Longitudinal Space Charge in LCLS S2E Z. Huang, M. Borland, P. Emma, J.H. Wu SLAC and Argonne Berlin S2E Workshop 8/21/2003

LSC driven microbunching instability (Saldin et al.) Initial studies suggest that accumulated energy modulation at the end of the injector is small at the most dangerous modulation wavelengths for LCLS, but there are residual density modulation Calculations and simulations presented in this talk assumes only initial density modulation at the end of the injector and examine the gain in density modulation and induced energy modulation for the rest of the LCLS accelerator Compare two options to suppress the instability Introduction

LCLS Accelerator Systems Linac 1 BC1BC2 SC wiggler DL2 DL1 Injector LSC, linac wakefield in Linac 1, 2, and 3 + CSR in DL 1, BC1, BC2, DL2 Density modulation induces energy modulation in DL1 and Linac 1, converted/amplified in BC1 to density modulation; More energy modulation is induced in Linac 2, converted/amplifed in BC2 to more density modulation Landau damping options: a SC-wiggler before BC2 or a laser heater before DL1 Linac 2Linac 3 Laser heater

LSC Impedance For a round, parallel electron beams with a uniform transverse cross section of radius r b, the longitudinal space charge impedance on axis is (cgs units) Off-axis LSC is smaller and can increase the energy spread (a small effect until near microbunching saturation) For a pencil beam, LSC impedance strong at very short

Elegant Simulation at I = 200  m

Elegant Simulation at I = 100  m

Elegant Simulation at I = 60  m

Elegant Simulation at I = 30  m

Elegant Simulation at I = 15  m

Total gain in density modulation LSC increases the peak gain significantly (3X) Assume laser heater increases the energy spread before BC1 by 10X (3 keV  30 keV), so that the energy spread reaches the value given by the SC wiggler at BC2

BC1 gain in density modulation BC1 gain is very different (due to LSC) at shorter between laser heater (Landau damping) and SC-wiggler (doesn’t do anything until beam reaches BC2) As a result, energy modulation at these short prior to BC2 is very large, and the Landau damping of the wiggler is ineffective to control these large energy spread

Wiggler Laser      

Wiggler Laser      

Stronger Landau Damping Current design has energy spread 1 £ for the FEL Since FEL  ~ 5 £ 10 -4, small increase in energy spread is allowed, say 1.7 £  Laser heater increases energy spread 3 keV  50 keV  Wiggler increases energy spread to 5 £ at 4.5 GeV

LSC further enhances microbunching gain in LCLS Summary and Discussion Landau damping of the density modulation is not too sensitive to the location of the energy-spread heater High-frequency energy modulation is very sensitive to the choice of the heater A true S2E must take into account gun and injector modulation study (1% density modulation at i = 15  m ?) A laser heater seems to be more effective in controlling growth of both density and energy modulations, and more flexible in tuning (but harder to tune…)