X-rays by Compton Scattering and Sources Driven by SRF Linacs

Transcription

1 X-rays by Compton Scattering and Sources Driven by SRF Linacs Geoffrey Krafft, Kirsten Deitrick, Jean Delayen, Randika Gamaga, Todd Satogata Center for Accelerator Science Old Dominion University and Jefferson Lab

2 Outline Basic Physics Wigglers, Undulators, and Insertion Devices Compton Effect Important Parameters Line Broadening and Narrowing by Chirping Laser Performance Self-Excited Arrangements External High Power Optical Cavities SRF Compton Sources New Ideas Layout Results

3 Argonne Advanced Photon Source

4 e Bend Undulator Wiggler hω e e h ω h ω hω white source partially coherent source powerful white source Flux [ph/s/0.1%bw] Brightness [ph/s/mm /mr /0.1%bw ] Flux [ph/s/0.1%bw] hω hω

5 Compton Effect A. H. Compton, Phys. Rev., 1, 483 (193)

6 Unpolarized Incident X-ray Beam

7 Scattered Photon Energy Layout Energy E ( θ, ϕ) Thomson limit γ Elaser = 1 β cosθ + E ( θ φ ) ( 1 β cosφ) ( 1 cos Θ) / laser << Elaser mc, Eγ, Elaser E e 1 β cos Φ 1 β cosθ

8 Field Strength Parameter Early 1960s: Laser Invented Brown and Kibble (1964): Earliest definition of the field strength parameters (normalized vector potential) K and/or a in the literature that I m aware of a = ee0λ0 Compton/Thomson Sources π mc eb0λ0 πmc Undulators Interpreted frequency shifts that occur at high fields as a relativistic mass shift. Sarachik and Schappert (1970): Power into harmonics at high K and/or a. Full calculation for CW (monochromatic) laser. Later referenced, corrected, and extended by workers in fusion plasma diagnostics. Alferov, Bashmakov, and Bessonov (1974): Undulator/Insertion Device theories developed under the assumption of constant field strength. Numerical codes developed to calculate real fields in undulators. Coisson (1979): Simplified undulator theory, which works at low K and/or a, developed to understand the frequency distribution of edge emission, or emission from short magnets, i.e., including pulse effects K =

9 Emission From a Short Magnet Coisson low-field strength undulator spectrum* duγ 4r c = γ % + dν dω µ e 0 ( ν 1 γ θ / γ ) ( ) ( 1+ γ θ f B ) f = f σ + f π f σ = 1 ( 1+ γ θ ) sinφ r e 4 e 16π ε m c 4 0 f π = 1 1 γ θ + γ θ 1 1 ( + γ θ ) cosφ *R. Coisson, Phys. Rev. A 0, 54 (1979)

10 Dipole Radiation r µ ( ) 0 ed&& t r / c B = sin ΘΦˆ xˆ 4π cr r µ ( ) 0 ed&& t r / c E = sin ΘΘˆ 4π r r r E B µ e d&& ( t r / c) 0 I = = sin Θrˆ µ 16π cr dp dω 0 && 1 e d ( t r / c) = sin Θ 3 16π ε 0 c Polarized in the plane containing and rˆ = r n ŷ Φ Θ xˆ r Φˆ Θˆ ẑ

11 Define the Fourier Transform ~ d ( ) iωt ω = d( t) e dt du Dipole Radiation d( t) = 1 π With these conventions Parseval s Theorem is ~ d 4 / π ε e ω d( ω) γ = sin Θ 3 3 Ω 3π ε 0 dωd c % ( ) i ω e ω t dω 1 ~ d ( t) dt = d ( ω) dω π du γ = e d && ( t r c) dt = e ω d % ( ω) dω dω 16π ε c 3 c Blue Sky! This equation does not follow the typical (see Jackson) convention that combines both positive and negative frequencies together in a single positive frequency integral. The reason is that we would like to apply Parseval s Theorem easily. By symmetry, the difference is a factor of two.

