Longitudinal Space Charge in LCLS S2E

1
Longitudinal Space Charge in LCLS S2E Z. Huang,
M. Borland, P. Emma, J.H. Wu SLAC and
Argonne Berlin S2E Workshop 8/21/2003
2
Introduction

• 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

3
LCLS Accelerator Systems
SC wiggler
Injector
DL1
DL2
Laser heater
Linac 1
Linac 2
Linac 3
BC1
BC2

• 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

4
LSC Impedance

• For a round, parallel electron beams with a
  uniform transverse cross section of radius rb,
  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 ?

5
Elegant Simulation at ?I 200 ?m
6
Elegant Simulation at ?I 100 ?m
7
Elegant Simulation at ?I 60 ?m
8
Elegant Simulation at ?I 30 ?m
9
Elegant Simulation at ?I 15 ?m
10
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

11
BC1 gain in density modulation

• BC1 gain is very different (due to LSC) at
  shorter ? between laser heater (Landau damping)
  and SC-wiggler (doesnt 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

12
Wiggler
? ?
Laser
? ?
13
Wiggler
? ?
Laser
? ?
14
Stronger Landau Damping

• Current design has energy spread 1 10-4 for
  the FEL
• Since FEL ? 5 10-4, small increase in energy
  spread is allowed, say 1.7 10-4
• Laser heater increases energy spread 3 keV ? 50
  keV
• Wiggler increases energy spread to 5 10-5 at
  4.5 GeV

15
Summary and Discussion

• LSC further enhances microbunching gain in LCLS

• 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)