CSR Microbunching including Linac Wakefields

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CSR Microbunching including Linac Wakefields Z.
Huang, M. Borland, P. Emma, K.-J. Kim SLAC and
Argonne Berlin S2E Workshop 8/19/2003
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CSR Microbunching in LCLS
SC-wiggler damps bunching
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Compressor and CSR
Formation length (overtaken length) lf (24 r2
l)1/3 , r is the bend radius
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CSR Impedance

• Ignore transverse effects
• Ignore shielding
• source size ltlt b (pipe
  radius)
• Ignore transient effect Lf ltlt Lb
• (not the usual case, but included in1D codes)
• ? Steady-state, free-space CSR longitudinal
  impedance (Derbenev et al., Murphy et al.)

k 2p/l w/c
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CSR Microbunching

• CSR emitted from sub-bunch structures for
  wavelengths l ltlt sz interacts back to the bunch,
  leading to a microbunching instability
• (similar to microwave instability in a ring)

• This process can be initiated by either density
  or energy modulation

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CSR Microbunching Simulation
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gex 0 sE/E0 2?10-6
G ? 11
energy modulation
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Theory

• Define a bunching parameter b at modulation
  wavelength l 2p/k (fourier decomposes the
  current)

• For arbitrary initial condition (density and/or
  energy modulation), this determines the final
  microbunching

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Staged Amplification

• Typical chicane
• dipole separation DL gtgt dipole length Lb

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1
3

• Ignore the induced bunching from energy
  modulation in the same dipole (Saldin et al.)
• Consider staged amplification from dipole to
  dipole by
• setting K(s,s)O(Lb/DL)0 if s-slt DL

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Iterative Solution

• Integral equation can be solved by two iterations

• Calculate gainbfinal/binitial as a function
  of l, and compare with simulation results

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Berlin CSR Benchmark Chicane

• Elegant and CSR_calc (matlab based) codes used
• a few million particles are loaded with 6D quiet
  start
• CSR algorithm based on analytical wake models

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LCLS Acceleration and Compression Systems
7 MeV ?z ? 0.83 mm ?? ? 5?10-4
rf gun
Linac-1 L ? 9 m ?rf ? -38
Linac-2 L ? 330 m ?rf ? -43
Linac-3 L ? 550 m ?rf ? -10
new
Linac-0 L ?6 m
undulator L ?120 m
X
...existing linac
SLAC linac tunnel
undulator hall
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BC1

• BC1 gain in density modulation is low (so is BC2)

sd1.210-5, en1 mm
after BC1
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BC1BC2

• BC2 not only amplifies density modulation gained
  in BC1, but turns BC1 energy modulation into gain
  in density modulation
• ?Total gain of BC1BC2 gt BC1 gain X BC2 gain

Wiggler off
Wiggler on
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LCLS CSR Microbunching Gain

• LCLS has four bend systems BC1, BC2, and two
  beam transport dog legs (DL1, DL2)
• DLs have very small R56 ? ignore induced density
  modulation but keep track of induced energy
  modulation

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Effect of Linac Wake

• For a density-modulated beam, linac wake or
  impedance induces energy modulation, which turns
  into additional density modulation at bunch
  compressors through R56
• Longitudinal high-frequency impedance of a
  periodic accelerator structure (to the leading
  order) is

BC1
BC2
DL1
Linac 1
Linac 2 L 330 m
(capacitive)

• ?(k) / Z(k) I(k) L, where L 300 m, comparable
  to energy modulation induced in BCs through CSR
  impedance

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Effect of Linac Wake (continued)

• Linac wakefields increase the gain by about a
  factor of 2

• Reasonable agreement with Elegant S2E gain
  simulation (nonlinear lattice wake, transient
  CSR and l compresses less than s)

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Summary

• CSR microbunching instability is governed by an
  integral equation which is solved by two
  iterations for a typical chicane

• Initialized by density and/or energy modulation,
  cascading through multiple chicanes and bends

• Two similar but independent CSR codes shows
  reasonable agreement with each other and with
  theory

• Geometric wakefields in the LCLS linac enhance
  the energy modulation and the total gain
• Further enhancement in gain when LSC is taken
  into account