanotips based e sources

5 Short wavelength FELs Progress in electron sources in the last 20 years is widely recognized as one of the enabling technologies for the XFEL development. Demands: High brightness beams Ultralow normalized emittance (~ 1 um) High current (kamp) Beam charge ranging from 10 pc 1 nc

6 High average power applications High average power FELs Soft X ray. IR THz radiation sources Beam based THz generation Energy Recovery Linacs Next Generation Light Source (LBNL) Jefferson Lab FEL (JLAB) Cornell ERL Requirements: mamp average currents MHz or higher repetition rates Low emittances

7 Electron diffraction and microscopy Dynamic Transmission Electron Microscope Femtosecond Relativistic Electron Diffraction FRED DTEM #of particles Bunch length 100 fs 10 ns Emittance 0.1 um few nm

8 Inverse Compton Scattering sources from ELI NP project Small emittances to allow focusing to micron spot sizes High charge to increase x ray yield Short bunches for ultrafast x ray pulses Repetition rate to match laser repetition rate

9 Injectors for HEP machines? Polarized electron sources Flat beams High gradient laser based accelerators Very low timing jitter for laser interaction Ultrashort bunch lengths Small emittances to fit small acceptances Plasma wave accelerator Laser driven dielectric structure 2 um

10 Particles per bunch. Charge. One of the most important parameter of a (pulsed) electron source. Peak current is not preserved since the bunch length can be controlled using compression techniques pc per bunch enable the generation of beams with smaller transverse and longitudinal normalized emittances. The resulting improved beam quality allows for shorter FEL gain lengths at a relatively moderate electron beam energy. Beams for HEP and plasma wakefield drivers require very large charges, over 1 nc 1 pc 10 pc 100 pc 1 nc For single shot electron diffraction and microscopy the number of particles per bunch should be enough to allow sufficient contrast in the diffraction pattern/image. For a diffraction pattern of a single crystal, we only need 10 5 particles. At least 10 8 particles are required to form an image. The main operational mode for X Ray FELs relies on a charge/bunch of a few 100s pc, a satisfactory tradeoff between the number of photons/pulse and a moderate transverse emittance Experiments in FELs and ERLs requiring large number of photons per pulse or very narrow transform limited photon bandwidth in seeded FEL schemes require longer bunches and hence higher charges per bunch that can approach the nc.

11 Beam brightness: early history Intuitively the peak current is an important parameter of the beam, but it is also important to be able to collimate and focus the beam. E. Ruska 1986 Nobel prize In 1939 von Borries and Ruska (Nobel prize in Physics for the invention of the Electron Microscope) introduced the so called beam brightness ( Richstrahlwert ) defined as: Ω Empirically constant along the microscope column. The smaller the spot the larger the divergence. This definition still holds today in the field of electron microscopy with peak numbers of B micr up to Amps/m 2 /sr

12 5D beam brightness The 5D brightness is often used in FEL community to compare electron sources and it is the relativistic analog of the microscope brightness 2 ~ For example it enters directly in FEL parameter The main difference with electron microscopy brightness is the use of normalized emittances to take into account relativistic effects. 2 ρ is the FEL parameter. It is important to have it as high as possible(~10 3 ), since:

13 Average and 4D beam brightness For high average power applications typically we are interested in the total amount of charge per second. For these applications people often use the 4D brightness where the longitudinal beam properties are not considered. The average 5D brightness will be B 4D f where f is the repetition rate of the accelerator. Another reason to introduce the 4D brightness is due to the development of bunch compressors which can reduce the bunch length by many times, increasing the final current (and thus 5D brightness).

14 Liouville s theorem Liouville theorem states that for Hamiltonian systems the phase space density stays constant. As long as the particle dynamics in the beamline elements (transport optics, accelerating sections) can be described by Hamiltonian functions (no binary collisions, stochastic processes, etc. ), the phase space density will stay constant throughout the accelerator. The phase space density obtained at the electron source is a critical parameter. It follows that research in optimizing electron sources is crucial in the field of particle accelerator. It makes sense to classify the various electron sources based on the 6D phase space density at the source. In practice 6D brightness is hard to measure!

