Linac Driven Free Electron Lasers (III)

Transcription

1 Linac Driven Free Electron Lasers (III)

2 SASE FEL Electron Beam Requirements: High Brightness B n ( ) 1+ K 2 2 " MIN r #$ % &B! B n 2 n K 2 minimum radiation wavelength energy spread undulator parameter B n = 2I B n " n 2 L g " # 3 2 K B n ( 1+ K 2 2) n gain length R. Saldin et al. in Conceptual Design of a 500 GeV e+e- Linear Collider with Integrated X-ray Laser Facility, DESY

3 Short Wavelength SASE FEL Electron Beam Requirement: High Brightness B n > A/m 2 B n " 2I # n 2 Bunch compressors (RF & magnetic) Laser Pulse shaping Emittance compensation Cathode emittance

4 The paradox of relativistic bunch compression Low energy electron bunch injected in a linac: " # 1 L b = 3mm = L $ b I = 100 A Length contraction? " = 1000 L b = L # b " = 3µm I = 100kA Why do we need a bunch compressor? L " b " = #L b = 30m L b = L " b " # = 3mm I = 100A

5 Magnetic compressor (Chicane)

6 Magnetic compressor (Chicane)!#/# " z0 chirp!#/# or overcompression!#/# undercompression z z z " E /E " z V = V 0 sin($%)!z = R 56!#/# RF Accelerating Voltage Path Length-Energy Dependent Beamline Courtesy P. Emma

7 Transfer Matrix including longidunial phase space

8 In general, any curved beam line section introduces a path length difference for particles with a relative energy (momentum) deviation!: (with " being the longitudinal dispersion) "S = #( $ )$ = R 56 $ +T 566 $ Path length: S (" ) = 4L B" sin" + 2#L cos" + #L c Additional Path length: "S(# ) = S (# ) $ 4L B + 2"L + "L c ( ) % # 2 2 ( & 3 L ) B + "L+ ' * Expandig # in terms of a small relative energy deviation $ : " 2 = " o 2 ( ) ( 1 +# ) 2 $ " o 2 1 % 2# + 3# we obtain: 2% 2 R 56 = "2# o ' 3 L B & + $L ( * "S = # R 56 ) 2 T 566 = # 3 2 R 56

9 Types of Compressor!L c L B & 4-dipole chicane LEUTL, LCLS, TTF-BC1,2, TESLA-BC1 simple, achromatic < 0 L T wiggler TESLA-BC2,3 achromatic < 0 FODO-cell arc & T SLC RTL, SLC arcs NLC BC2 reverse sign > 0 But T 566 > 0 in all cases

10 Single-Stage Bunch Compression ev 0 ev Energy of a particle after acceleration in a RF linac where z is the longitudinal position in the bunch: z ' < 0 The bunch head is in the z<0 direction Defining the Energy Chirp factor h: The relative correlated energy deviation of a particle at a longitudinal position z o becomes:

11 Taking the average over all particles we obtain the final bunch length: " z2 = z 2 2 = ( 1 + hr 56 ) 2 " 2 zo + R " # i Initial uncorrelated energy spread: " # i = # i 2 Such that: z o " i = 0 % $ in a FEL is extremely small and we can simplify : " z2 = 1 + hr 56 " zo = " z o C bunch length stability with RF phase jitter Compression factor C = " z o " z2 >> 1

12 Two-Stage Compression Used for Stability!t 0 ( late arrival, higher energy, less chirp longer bunch, more chirp ~same bunch length!t 0!t 1!t 2 Courtesy P. Emma System can be optimized for stability against timing & charge jitter

13 Laminarity parameter " = 2I# 2 $I A % & 2I# 2 q 2 n $I A % = 4I 2 2 n $ ' 2 I 2 A % 2 n $ 2 Transition Energy (&=1) " tr = 2I # " I A $ n & I=4 ka ' th = 0.6 µm E acc = 25 MV/m I=1 ka Potential space charge emittance growth I=100 A & = 1

14 Longitudinal Geometric Wakefields b d L There is a longitudinal E z (r,z) field in the transition

15 Longitudinal Geometric Wakefields Longitudinal point-wake: K. Bane " s V(s)/MV/nC/m 1 mm 500 µm 250 µm 100 µm 50 µm 25 µm SLAC S-Band: s 0 ( 1.32 mm a ( 11.6 mm s < ~6 mm Induced voltage along bunch: s/!s FW

16 LCLS Example of Wakefield Use wakefield OFF " ( ( 0.26 % end of LCLS linac " ( < 0.02 % wake-induced energy spread *head *head wakefield ON L ( 550 m, N ( 6.2)10 9,!z ( 75 µm, E = 14 GeV for uniform distribution

17 For chicane and accelerating phase, RF curvature and T 566 always add, limiting the minimum bunch length... ev e ) z " z /µm ev e ) 2 nd -order linear z R 56 /m

18 Courtesy Joerg Rossbach RF gun superconducting TESLA module bunch compressor 127 MeV bunch compressor 380 MeV 12/20 MV/m ~ 20 fs Laser 4-5 MeV before 1 st BC 1m after 1 st BC 1m after 2 nd BC Long initial bunch to reduce space charge on cathode s L = 4.4 ± 0.1 ps Time (ps)! Very complicated beam dynamics due to coherent synchrotron radiation! Difficult access to relevant parameters! Ultra-short photon pulses created ~20fs FWHM

