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High Brightness Electron Beam Magnetic Compression: Physics and Compressor Design

High Brightness Electron Beam Magnetic Compression: Physics and Compressor Design. Paul Emma Stanford Linear Accelerator Center July 2, 2002. “ Any fool with four dipoles can compress a bunch ” — anonymous. OK, but there may be a few details to consider…. D E/E. D E/E. D E/E.

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High Brightness Electron Beam Magnetic Compression: Physics and Compressor Design

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  1. High Brightness Electron Beam Magnetic Compression:Physics and Compressor Design Paul Emma Stanford Linear Accelerator Center July 2, 2002

  2. “Any fool with four dipoles can compress a bunch” —anonymous OK, but there may be a few details to consider…

  3. DE/E DE/E DE/E …or over-compression under-compression sz0 ‘chirp’ z z z sz sE/E V = V0sin(wt) Dz = R56DE/E RF Accelerating Voltage Path Length-Energy Dependent Beamline Magnetic Bunch Compression

  4. TESLA XFEL at DESY 3 compressors 0.85-60 Å X-FEL Integrated into linear collider

  5. LCLS at SLAC 2 compressors LCLS 1.5-15 Å X-FEL based on last 1-km of existing SLAC linac

  6. Single-Stage Bunch Compression eV eV0 z ‘chirp’ j < 0 T. Raubenheimer final bunch length and energy spread… bunch length stability with RF phase jitter…

  7. Two-Stage Compression Used for Stability Dt0 d longer bunch, less wake, more chirp ~same bunch length Dt1 Dt2 Dt0 late arrival, higher energy, less chirp System can be optimized for stability against timing & charge jitter

  8. Types of Compressors DLc LB q > 0 4-dipole chicane LT reverse sign < 0 simple, achromatic FODO-cell arc qT wiggler < 0 achromatic, cancellation? (bunch head at z< 0) LEUTL,… LCLS, TTF-BC1,2, TESLA-BC1 TESLA-BC2,3 SLC RTL, SLC arcs NLC BC2 But T566> 0 in all cases…

  9. 2nd Order Compression Limitations r  T566/R56 For chicane or wiggler (any ‘non-focusing’ compressor), the path length... Now add 2nd order term of sinusoidal rf accelerating voltage... For a uniform temporal distribution [z04 = (9/5)z04] andz00 = 0...

  10. For chicane and accelerating phase, RF curvature and T566 always add, limiting the minimum bunch length ... eV e- z sz /mm eV 2nd-order e- linear z R56 /m Decelerating phase can be used to compensate T566, but not practical in low energy compressors (used in NLC and TESLA)... rT566/R56 e-

  11. 830 mm lx = ls/4 Slope linearized 200 mm avoid! 1  -40° x = p 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 3rd harmonic used at TTF/TESLA 4th harmonic used at LCLS 0.5-m X-band section for LCLS (22 MV, 11.4 GHz)

  12. eV eV e- e- eV R56< 0 e- z z z chicane or wiggler  FODO-cell arc eV R56> 0 e- z Reverse-Sign R56 to Linearize Compression TESLA-BC arc example   70°

  13. Longitudinal Geometric Wakefields Longitudinal point-wake: ss K. Bane 1 mm 500 m V(s)/MV/nC/m 250 m 100 m 50 m 25 m s/DsFW RF slope (+ for chicane) Wakefield induced slope (–) SLAC S-Band: s0 1.32 mm a 11.6 mm s < ~6 mm Induced voltage along bunch: For a uniforms-distribution (s = 23s)...

  14. LCLS Example of Wakefield Use   0.26 % wakefield ‘OFF’ head  < 0.02 % wakefield ‘ON’ head wake-induced energy spread for uniform distribution end of LCLS linac L 550 m, N  6.2109, z  75 m, E = 14 GeV

  15. Advantages and Disadvantages of Wakefield • Wake cancels energy chirp after compression (weaker chicane, less CSR), • but also forms current spikes during compression, • …and transverse wakes may dilute emittance of long bunch • Best of both: use SC-L-band before compression and S- or C-band after ?