15 6D beam brightness The meaningful quantity to use to describe electron sources should then be the 6D beam brightness defined as nx ny nz where V 6D is the volume occupied by the beam in the 6D phase space (x, px, y, py, z, pz). V 6D is proportional to the product of the 3 rms normalized emittances nx ny nz Neglecting factors of and m 0 c RMS emittances are conserved only when linear forces act on the distribution. There might be regions of the beam (usually the center) where the phase space density is higher. Filtering particles increases the brightness, at the expenses of beam charge. Ratio between peak center brightness and rms beam brightness typically depends on the beam distribution. (for 3D gaussian F = 1/8)

16 Brightness quantum limit Pauli exclusion principle prevents electrons from being in the same quantum state. Since the elementary quantum of phase space area is set by Heisenberg uncertainty principle, we find a quantum limit for the maximum beam brightness No beam can ever beat this limit. In practice state of the art electron sources, as we will see, do not even come close and have B 6D ~ 10 4 B quantum or worse. We can introduce the Degeneracy Factor representing the number of particles per elementary volume of phase space / M. B. Callaham, IEEE J. quantum electronics, 24:1958, 1988 ~ / 2 W. Pauli Nobel prize 1945 W. Heisenberg Nobel prize 1932

17 Number of electrons per transverse coherence area A coherent photon beam has all the particles in the same quantum state. A coherence electron beam will have degeneracy factor approaching 1 Beam coherence is important for some applications such as for example coherent diffractive imaging. In particular no coherent imaging is possible if the number of electrons per coherent transverse area of the beam is smaller than one. TEM solution is to use very long pulse (very large longitudinal emittance) to recover transverse coherence. Aberration correction Courtesy of B. Reed

18 Single electron beam brightness F. O. Kirchner, S. Lahme, F. Krausz and P. Baum. New J. Phys. 15, (2013). To avoid space charge effects, in some applications beams formed by a single electron are used. But a single electron beam does not mean a quantum degenerate beam! Brightness is still limited by the electron source type. Beam parameters in this case have statistical meaning.

19 Cathode physics Cathodes are obviously a fundamental part of electron sources. The gun performance heavily depends on cathodes. Photocathodes are most commonly used in present injector systems with one notable exception (SACLA XFEL uses a thermoionic cathode) In the lower charge regime the ultimate brightness performance of the linac is set by the cathode intrinsic emittance. In high repetition rates photo sources high quantum efficiency photocathodes are required to operate with present laser technology Advanced cathodes is an active area of research (photoassisted field emission, needle arrays, photo thermoionic, diamond amplifier, nanopatterned cathodes, ) Important References: D. Dowell et al. Cathode R&D for future light sources. Nucl Instrum Methods Phys Res A 622:13 (2010) with many references Photocathode Physics for Photoinjectors workshop series.

20 Quantum efficiency Quantum efficiency: Number of photo emitted electrons per photon impinging on the cathode. High QE at the longest possible wavelength. Fast response time: <100 ps Uniform emission

21 Thermal/Intrinsic emittance Thermal emittance: Spread in velocities of emitted electrons As low as possible Atomically flat surface: ~few nm p p, to minimize emittance growth due to surface roughness and space charge Tunable, controllable with photon wavelength Better at cryogenic temperatures? Lifetime, survivability, robustness, operational properties Require >1 year of operating lifetime reasonable vacuum level: Torr range Easy, reliable cathode cleaning or rejuvenation or re activation Low field emission at high electric fields Reliable installation and replacement system (load lock)

