Simulation of Microbunching Instability in LCLS with Laser-Heater Juhao Wu, M. Borland (ANL), P. Emma, Z. Huang, C. Limborg, G. Stupakov, J. Welch - PowerPoint PPT Presentation

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Simulation of Microbunching Instability in LCLS with Laser-Heater Juhao Wu, M. Borland (ANL), P. Emma, Z. Huang, C. Limborg, G. Stupakov, J. Welch

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Simulation of Microbunching Instability in LCLS with Laser-Heater. Juhao Wu, M. Borland (ANL), P. Emma, Z. Huang, C. Limborg, G. Stupakov, J. Welch ... – PowerPoint PPT presentation

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Title: Simulation of Microbunching Instability in LCLS with Laser-Heater Juhao Wu, M. Borland (ANL), P. Emma, Z. Huang, C. Limborg, G. Stupakov, J. Welch


1
Simulation of Microbunching Instability in LCLS
with Laser-HeaterJuhao Wu, M. Borland (ANL), P.
Emma, Z. Huang, C. Limborg, G. Stupakov, J.
Welch
  • Longitudinal Space Charge (LSC) modeling
  • Drift space and Accelerator cavity as test-bed
    for a LSC model
  • Implement of LSC model in ELEGANT
  • Simulation of microbunching instability (ELEGANT)
  • Without laser-heater
  • With laser-heater

2
Motivation
  • Whats new? ? LSC important in photoinjector and
    downstream beam line (see Z. Huangs talk)
  • PARMELA / ASTRA simulation time consuming for
    S2E difficult for high-frequency microbunching
    (numerical noise)
  • Find simple, analytical LSC model, and implement
    it to ELEGANT for S2E instability study
  • Starting point - free-space 1-D model
    (justification)
  • Transverse variation of the impedance ?
    decoherence small? 2-D?
  • Pipe wall ? decoherence small?
  • Test LSC model in simple element
  • Use such a LSC model for S2E instability study

3
LSC Model (1-D)
  • Free space 1-D model transverse uniform coasting
    beam with longitudinal density modulation
    (on-axis)
  • where, rb is the radius of the coasting beam

?
rb
pancake beam
pencil beam
  • For more realistic distribution ? find an
    effective rb, and use the above impedance
  • Radial-dependence of the impedance will increase
    energy spread and enhance damping small?

4
Space Charge Oscillation in a Coasting Beam
  • Distinguish low energy case ? high energy case
  • Space charge oscillation becomes slow, when the
    electron energy becomes high the residual
    density modulation is then frozen in the
    downstream beam line.

rb0.5 mm, I0100 A
E 12 MeV
E 6 MeV
5
Two Quantities
  • The quantities we concern are density modulation,
    and energy modulation

Heifets-Stupakov-Krinsky(PRST,2002)
Huang-Kim(PRST,2002)? (CSR)
Density modulation
Integral equation approach
Energy modulation
R56
6
Testing the LSC model
  • Analytical integral equation approach
  • Find an effective radius for realistic transverse
    distributions and use 1-D formula for LSC
    impedance for parabolic Gaussian
  • Generalize the momentum compaction function to
    treat acceleration in LINAC, and for drift space
    as well
  • Simulation
  • PARMELA
  • ASTRA
  • ELEGANT

?
7
Integral Equations
Density modulation
Energy Modulation
  • Applicable for both accelerator cavity and drift
    space
  • Impedance for LSC

8
Analytical Approach Two Limits
  • Analytical integral equation approach two
    limits
  • Density and energy modulation in a drift at
    distance s
  • At a very large ?, plasma phase advance (?s/c) ltlt
    1,
  • ? frozen, energy modulation gets accumulated
  • (Saldin-Schneidmiller-Yurkov,
    TESLA-FEL-2003-02)
  • Integral equation approach deals the general
    evolution of the density and energy modulation

?
9
Analytical vs. ASTRA (energy modulation)
  • 3 meter drift without acceleration
  • In analytical approach
  • Transverse beam size variation due to transverse
    space charge included
  • Slice energy spread increases not included
  • 1 keV resolution? Coasting beam vs. bunched beam?

10
Analytical vs. ASTRA (density modulation)
  • 3 meter drift without acceleration

11
Analytical vs. PARMELA (energy modulation)
  • Assume 10 initial density modulation at gun exit
    at 5.7 MeV
  • After 67 cm drift 2 accelerating structures
    (150 MeV in 7 m), LSC induced energy modulation

PARMELA simulation
Analytical approach
12
S2E Simulation
  • LSC model
  • Analytical approach agrees with PARMELA / ASTRA
    simulation
  • Wall shielding effect is small as long as
    (typical in our study)
  • Free space calculation overestimates the results
    (10 20)
  • Radial-dependence and the shielding effect ?
    decoherence (effect looks to be small)
  • Free space 1-D LSC impedance with effective
    radius has been implemented in ELEGANT
  • S2E simulation
  • Injector simulation with PARMELA / ASTRA (see C.
    Limborgs talk)
  • downstream simulations ? ELEGANT with LSC model
    (CSR, ISR, Wake etc. are all included)