  16. Synchrotron Radiation N  1010 Power ~l-1/3 vacuum chamber cutoff sz Wavelength coherent power incoherent power

  17. ISR Emittance Growth for Chicane T. Raubenheimer LB bx q DL L Incoherent synchrotron radiation (ISR) increases at high energies - dilutes ‘slice’ emittance... For, symmetric beta-functions, the effect is minimum when... And substituting R56 for ... Total chicane length, L, set by tolerable N (e.g., /0  1%)… LCLSBC2 (E = 4.50 GeV,|R56|= 22 mm) needs L 6.4 m LCLSBC1 (E = 0.25 GeV, |R56|= 36 mm) needs L 0.06 m

  18. sz l DE/E = 0 L0 s R Dx e– DE/E < 0  CSR wake is strong at very small scales (~1mm) ~ Coherent Synchrotron Radiation (CSR) • Powerful radiation generates energy spread in bends • Energy spread breaks achromatic system • Causes bend-plane emittance growth (short bunch worse) bend-plane emittance growth coherent radiation forl > sz Dx = R16(s)DE/E overtaking length: L0  (24szR2)1/3

  19. Projected Emittance Growth B2 B4 B3 B1 Berlin Workshop Case E /E0 -0.043% sd 0.021% B2 B4 B3 B1 gex 1.52 mm x/mrad z /mm

  20. Projected Emittance growth reduced by b-matching ge 1.15 mm slice centroids after CSR ge 1.52 mm geCSR 0.145 mm geCSR 0.145 mm ge0 = 1.00 mm ge0 = 1.00 mm bbopt aaopt Now rematch incoming beam bopt 1.37 m aopt-1.10

  21. Double-Chicane Emittance Growth Cancellation hx 244 mm -I hx 107 mm R56= -21 mm R56= -4 mm ss 200 mm E0 = 5 GeV ss 50 mm ss 20 mm

  22. CSR Emittance Growth Reduced in Double-Chicane single-chicane double-chicane gex 1.01 mm projected emittance growth is greatly reduced using double-chicane, however, microbunching can be more severe

  23. energy profile long. space temporal profile CSR can amplify small current modulations: micro-bunching sd 310-6 230 fsec Super-conducting wiggler prior to BC increases uncorrelated E-spread (310-6 310-5) sd 310-5 R. Carr CSR Microbunching* in LCLS SC-wiggler damps bunching * First observed by M. Borland (ANL) in LCLSElegant tracking

  24. CSR Microbunching Gain in LCLS BC2 ‘cold’ beam sE/E0 = 310-6 add 2% current & energy modulation gex0 = 0 after compressor

  25. CSR Microbunching Animation f(s) DE/E0 gex

  26. LCLS BC2 CSR Microbunching Gain vs. l gex=1mm ‘cold’ beam Microbunching Gain gex=1mm, sd=310-5 see also E. Saldin, Jan. 02, and Z. Huang, April 02 Initial modulation wavelength prior to compressor “theory”: S. Heifets et al., SLAC-PUB-9165, March 2002

  27. …Energy Profile also modulated energy profile DE/E vs. z Next set of bends will magnify this again…  ‘slice’ effects current profile

  28. LCLS BC1/BC2 Compound Gain Curve gex= 1 mm sd= 310-6 curves: Z. Huang et al., PRSTAB April 2002 points: 1D tracking code Compound Gain SC-wiggler: sd= 310-5 wavelength at entrance to BC2

  29. Damping by Emittance and Energy Spread E. Schneidmiller, et al. (no compression) Microbunching is damped by x-emittance or uncorrelated energy spread for wavelengths less than… • To reduce microbunching… • long bends, Lb • large bxorex • large uncorrelated energy spread, sdu

  30. Dipole Field Quality LCLS BC2 B2 & B3 bends: |b1/b0| < 0.01 % |b2/b0| < 0.05 % at r0 = 2 cm Large beam size in chicane — need constant bend field over wide aperture Quadrupole field component at radiusr0 …causes dispersion error and beta-mismatch Sextupole field component at radiusr0 …causes 2nd-order dispersion, with chromatic and geometric aberrations |b1/b0| is correctable…

  31. ‘Tweaker’ quadrupoles allow dispersion correction LEUTL chicane (ANL) Dx  /2 M. Borland with two quads… correct h and (ah + bh), orthogonally

  32. Feedback Systems BPM (DE/E) f, V relative bunch length (sz) tolerances: ~ 0.1 deg-S ~0.1% DV/V Feedback at each compressor, plus charge-feedback at gun… …needs work (algorithm, diagnostics, full-system simulations)

  33. Final Comments • Many details need attention so that brightness is increased, not decreased after compression • Compression system design should be well integrated into entire machine • Stability • Emittance preservation • Diagnostics • Feedback systems may be critical • Progress made at SLC only after feedback systems up and running

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