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23 Common photocathodes

24 Electron initial distribution Electron are fermions. Thus, the probability of occupied single particle energy states in a crystalline solid obey the Fermi Dirac distribution: where E f is the Fermi level (metal physics). For high energy tails (E>E f ) the FD distribution and the Maxwell Boltzmann distribution coincide, and the simpler MB can be used the MB distribution is the approximation of FD and BE distr. in case of high energies and low densities (interactions between particles negligible) In calculating the probability of electron escape from a material, the specific emission process determines what distribution to use. The MB distribution (high energy tails) is used for thermionic emission, while field and photo emission calculations use the FD distribution, since the excited electrons come from energy levels below the Fermi level

25 Metals vs. semiconductors the Fermi level for metals is in the conduction band simplified semiconductor energy bands: E f =E G /2 T~0K T>>0K thermionic em. in semicond. K. Flottmann, Tesla FEL report photoemission in semicond. The electronic properties of a semiconductor are dominated by the highest partially empty band and the lowest partially filled band, it is often sufficient to only consider those bands. Electron affinity is defined only for semiconductors and is the energy difference between the Vacuum level and the beginning of the conduction band

26 Effective potential image charge metal vacuum e+ e x x Schottky effect applied ext. field lower the barrier 3 different emission processes: 1) Thermionic emission 2) Photo emission 3) Field emission Require electrons to overcome the barrier; Consequence of the Schottky effect. Electrons tunnelling the barrier. Very fast dependence on appl. field. DARK CURRENT

27 Thermionic emission Electron kinetic energy higher than the effective potential MB distribution may be used in the calculation of the electron current density Richardson Dushman equation electron kinetic energy in the direction normal to the surface> work function A is Richardson constant Limit is ~ 1 A/mm 2 if we have The velocity spread of emitted thermo electrons is given by: We ll use this result to calculate the emittance of emitted beam Operating temperature 1500 K So excess kinetic energy ~ 0.5 ev

28 Field emission Strongly depends on applied electric field material characteristics surface roughness Fowler Nordheim equation for the field emitted current work function I [A ] A E 2 6 [m 2 ] [V / m] e E [ev ] enhancement factor A effective area; work function In rf fields is localized at high E field phases, and is then transported trough the machine L.W.Nordheim, Proc. R. Soc. Lond. A , doi: /rspa

29 Three step process 1. Photon Absorption Photoemission physics Optical depth (~14nm for UV light on copper) 2. Electron Transport Electron electron (phonon) scattering; MFP ~5 6nm for 4.5eV exited electrons 3. Vacuum Boundary Crossing maximum angle of emission; p z

30 Electron refraction Electrons need to have enough kinetic energy in the direction normal to the exit surface in order to escape the material: Refraction law for electrons at the metal vacuum boundary. usual numbers for θ max in <~ 10deg, θ max out ~90deg Courtesy of D. Dowell

31 QE for metals E is the electron energy E F is the Fermi Energy eff is the effective work function eff W Schottky Step 1: Optical Reflectivity ~40% for metals ~10% for semi conductors Optical Absorption Depth ~120 angstroms Fraction ~ 0.6 to 0.9 QE( ) 1 R( ) F e e E F F 1 d(cos ) 2 EF eff eff E 0 E 1 2 E Step 3: Escape over the barrier F E F de de d(cos ) 1 0 d d Azimuthally isotropic emission Fraction 1 Step 2: Transport to Surface e e scattering esp. for metals e phonon scattering semiconductors Fraction ~ 0.2 Sum over the fraction of occupied states which are excited with enough energy to escape, Fraction ~0.04 Fraction of electrons within max internal angle for escape, Fraction ~0.01 QE(Cu) ~ 0.5*0.2*0.04*0.01*1 = 4x10 5 Courtesy of D. Dowell, D. H. Dowell et al., PRST AB 9, (2006)

32 Cathode emittance The spread in momentum can be computed in the same way E f hν+ϕ eff E f E f +ϕ eff E f +hν Scaling of QE and thermal emittance! Expand integrals for small h eff QE~ Φ 2 ε nx ~ Φ So chasing the work function with the laser frequency is useful to increase QE, but not to decrease thermal emittance