12 Weak Field Undulator Emission ( ω '/ cβ γ ) r % ec B% z d '( ω ') = d% '( ω ') xˆ = xˆ mc ω ' ~ B ikz ( k) B( z) e dz = du ( ( ) ) 4, 1 B% e ω 1 βz cos θ / cβ γ σ z = sin 3 3 ( ) Ω 3π ε 0 γ 1 β z cosθ dωd m c du ( ( ) ) 4, 1 e B ω 1 βz co sθ / cβ γ π z cosθ β z = cos 3 3 ( ) Ω 3π ε 0 γ 1 β cos 1 βz cosθ z θ dωd m c λ = λ γ 0 % 1 γ ( 1 β z cosθ )( 1+ β z ) + θ + K φ 1+ γ θ γ Generalizes Coisson results to arbitrary observation angles φ

13 Weak Field Thomson Backscatter With Φ = π and a << 1 the result is identical to the weak field undulator result with the replacement of the magnetic field Fourier transform by the electric field Fourier transform Driving Field cb% Undulator ( ) ( ω 1 β cos θ / cβ ) y z z ~ E x Thomson Backscatter ( ω ( 1 β cosθ )/( c( 1+ β ))) z z Forward Frequency λ λ 0 0 λ λ γ 4γ Lorentz contract + Doppler Double Doppler

14 Handy Formulas γ re ε ω β θ 0 = % ( 1 cos ) c ( 1 + β ) d U E dω d Ω π c U γ ( ) + ( ) γ ( 1 β cosθ ) sin φ 1 β cosθ cos φ cosθ β = + N γ γ N = e T ( 1 β ) ( σ ) e + σ laser σ T γ,per e π σ = e N N N σ laser ( ) e + σ laser πα N a 3 λ U laser

15 Number Distribution of Photons

16 Flux Percentage in 0.1% bandwidth (θ = 0) N0.1% = N γ Flux into 0.1% bandwidth F = & N γ Flux for high rep rate source F = fn γ

17 Scattered Photon Energy Spread Source Term Estimate Comment Beam energy spread Laser pulse width Sources of Energy Spread in the Scattered Pulse Finite θ acceptance (full width) Finite beam emittance σ Ee / Ee σω / ω γ θ γ ε / βe From FEL resonance Doppler Freq Independent θ = 0 for experiments Beta-function

18 Spectral Brilliance In general B = F 4π σ σ σ σ x x y y F 4 π β ε ε / β x x x x + λ / L β ε ε y y y / βy + λ / L For Compton scattering from a low energy beam B = F 4π ε ε x y

19 High a/k "Figure Eight" Orbits 0.01 x z K=0.5 K=1 K= xz γ = 100, distances are normalized by λ 0 / π

20 1 ea( ξ ) ( ) iφ ( ω, ξ ; θ, ϕ) Dt ω; θ, ϕ = e dξ γ ( 1 β cos Φ) mc 1 e A ( ξ ) ( ) iφ ( ω, ξ ; θ, ϕ) Dp ω; θ, ϕ = e dξ γ 1 β cos Φ m c ( ) And the (Lorentz invariant!) phase is ϕ ω, ξ; θ, φ ( ) Effective Dipoles ( 1 β cosθ ) ξ sinθ cosφ ea( ξ ') ξ dξ ' ω ( 1 β cos Φ) γ ( 1 β cos Φ) mc c 1 sinθ sinφ sin cosθ cos e A ( ξ ') Φ Φ + dξ ' ( ) γ 1 β cos Φ m c = ξ

21 High Field Backscatter For a flat incident laser pulse the main results are very similar to those from undulaters with the following correspondences Undulator Thomson Backscatter Field Strength K a Forward Frequency λ λ 1 K 0 + γ λ 0 a λ 1 + 4γ Transverse Pattern β * + cosθ ' z 1+ cosθ ' NB, be careful with the radiation pattern, it is the same at small angles, but quite a bit different at large angles

22 Ponderomotive Broadening A x ( ) cos( πξ / λ ) ( ξ ) = A exp z / ( 8.156λ ) peak 0 0 a = ea / mc peak peak G. A. Krafft, Phys. Rev. Lett., 9, 0480 (004)