13
Comparison with ELEGANT
  • Free space 1-D LSC model with effective radius
  • Example with acceleration current modulation at
    different wavelength

I100 A, rb0.5 mm, E05.5 MeV, Gradient 7.5 MV/m
--- 1 mm, --- 0.5 mm, --- 0.25 mm, --- 0.1 mm
Elegant tracking
Analytical calculation
14
Simulation Details
  • Halton sequence (quiet start) particle generator
  • Based on PARMELA output file at E135 MeV, with
    200 k particles
  • Longitudinal phase space keep correlation
    between t and p --- fit p(t), and also local
    energy spread ?p(t)
  • Multiply density modulation (? 1 )
  • Transverse phase space keep projected emittance
  • 6-D Quiet start to regenerate 2 million particles
  • Bins and Nyquist frequency --- typically choose
    bins to make the wavelength we study to be larger
    than 5 Nyquist wavelength
  • 2000 bins for initial 11.6 ps bunch
  • Nyquist wavelength is 3.48 ? m
  • We study wavelength longer than 20 ? m

15
Simulation Details
  • Wake
  • Low-pass filter is essential to get stable
    results
  • Smoothing algorithms (e.g. Savitzky-Golay) is not
    helpful
  • Non-linear region
  • Synchrotron oscillation ? rollover ? harmonics
  • Low-pass filter is set to just allow the second
    harmonic

Current form-factor
Low-pass filter
Impedance
16
Simulation Details
  • Gain calculation (linear region)
  • Choose the central portion to do the analysis
  • Use polynomial fit to remove any gross variation
  • Use NAFF to find the modulation wavelength and
    the amplitude

17
Phase space evolution along the beam line
  • Without laser-heater (? 1 initial density
    modulation at 30 ?m )
  • Really bad
  • With matched laser-heater (? 1 initial density
    modulation at 30 ?m )
  • Microbunching is effectively damped

18
5?10-5
5?10-5
30 mm
injector output (135 MeV)
?1
LCLS
l0 30 mm
NO HEATER
19
5?10-5
5?10-5
30 mm
after DL1 dog-leg (135 MeV)
LCLS
l0 30 mm
NO HEATER
20
1?10-3
1?10-3
30 mm
before BC1 chicane (250 MeV)
LCLS
l0 30 mm
NO HEATER
21
1?10-3
1?10-3
30/4.3 mm
after BC1 chicane (250 MeV)
LCLS
l0 30 mm
NO HEATER
22
5?10-4
5?10-4
30/4.3 mm
before BC2 chicane (4.5 GeV)
LCLS
l0 30 mm
NO HEATER
23
2?10-3
2?10-3
30/30 mm
after BC2 chicane (4.5 GeV)
LCLS
l0 30 mm
NO HEATER
24
1?10-3
1?10-3
0.09 rms
30/30 mm
before undulator (14 GeV)
LCLS
l0 30 mm
NO HEATER
25
5?10-5
5?10-5
30 mm
injector output (135 MeV)
?1
LCLS
l0 30 mm
MATCHED HEATER
26
5?10-4
5?10-4
30 mm
just after heater (135 MeV)
LCLS
l0 30 mm
MATCHED HEATER
27
5?10-4
5?10-4
30 mm
after DL1 dog-leg (135 MeV)
LCLS
l0 30 mm
MATCHED HEATER
28
1?10-3
1?10-3
30 mm
before BC1 chicane (250 MeV)
LCLS
l0 30 mm
MATCHED HEATER
29
2?10-3
2?10-3
30/4.3 mm
after BC1 chicane (250 MeV)
LCLS
l0 30 mm
MATCHED HEATER
30
5?10-4
5?10-4
30/4.3 mm
before BC2 chicane (4.5 GeV)
LCLS
l0 30 mm
MATCHED HEATER
31
5?10-4
5?10-4
30/30 mm
after BC2 chicane (4.5 GeV)
LCLS
l0 30 mm
MATCHED HEATER
32
2?10-4
2?10-4
0.01 rms
30/30 mm
before undulator (14 GeV)
LCLS
l0 30 mm
MATCHED HEATER
33
LCLS gain and slice energy spread
End of BC2
Nonlinear region / Saturation
?1, 30?m
Undulator entrance
34
Discussion and Conclusion
  • Instability not tolerable without laser-heater
    for ? lt 200 -- 300 ?m with about ? 1 density
    modulation after injector
  • Laser-heater is quite effective and a fairly
    simple and prudent addition to LCLS
  • Injector modulation study also important, no
    large damping is found to confidently eliminate
    heater. (see C. Limborgs talk)
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