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34 Multiphoton photoemission Violating Einstein photoelectric effect o For a given metal and frequency of incident radiation, the rate at which photoelectrons are ejected is directly proportional to the intensity of the incident light. o For a given metal, there exists a certain minimum frequency of incident radiation below which no photoelectrons can be emitted. This frequency is called the threshold frequency..and few years of RF photoinjector common practice spent on getting ready the UV on the cathode Two or more small photons can do the job of a big one. Generalized Fowler Dubridge theory: photoelectric current can be written as sum of different terms. J n J n n nh e 0 J n e n A h where n n 2 1 R I T e F kte Fowler function selects the dominant n order of the process

35 Save laser energy. Use IR photons on the cathode BUT conversion efficiency is ~10% P. Musumeci et al., Phys. Rev. Lett, 104, (2010) Autocorrelation signal (arb. units) Charge autocorrelation Polarization gating autocorrelation Time (fs) Autocorrelation of two IR pulses on the cathode shows promptness of emission. Question: Why hasn t this been done before? Recent interest in pancake regime. Ultrashort beam at cathode => uniformly filled ellipsoidal beam. Very high extraction field in RF photoinjector: away from space charge induced emission cutoff. (Early experiments using low gradient setups.) Damage threshold few 100 GW/cm 2 at sub 100 fs pulse lengths. AR coating on the cathode improves charge yield. (at Pegasus 2 Jof 800 nm > 50 pc )

36 Surface plasmon assisted photoemission from a nano structured cathode R. K. Li UCLA Summary: Fabricating nano structures on a flat pure Cu surface. The nano structures have dimensions on the same order of ir laser wavelength (800 nm). Enhanced EM density leads to great enhancement of charge yield. (2) SEM images of fabricated nanohole array (1) 3D simulation geometry reflectivity ~10 nm FWHM 800 nm (5) summary of experiment results installed in S band rf gun and conditioned to > 70 MV/m 125 um > 100 times more charge compared to flat surface 25 um square prompt emission and 3 photon process thermal emittance better than 2 mm mrad/mm rms (3) measured charge yield map (4) how to measure ultralow emittance (6) next step on single crystal substrate optical damage threshold nm beamlet dynamics imaging single electron Measured nm emit.

37 Space charge effects in emission Child Langmuir Law As emitted particles come out from the cathode they create their own electric field. This field in the beam tail field is opposed to the external field, growing with the extracted charge. The effective total potential is distorted by this field. The potential distortion creates asymmetries in the electron beam (tails) and sets a maximum extractable current in the steady state regime The maximum current is given by the Child Langmuir law V + F ext V anode F SC cathode d anode z=d z

38 Child Langmuir law The Child Langmuir law expresses how the steady state current varies with both the gap distance and bias potential of the parallel plate system. It is a 1D derivation, assuming initial electron velocity equal to 0 and non relativistic motion

39 Child Langmuir Law for short beams 2 cases: R > z e pancake aspect ratio R < z e cigar aspect ratio Pancake aspect ratio case Maximum surface charge density set by the cathode extraction field Cigar aspect ratio case Only a small part of the beam contributes to the space charge field and higher charge can be extracted. Q

40 Time dependent behaviour What happens if we force more current density than CL limit into the diode? As injected current increase the space charge potential increases, slowing down particles. If enough current is injected, the SC potential energy becomes higher than the particle kinetic energy and some particles will eventually stop and reflect back to the photocathode (Virtual cathode). The reflection weaken the SC potential and the emission starts again This phenomena is called VIRTUAL CATHODE INSTABILITY. Virtual cathode instability observed in a photo injector The oscillation frequency is a function of the current density and the e beam momentum (plasma frequency) D. Dowell et al., Phys. Plasmas, Vol. 4, No. 9, September 1997

