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

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

Magnetic Bunch Compression z0z0 z0z0  z z zz zz under- compression V = V 0 sin(  ) RF Accelerating Voltage Voltage  z = R 56  Path Length-Energy Dependent Beamline Path Length-Energy Dependent Beamline …or over- compression  z z E/EE/E E/EE/E z z ‘chirp’

TESLA XFEL at DESY X-FEL Integrated into linear collider Å 3 compressors

X-FEL based on last 1-km of existing SLAC linac LCLS at SLAC LCLSLCLS Å 2 compressors

eV z  eV 0 Single-Stage Bunch Compression final bunch length and energy spread… bunch length stability with RF phase jitter… T. Raubenheimer ‘chirp’

  t0t0 t0t0 t0t0 t0t0 t1t1 t1t1 late arrival, higher energy, less chirp late arrival, higher energy, less chirp longer bunch, less wake, more chirp longer bunch, less wake, more chirp t2t2 t2t2 Two-Stage Compression Used for Stability System can be optimized for stability against timing & charge jitter ~same bunch length

Types of Compressors wiggler FODO-cell arc TT TT SLC RTL, SLC arcs NLC BC2 SLC RTL, SLC arcs NLC BC2 LEUTL,… LCLS, TTF-BC1,2, TESLA-BC1 LEUTL,… LCLS, TTF-BC1,2, TESLA-BC1 TESLA-BC2,3 But T 566 > 0 in all cases… (bunch head at z < 0 ) > 0 reverse sign < 0 simple, achromatic < 0 achromatic, cancellation? LTLT LTLT 4-dipole chicane LBLB LBLB LcLc LcLc  

For chicane or wiggler (any ‘non-focusing’ compressor), the path length... Now add 2 nd order term of sinusoidal rf accelerating voltage... For a uniform temporal distribution [  z 0 4  = (9/5)  z0 4 ] and  z 0  0  = nd Order Compression Limitations r  T 566 /R 56

For chicane and accelerating phase, RF curvature and T 566 always add, limiting the minimum bunch length... eV z ee z ee r  T 566 /R 56 Decelerating phase can be used to compensate T 566, but not practical in low energy compressors (used in NLC and TESLA)... ee linear 2 nd -order R 56 /m  z /  m

 1   40°  x =  Slope linearized x = s /4 Harmonic RF used to Linearize Compression RF curvature and 2 nd -order compression cause current spikes Harmonic RF at decelerating phase corrects 2 nd -order and allows unchanged z -distribution avoid! 0.5-m X-band section for LCLS (22 MV, 11.4 GHz) 3 rd harmonic used at TTF / TESLA 4 th harmonic used at LCLS 3 rd harmonic used at TTF / TESLA 4 th harmonic used at LCLS  m  m

eV z ee z ee Reverse-Sign R 56 to Linearize Compression eV z ee z ee   TESLA-BC arc example   70° TESLA-BC arc example   70° chicane or wiggler R 56 < 0 FODO-cell arc R 56 > 0

SLAC S-Band: s 0  1.32 mm a  11.6 mm s < ~6 mm SLAC S-Band: s 0  1.32 mm a  11.6 mm s < ~6 mm Wakefield induced slope (–) RF slope (+ for chicane) For a uniform s -distribution (  s = 2  3  s )... Induced voltage along bunch: Longitudinal Geometric Wakefields V(s)/MV/nC/m s/  s FW 1 mm 500  m 250  m 100  m 50  m 50  m 25  m 25  m ss Longitudinal point-wake: K. Bane

L  550 m, N  6.2  10 9,  z  75  m, E = 14 GeV LCLS Example of Wakefield Use wakefield ‘OFF’ wakefield ‘ON’ for uniform distribution wake-induced energy spread  head    0.26 %  head   < 0.02 % end of LCLS linac

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

Synchrotron Radiation zz zz   1/3 Power Wavelength coherent power incoherent power vacuum chamber cutoff N  10 10