23 Terzic, Deitrick, Hofler, and Krafft, Phys. Rev. Lett., 11, (014) Compensation By Chirping

24 Beam Illumination Methods Direct illumination by laser Earliest method Deployed on storage rings Optical cavities Self-excited Externally excited Deployed on rings, linacs, and energy recovered linacs

25 Early Gamma Ray Source Compton Edge 78 MeV Federici, et al. Nouvo. Cim. B 59, 47 (1980)

26 Optical Cavities mirror spot size w=σ mirror Rayleigh Range (w π/λ) Quantity Dimensions Wavelength Circulating Power Spot Size Rayleigh Range 00 nm-10 microns kw microns 40 cm-5 m

27 Self Excited electrons laser Location Wavelength Circulating Power Spot Size Rayleigh Range Orsay 5 microns 100 W mm 0.7 m UVSOR 466 nm 0 W 50 microns 0.4 m Duke Univ. 545 nm 1.6 kw 930 microns 5 m Super-ACO 300 nm 190 W 440 microns m Jefferson Lab FEL 1 micron 100 kw 150 microns 1 m

28 Externally Excited electrons laser Location Wavelength Input Power Circulating Power Spot Size (rms) Jefferson Lab Polarimeter 1064 nm 0.3 W 1.5 kw 10 microns TERAS 1064 nm 0.5 W 7.5 W 900 microns Lyncean 1064 nm 7 W 5 kw 60 microns HERA Polarimeter 1064 nm 0.7 W kw 00 microns LAL 53 nm 1.0 W 10 kw 40 microns

29 Lyncean Compact X-ray Source

30 Lyncean Source Performance Parmeter Value Unit Photon Energy 10-0 kev Production Rate photons/sec Laser Wavelength 1064 nm Circulating Power 5 kw Polarization 100% Ultimate Brilliance p/(sec mm mrad 0.1%)

31 The Jefferson Lab IR FEL Wiggler assembly Neil, G. R., et. al, Physical Review Letters, 84, 6 (000)

32 Thomson Source Scattering Geometry

33 60 sec FEL Short-pulse X-ray Spectrum FEL X-ray Spectra E e- = 36.7 MeV λ L = µm IR = 50 Watts, cw Live run time = 60 sec. E X-ray = 5.1 kev FWHM = kev B o yce, Krafft, et al. Sept. 30, 1999 P relim inary Counts 1000 Lasing Not Lasing Channel number Boyce, et al., 17 th Int. Conf. Appl. Accel., 35 (00)

34 High Power Optical Cavities V. Brisson, et al., NIM A, 608, S75 (009) N.B., 10 kw FEL there, sans spot! In this paper we described our first results on the locking of a Ti:sapph oscillator to a high finesse FPC. For the first time, to our knowledge, we demonstrate the possibility of stacking picosecond pulses inside an FPC at a very high repetition rate with a gain of the level of By studying the stability of four-mirrors resonators, we developed a new promising nonplanar geometry that we have just started to study experimentally. Finally, we mentioned that we shall next use the recent and powerful laser fiber amplification scheme to reach the megawatt average power inside FPC as required by the applications of the Compton X and gamma ray sources.

35 LAL/Thales THomX BES Workshop on Compact Light Sources (010)

36 Hajima, et al. Uranium Detection Hajima, et al., NIM A, 608, S57 (009) TRIUMF Moly Source?

37 Graves, et al., NIM A, 608, S103 (009) MIT CUBiX

38

39 ODU Compton Light Source 01 June 015

40 Parameters Parameter Quantity Units Energy 5 MeV Bunch charge 10 pc Repetition rate 100 MHz Average current 1 ma Trans. norm. emittance 0.1 mm-mrad β x,y 5 mm FWHM bunch length 3.0 (0.9) psec (mm) RMS energy spread 7.5 kev Electron beam parameters at collision point.

41 Parameters Parameter Quantity Units Wavelength 1 (1.4) µm (ev) Circulating power Number of photons/bunch 1 MW 5 x Spot size 3. µm Peak strength 0.06 X-ray energy Up to 1 kev Photons/bunch 1.6 x 10 6 Flux 1.6 x photon/sec Avg. brilliance 1.6 x photon/(sec-mm - mrad -0.1%BW) Optical cavity parameters. Compton source parameters.