41 Maximum Brightness for photoinjectors Using the space charge limited charge density, we can find a limit on the transverse emittance and then on the beam brightness., I. Bazarov et al., PRL 102, (2009) For pancake aspect ratios, the maximum transverse brightness does not depend on the beam charge!!! It only depends on the acceleration field and on the emission process. The above brightness limit, such as the minimum emittance values calculated in the previous slide, consider a beam extraction at the onset of the virtual cathode formation. In practice, extracting beams with charge density close to the SCL limit may lower the overall brightness of the beam

42 Brightness limitations and core emittance Approaching the SCL the accelerating electric field is significantly reduced in the cathode region. Particles in the back of the beam experience lower fields and non linear potentials. The formation of an asymmetric tail and the non linearity of involved space charge fields lower the beam brightness. EXAMPLE: Emittance and Brightness of a beam at the edge and below the SCL (CORNELL): simulated bunch length at 1mm from the photocathode for the CORNELL photo gun (DC, ~2.7MV/m acc. field) The two beams have the same starting aspect ratio.

43 Various types of photoguns

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49 Outline Electron source applications Electron source figures of merit Cathode physics Photoemission. Thermal emittance and quantum efficiency Child Lamguir law and space charge limits Maximum achievable brightness Photoinjector gun types RF DC SRF Beam Dynamics in RF guns Longitudinal equation of motion RF effects on the beam Scaling laws Space charge effects Laminar flow and envelope equation with space charge Ferrario working point Blow out, pancakes and cigars Magneto Optical Trap based ultracold sources Nanotips based e sources

50 RF guns o o o o o o RF guns are widely used to produce high peak current electron beams Last generation of low repetition rate normal conducting guns LCLS like, works at GHz frequencies (typically 3GHz). The cavity structure is n+1/2 cell (n=1,3 ) Standing wave structure, TM mode to accelerate the beam The cathode is placed in the half cell (max field) first order approx. from Maxwell equations solution for fundamental accelerating mode in a pillbox

51 Electron capture and acceleration Length needed by the acc. electron to gain 1 unit of. Capture parameter. It should be greater than 1, so that electrons become relativistic within half the rf period, and are thus captured by the forward wave of the field Shorter wavelengths require higher fields! At LCLS α ~ 2; L c = 4 mm Intuitively, an electron is captured when it gains enough momentum from the wave to surf it until the exit of the cavity, without slipping back to decelerating phases. The fast acceleration peculiar of rf guns is crucial in maintaining the beam characteristics set by the laser beam (current, shape, starting emittance ). It greatly diminishes the effect of space charge forces (later)

52 Longitudinal equations of motion Backward wave Using dβ Forward wave These equations can be numerically solved. But before we do that, we can make some analytical approximation to help us understand better the dynamics.

53 Kim s approximation At first order we can calculate the energy assuming the phase to be constant main contribution to phase slippage very close to the cathode, z ~ 0 and then solve for the phase slippage when the particles are ultrarelativistic, there is no more slippage 135 Final phase vs. initial phase sin sin 0 0 Kim vs. Numerical solution 1.5 cell gun 120 MV/m

54 Energy and bunching in RF gun We can see immediately the bunching properties of the RF gun f o d 1 1 d cot 2 sin 12 Energy vs. phase 1 Compression factor vs. phase Max energy from 1.5 gun at 120 MV/m is at 63 degrees. For 1.6 cell guns is at 30 degrees 1 sin 1 2 cos cos 2

55 RF effects on the beam: transverse We now try to calculate the effect of radial rf fields on transv.emittance at the exit. phase space TM 01 like mode (E z,e r, B θ ). We calculate radial field close to axis, in the approx. that E z does not depends on r. E z E r /r x This represents a defocussing kick when 0 < < x pr r 10 S band,100 MV / m Thus it usually will be necessary P. Musumeci, to focus SSSEPB, the SLAC, beam July 2013 immediately after leaving the cavity.