Incoherent synchrotron radiation (ISR) increases at high energies - dilutes ‘slice’ emittance... For, symmetric beta- functions, the effect is minimum when... And substituting R 56 for ... Total chicane length, L, set by tolerable  N (e.g.,  /  0  1% )… LCLS BC2 ( E = 4.50 GeV, |R 56 | = 22 mm ) needs L  6.4 m LCLS BC1 ( E = 0.25 GeV, |R 56 | = 36 mm) needs L  0.06 m LCLS BC2 ( E = 4.50 GeV, |R 56 | = 22 mm ) needs L  6.4 m LCLS BC1 ( E = 0.25 GeV, |R 56 | = 36 mm) needs L  0.06 m ISR Emittance Growth for Chicane xx xx LL LL LBLB LBLB L L   T. Raubenheimer

  x = R 16 (s)  E/E bend-plane emittance growth e–e–e–e– R Coherent Synchrotron Radiation (CSR) zzzz coherent radiation for  z overtaking length: L 0  (24  z R 2 ) 1/3  s s xx xx  Powerful radiation generates energy spread in bends  Causes bend-plane emittance growth (short bunch worse)  Energy spread breaks achromatic system  L0L0L0L0  CSR wake is strong at very small scales (   m )

B1 B2 B3 B4  x  1.52  m Projected Emittance Growth B1 B2 B3 B4    0.021%     0.043% Berlin Workshop Case x/mrad z /mm

Now rematch incoming beam  opt  1.37 m  opt   1.10  opt  1.37 m  opt   1.10   1.52  m  0 = 1.00  m  CSR   m Projected Emittance growth reduced by  -matching slice centroids after CSR    opt    opt    opt    opt   1.15  m  0 = 1.00  m  CSR   m

 x  244 mm  x  107 mm II R 56 =  21 mm R 56 =  4 mm Double-Chicane Emittance Growth Cancellation  s  50  m  s  200  m  s  20  m E 0 = 5 GeV

CSR Emittance Growth Reduced in Double-Chicane  x  1.01  m projected emittance growth is greatly reduced using double- chicane, however, microbunching can be more severe single-chicanesingle-chicane double-chicanedouble-chicane

CSR Microbunching* in LCLS SC-wiggler damps bunching    3  10  5 Super-conducting wiggler prior to BC increases uncorrelated E -spread (     ) R. Carr energy profile long. space temporal profile micro- bunching    3  10  fsec CSR can amplify small current modulations: *First observed by M. Borland (ANL) in LCLS Elegant tracking

 E /E 0 = 3  10  6  x0 = 0 ‘cold’ beam CSR Microbunching Gain in LCLS BC2 add 2% current & energy modulation after compressor

CSR Microbunching Animation E/E0E/E0 E/E0E/E0 f(s)  x

LCLS BC2 CSR Microbunching Gain vs. “theory”: S. Heifets et al., SLAC-PUB-9165, March 2002 Initial modulation wavelength prior to compressor Microbunching Gain ‘cold’ beam  x =1  m  x =1  m,   =3  10  5 see also E. Saldin, Jan. 02, and Z. Huang, April 02

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

 x = 1  m curves: Z. Huang et al., PRSTAB April 2002 points: 1D tracking code LCLS BC1/BC2 Compound Gain Curve wavelength at entrance to BC2 Compound Gain    = 3  10  6 SC-wiggler:    = 3  10  5

Microbunching is damped by x -emittance or uncorrelated energy spread for wavelengths less than… Damping by Emittance and Energy Spread E. Schneidmiller, et al. (no compression) To reduce microbunching…  long bends, L b  large  x or  x  large uncorrelated energy spread,   u To reduce microbunching…  long bends, L b  large  x or  x  large uncorrelated energy spread,   u

Dipole Field Quality Quadrupole field component at radius r 0 Sextupole field component at radius r 0 Large beam size in chicane — need constant bend field over wide aperture LCLS BC2 B2 & B3 bends: |b 1 /b 0 | < 0.01 % |b 2 /b 0 | < 0.05 % LCLS BC2 B2 & B3 bends: |b 1 /b 0 | < 0.01 % |b 2 /b 0 | < 0.05 % at r 0 = 2 cm …causes dispersion error and beta-mismatch …causes 2 nd -order dispersion, with chromatic and geometric aberrations |b 1 /b 0 | is correctable…

 x   /2 ‘Tweaker’ quadrupoles allow dispersion correction with two quads… correct  and (  ), orthogonally with two quads… correct  and (  ), orthogonally LEUTL chicane (ANL) M. Borland

relative bunch length (  z ) BPM (  ) Feedback Systems , V Feedback at each compressor, plus charge-feedback at gun… …needs work (algorithm, diagnostics, full-system simulations) Feedback at each compressor, plus charge-feedback at gun… …needs work (algorithm, diagnostics, full-system simulations) tolerances: ~ 0.1 deg-S ~0.1%  V / V tolerances: ~ 0.1 deg-S ~0.1%  V / V

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  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