1. Intra-beam Scattering in the LCLS Linac Zhirong Huang, SLAC Berlin S2E Workshop 8/21/2003

2. 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

3. 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’

4. 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

5. 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 £ 10 - 5 ) before BC2, use  s = 190  m,  s = 360 m  IBS doubles energy spread before BC2 (3 ! 7 £ 10 -6 ) after BC2, use  s = 22  m,  s = 800 m  IBS adds 1 £ 10 -5 energy spread at the end of linac, not a problem for LCLS (FEL parameter  ~ 10 -4 )

6. LCLS Linac-2 P. Emma

7.  z  190  m, Q = 1 nC LCLS Linac-2

8. 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

9. 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