42 Electron gun Parameter Quantity Units Originally based on quarter-wave SRF electron gun developed by Harris et al. Highly reentrant to mitigate growth of normalized emittance due to space charge. Freq. of accelerating mode MHz λ/4 150 mm Design β 0.95 Stored energy 44 mj QR S 83.5 Ω R/Q 154 Ω Peak electric surface field (E P ) Peak magnetic surface field (B P ) 3.67 MV/m 6.64 mt E P /B P 1.81 mt/(mv/m) RF Properties at E acc = 1 MV/m

43 Electron gun EM fields calculated by SUPERFISH Particle tracking simulated by ASTRA Diameter/length 30 cm Beam travels 15 cm Top: Transverse phase space and spot. Bottom: Electron beam properties at gun exit. Parameter Quantity Units E kin 1.55 MeV RMS Energy spread 0.56 kev σ x,y mm Normalized RMS ε x,y 0.1 mm-mrad

44 Linac Consists of 4 high-velocity, double-spoke cavities. Alternating orientation to produce roundest beam at exit. 500 MHz Diameter of 41.6 cm Length of 80.5 cm EM fields calculated by CST Microwave Studio. Particle tracking simulated by ASTRA. Entire accelerating section has 5 m x 1 m footprint

45 Linac Parameter Quantity Units Energy 5.0 MeV RMS Energy spread kev σ z.1 (7.0) mm (psec) σ x,y 0.511, 0.48 mm Norm. RMS ε x,y 0.16, 0.15 mm-mrad α x,y.34, β x,y 8.7, 75.5 m Transverse phase spaces are bowties, not ellipses. Top: Electron beam properties at linac exit. Bottom: Transverse phase spaces and beam spot.

46 Matching Solenoid transforms bowties into phase spaces. Normalized RMS ε x,y : 0.16, , 0.18 mm-mrad. As solenoid strength increases, so does emittance growth. Followed by a quadrupole and skew quadrupole, to get α x = α y and to remove x y coupling, respectively. ~1 m in length. Modeled by elegant.

47 Bunch Compressor Consists of four dipole s-chicane. Two designs: 3π phase advance (symmetric dispersion) 4π phase advance (antisymmetric dispersion) M 56 is tunable by adjusting bend angle of inner dipole pair. Sextupoles to remove longitudinal curvature. Followed by uncoupling and final focusing sections. Modeled by elegant.

48 Tunable M56

49 3π Design Parameter Quantity Units Final β x,y 5, 8 mm M m Dipole lengths 0.8, 0.8, 0.8, 0.8 m Dipole bend angles 60, -108, -108, 60

50 4π Design Parameter Quantity Units Final β x,y 6, 11 mm M m Dipole lengths 0.35,1.1,1.1,0.35 m Dipole bend angles 40,-180,180,-40

51 Beam spot and phase spaces

52 Results vs Goals Parameter Goal 3π Design 4π Design Units Energy MeV RMS energy spread kev FWHM bunch length 3.0 (0.9) psec (mm) Normalized RMS ε x,y , ,1.4 mm-mrad β x,y 5 5, 8 6, 11 mm σ x,y 3. 7, 8 9, 18 µm

53 Summary Compton sources of high energy photons have existed for about thirty years The have followed the usual progression: [1] borrow an existing machine (1 st generation), and [] make it better by technological innovation ( nd generation?) We are perhaps approaching 3 rd generation devices, i.e., electron accelerators specifically designed for Compton/Thomson sources. ODU or Uppsala design? Our design ideas are having convergence with high energy collider design ideas Lots of ideas, but still looking for the killer ap.

54 Summary A new calculation scheme for high intensity pulsed laser Thomson Scattering has been developed. This same scheme can be applied to calculate spectral properties of short, high-k wigglers, and to compute optimal incident laser chirping. Due to ponderomotive broadening, it is simply wrong to use single-frequency estimates of flux in many situations The new theory is needed for Thomson scattering of Table Top TeraWatt lasers, which have exceedingly high field and short pulses. Proper laser chirping is important in this regime.