56 Rewriting p r in Cartesian coordinates: Transverse RF emittance It gives the phase space distribution: a collection of lines with different slopes corresponding to different The normalized transverse emittance is: By inserting p x we obtain

57 writing and assuming that is small so that sin sin cos 2 2 sin sin 2 sin 2 2cos sin 2 2 cos 2 sin 2 one obtains from: which has a minimum for < >= /2 For Gaussian distributions

58 Solenoid focusing in a solenoid lens the beam gets focused and rotated: <0, focusing parallel beam at the entrance, thin lens, r~const inside the lens solving the paraxial equation we find, for a lens of length L: used in the derivation of paraxial equation The fringe field (divergence of B=0) is the key for beam focusing. The particle interact with B r in the fringe and acquire a transverse velocity that inside the solenoid couples with B z generating a net transverse force

59 Magnetic Emittance If particles born in a region where static magnetic field is present, a transverse momentum is added to their intrinsic one, that leads to an emittance increase. The conservation of canonical momentum leads to the Busch s theorem: For a constant magnetic field B z =B 0 in the considered surface S: Larmor Frequency, ω L initial uniform distribution with x rms =r 0 /2 Also, out from the magnetic field, the beam will keep a net defocusing kick x :

60 Aberrations and emittance growth in solenoids: chromatic effects Because of rf (and space charge) defocusing it is important to focus the beam right after the gun with strong magnetic fields. Solenoids are usually used at low energies, because of their ability of focusing at the same time in both transverse planes. By comparing the centrifugal and the Lorentz force on a particle with an external magnetic field we find the magnetic rigidity: the bending radius ρ is energy dependent. Substituting into the formula for k we find: the sol. focal length is energy dependent (1/f=ksin(kL)) it can be shown that the associated emittance increase is: D.H. Dowell, US Particle Accelerator School, June 14 18, 2010, Boston, MA.

61 Aberrations and emittance growth in solenoids: geometric effects All magnetic field solenoids exhibit a 3rd order angular aberration also known as the spherical aberration Example for a LCLS like sol parameters: Pincushion aberration at the beam waist ~50cm after the solenoid Initial beam has zero divergence (zero emittance) and is a uniform radial distribution, radius = 2 x L eff =19.35 cm B sol = 2.5kG 4 th order fit of the aberration emittance vs. rms beam size at the solenoid The fields producing this aberration are usually located at the ends of the solenoid. The aberration depends upon the second derivative of the axial field Small contribution for usual beam sizes (1 2mm) D.H. Dowell, Beam Physics At, Near and Far from the Cathode, Max Zolotorev s 70 th Birthday,LBNL, nov

62 Emittance growth in solenoids: quadrupole fields due to lack of symmetry The quadrupole phase angle is the angular rotation of the poles relative to an aligned quadrupole Measured magnetic fields, LCLS quadrupole rotation + solenoid rotation xqs, xsol, ysol, sin 2 KL f q quad solenoid D.H. Dowell, Beam Physics At, Near and Far from the Cathode, Max Zolotorev s 70 th Birthday,LBNL, nov. 2011

63 Solenoid emittance growth D.H. Dowell, US Particle Accelerator School, June 14 18, 2010, Boston, MA.

64 Relativistic paraxial ray equation 1. write the equations of motions in cylindrical coordinates 2. consider axially symmetric fields; expand fields in power series, keep the first order 3. find the electric and magnetic field relations at the first order, and substitute in eq of motion change in slope of particle trajectory static magnetic field centrifugal force related to a non zero angular momentum adiabatic damping of transverse particle angles focusing/defocusing of transverse electric field if we introduce the Larmor frame which is a rotating frame with angular velocity ω L =dϑ/dt, then we have p ϑ =0. We can then solve the equation without the last term, and then calculate the particle angle respect to the stationary frame:

65 Transverse envelope equation w/o space charge We now want to write the equation for the beam envelope. It can be derived from the paraxial equation (single particle) by averaging over the distribution: Using the relations: multiply by r and average r r 2 (k r '' 2 2 ) r n r 3 0 The envelope equation describes the evolution of transverse electron beam moments in hypothesis of linear fields. In the same hypothesis later we will add a term coming from self field forces. The emittance enters in the equation as a source of pressure.