Intra-beam Scattering in the LCLS Linac Zhirong Huang, SLAC Berlin S2E Workshop 8/21/2003
Introduction Intra-beam scattering (IBS) – multiple coulomb scattering redistribute the beam momenta to approach “thermal” equilibrium in the beam frame Beams in accelerators are typically much “colder” longitudinally than transversely heat transfer from transverse dimensions to longitudinal induce energy spread (in a ring, IBS induced energy spread in a dispersive region turns into emittance growth after many turns) In a single-pass linac, IBS is typically negligible FEL beams are very bright (~a few keV intrinsic energy spread), increase in energy spread may help damp the microbunching instability
IBS Formula IBS growth rate for energy spread (Piwinski) Take a transversely round beam and set =1 (v=c) norm. emittance rms Coulomb Log ¿ x’ » y’
Coulomb Log The Coulomb log ~ 16 for all scatterings (soft and hard) Scattering distribution has a nearly gaussian core with long tail (due to hard scatterings) Keep the core, cut off the tail max ~ ×10 -5 Coulomb log ~ 8 (somewhat arbitrary but insensitive) Increase in incoherent energy spread if I use average beam size h x i and bunch length s between compression
LCLS Linac Take N b = 6.2 £ 10 9 (1 nC), x n = 1 m, h x i = 100 m, before BC1, use s = 830 m, s = 40 m IBS adds 50% energy spread before BC1 (1.2 ! 1.8 £ ) before BC2, use s = 190 m, s = 360 m IBS doubles energy spread before BC2 (3 ! 7 £ ) after BC2, use s = 22 m, s = 800 m IBS adds 1 £ energy spread at the end of linac, not a problem for LCLS (FEL parameter ~ )
LCLS Linac-2 P. Emma
z 190 m, Q = 1 nC LCLS Linac-2
Effect of IBS on CSR microbunching IBS induced energy spread reduces CSR microbunching -Wiggler off -Wiggler off, IBS -Wiggler on Not strong enough to replace the damping wiggler in LCLS
Conclusion IBS induces energy spread comparable to the intrinsic energy spread of FEL beams Is NOT a problem for FEL operations Slightly reduce the CSR microbunching but not nearly enough