19 + x = + s /4 Slope linearized ' 1 ( +40 ' x = * 0.5-m X-band section for LCLS (22 MV, 11.4 GHz)

20 Harmonic RF used to Linearize Compression RF curvature and 2nd-order compression cause current spikes Harmonic RF at decelerating phase corrects 2nd-order and allows unchanged z-distribution 830 µm avoid! 200 µm

21 Coherent Synchrotron Radiation (CSR) e Powerful radiation generates energy spread in bends Energy spread breaks achromatic system Causes bend-plane emittance growth (short bunch worse) coherent radiation for # > " z " z # R $ L 0 bend-plane emittance growth s!!/! = 0!!/! < 0!x overtaking length: L 0 " (24" z R 2 ) 1/3!x = R 16 (s)!e/e Courtesy P. Emma

22 Projected Emittance Growth B1 B2 B3 B4 #!! $/! 0 " %0.043% " ' " 0.021% B1 B2 B3 B4 %& x " 1.52 µm

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25 CSR Microbunching in LCLS CSR can amplify small current modulations: energy profile long. space temporal profile " ' " 3&10 %6 microbunching 230 fsec

26 CSR Microbunching Gain in LCLS BC2 add 2% current & energy modulation cold beam " E /E 0 = 3&103 %& x0 = 0 10 %6 after compressor

27 Laser heater Motivation: Collective effect: SP/CSR drive micro-bunch instabilities Residual energy-spread ~ 1-3keV ' No Landau damping Energy-spread can be larger for FELs (( E /E < ) ~ 5e-4) ' increase * E kev Example LCLS design Courtesy H. Schlarb Z. Huang et al., Phys. Rev. STAB 7, (2004) J. Wu et al., SLAC-PUB-10430

28 Laser heater heating ( L ~ 40keV Residual ( E ~ 1-3keV R 56 = Before undulator R 56 =0

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30 LCLS BC2 CSR Microbunching Gain vs. # Microbunching Gain Initial modulation wavelength prior to compressor %& x =1 µm cold beam see also E. Saldin, Jan. 02, and Z. Huang, April 02 %& x =1 µm, " ' =3&10 %5 theory : S. Heifets et al., SLAC-PUB-9165, March 2002

31 Laser Comb: a giant microbunch instability 1 R 56 < bis 5

32 Example of typical behavior: N = 4 15 cm 150 cm longitudinal profile Current modulation washes out energy modulation sawtooth x-, spatial configuration Roughly to original size, small wiggle

33 Laser Comb: a giant microbunch instability

34 Velocity bunching concept (RF Compressor) If the beam injected in a long accelerating structure at the crossing field phase and it is slightly slower than the phase velocity of the RF wave, it will slip back to phases where the field is accelerating, but at the same time it will be chirped and compressed. The key point is that compression and acceleration take place at the same time within the same linac section, actually the first section following the gun, that typically accelerates the beam, under these conditions, from a few MeV (> 4) up to MeV.

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36 Average current vs RF compressor phase Average current (A) OVER- COMPRESSION HIGH COMPRESSION MEDIUM COMPRESSION RF compressor phase (deg) LOW COMPRESSION

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38 <I> = 860 A * nx = 1.5 µm

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40 RF deflector L B DEFLECTING VOLTAGE x z s! x x B z x B = " f RF LLBV ce / e! DEFLECTOR BUNCH L SCREEN V # = " ce / e! f x RF LL res LINAC DEFLECTOR ONDULATOR

41 SPARC Diagnostic Section phase Q T 1 Q T 3 Energy Q T 2 RFD Q Q T 4 T 6 Q T 5 to undulator

42 Slice emittance measurements

43 Preliminary results for the velocity bunching at SPARC phase phase Energy Energy Compression factor measurements PARMELA 5 ps 132 MeV 2.5 ps 90 MeV Q=250 pc TW1 Section RF phase (deg) 1

44 ( ) = ee sin kz # $t +% o d dz "mc 2 d" dz = ee mc 2 sin kz # $t +% o d" = &k sin (% ) dz Velocity bunching equations ( ) ( ), d". = #k sin ( $ ). dz - & ). d$ dz = k ( 1 % " +. ( ' " 2 % 1 + / * d" dz = d dz kz # $t +" o ( ) = ' k # $ dt % = k 1 # 1 ( % ' * = k' 1 # & + ) ' & % & (, *, 2 # 1 * ) ( % * = k # $ ( ' * dz ) & +c ) Such a system is solved using the variable separation technique to yield a constant of the motion (total energy):

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46 Second order effects

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48 References: - M. Dohlus, T. Limberg, DESY and P. Emma, SLAC, Electron Bunch Length Compression, ICFA Beam Dynamics Newsletters Zhirong Huang, Juhao Wu (SLAC) Timur Shaftan (BNL), Microbunching instability due to bunch compression, ICFA Beam Dynamics Newsletters L. Serafini and M. Ferrario, Velocity Bunching In Photo-injectors, AIP Conference Proceedings, 581, 87, (2001) also in LNF note LNF-00/036 (P)