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
1Simulation 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
2Motivation
- 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
3LSC 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?
4Space 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
5Two 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
6Testing 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
?
7Integral Equations
Density modulation
Energy Modulation
- Applicable for both accelerator cavity and drift
space - Impedance for LSC
8Analytical 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
?
9Analytical 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?
10Analytical vs. ASTRA (density modulation)
- 3 meter drift without acceleration
11Analytical 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
12S2E 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)
13Comparison 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
14Simulation 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
15Simulation 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
16Simulation 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
17Phase 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
185?10-5
5?10-5
30 mm
injector output (135 MeV)
?1
LCLS
l0 30 mm
NO HEATER
195?10-5
5?10-5
30 mm
after DL1 dog-leg (135 MeV)
LCLS
l0 30 mm
NO HEATER
201?10-3
1?10-3
30 mm
before BC1 chicane (250 MeV)
LCLS
l0 30 mm
NO HEATER
211?10-3
1?10-3
30/4.3 mm
after BC1 chicane (250 MeV)
LCLS
l0 30 mm
NO HEATER
225?10-4
5?10-4
30/4.3 mm
before BC2 chicane (4.5 GeV)
LCLS
l0 30 mm
NO HEATER
232?10-3
2?10-3
30/30 mm
after BC2 chicane (4.5 GeV)
LCLS
l0 30 mm
NO HEATER
241?10-3
1?10-3
0.09 rms
30/30 mm
before undulator (14 GeV)
LCLS
l0 30 mm
NO HEATER
255?10-5
5?10-5
30 mm
injector output (135 MeV)
?1
LCLS
l0 30 mm
MATCHED HEATER
265?10-4
5?10-4
30 mm
just after heater (135 MeV)
LCLS
l0 30 mm
MATCHED HEATER
275?10-4
5?10-4
30 mm
after DL1 dog-leg (135 MeV)
LCLS
l0 30 mm
MATCHED HEATER
281?10-3
1?10-3
30 mm
before BC1 chicane (250 MeV)
LCLS
l0 30 mm
MATCHED HEATER
292?10-3
2?10-3
30/4.3 mm
after BC1 chicane (250 MeV)
LCLS
l0 30 mm
MATCHED HEATER
305?10-4
5?10-4
30/4.3 mm
before BC2 chicane (4.5 GeV)
LCLS
l0 30 mm
MATCHED HEATER
315?10-4
5?10-4
30/30 mm
after BC2 chicane (4.5 GeV)
LCLS
l0 30 mm
MATCHED HEATER
322?10-4
2?10-4
0.01 rms
30/30 mm
before undulator (14 GeV)
LCLS
l0 30 mm
MATCHED HEATER
33LCLS gain and slice energy spread
End of BC2
Nonlinear region / Saturation
?1, 30?m
Undulator entrance
34Discussion 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)