Transcript Simulation of Microbunching Instability in LCLS with Laser-Heater

Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
Simulation of Microbunching Instability
in LCLS with Laser-Heater
Juhao 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
Laser-Heater Physics Review, March 01, 2004
1
Simulation of Microbunching Instability in LCLS with Laser-Heater
Juhao Wu, SLAC
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
Motivation
• What’s new?  LSC important in photoinjector and
downstream beam line; (see Z. Huang’s 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
Laser-Heater Physics Review, March 01, 2004
2
Simulation of Microbunching Instability in LCLS with Laser-Heater
Juhao Wu, SLAC
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
LSC Model (1-D)
• Free space 1-D model: transverse uniform coasting beam with
longitudinal density modulation (on-axis)
λ
rb
pancake beam
pencil beam
where, rb is the radius of the coasting 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?
Laser-Heater Physics Review, March 01, 2004
3
Simulation of Microbunching Instability in LCLS with Laser-Heater
Juhao Wu, SLAC
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
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.
rb=0.5 mm,
I0=100 A
E = 12 MeV
E = 6 MeV
1/ 2
sc
 I0

 c 3
k0 Z LSC k0  
  I A

2c  I 0

rb   3 I A
Laser-Heater Physics Review, March 01, 2004
4
Simulation of Microbunching Instability in LCLS with Laser-Heater
1/ 2




 p
plasma freq.
Juhao Wu, SLAC
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
Two Quantities
• The quantities we concern are density modulation, and
energy modulation
Density modulation
Heifets-Stupakov-Krinsky(PRST,2002);
Huang-Kim(PRST,2002) (CSR)
Integral equation approach
1
b( k ; s ) 
N
ikz
d
X
e
f X; s 

Energy modulation
R56
I 0 Z [k ( ); ]b[k ( ); ]
 ( s)    d
0
IA
s
Laser-Heater Physics Review, March 01, 2004
5
Simulation of Microbunching Instability in LCLS with Laser-Heater
Juhao Wu, SLAC
[email protected]
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
Linac Coherent Light Source
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
rb  1.7 x
Generalize the momentum compaction function to treat
acceleration in LINAC, and for drift space as well
56 (  s)  
s


dx
 ( x) 1   ( x)
3
2


Simulation
PARMELA
ASTRA
ELEGANT
Laser-Heater Physics Review, March 01, 2004
6
Simulation of Microbunching Instability in LCLS with Laser-Heater
Juhao Wu, SLAC
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
Integral Equations
Density modulation
s
b[k ( s); s]  b0 [k ( s); s]   dK ( , s)b[k ( ); ]
0
I ( ) Z [ K ( ); ]
K ( , s)  ik ( s)56 (  s)
IA
Energy Modulation:
I 0 Z [k ( ); ]b[k ( ); ]
 ( s)    d
0
IA
s
• Applicable for both accelerator cavity and drift space
• Impedance for LSC
Laser-Heater Physics Review, March 01, 2004
7
Simulation of Microbunching Instability in LCLS with Laser-Heater
Juhao Wu, SLAC
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
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) << 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
Laser-Heater Physics Review, March 01, 2004
8
Simulation of Microbunching Instability in LCLS with Laser-Heater
Juhao Wu, SLAC
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
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?
Laser-Heater Physics Review, March 01, 2004
9
Simulation of Microbunching Instability in LCLS with Laser-Heater
Juhao Wu, SLAC
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
Analytical vs. ASTRA (density modulation)
• 3 meter drift without acceleration
Laser-Heater Physics Review, March 01, 2004
10
Simulation of Microbunching Instability in LCLS with Laser-Heater
Juhao Wu, SLAC
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
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
Laser-Heater Physics Review, March 01, 2004
11
Simulation of Microbunching Instability in LCLS with Laser-Heater
Juhao Wu, SLAC
[email protected]
Linac Coherent Light Source
• LSC model
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
S2E Simulation
• Analytical approach agrees with PARMELA / ASTRA simulation;

• Wall shielding effect is small as long as
 R pipe (typical in
k
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. Limborg’s talk);
• downstream simulations  ELEGANT with LSC model (CSR, ISR,
Wake etc. are all included)
Laser-Heater Physics Review, March 01, 2004
12
Simulation of Microbunching Instability in LCLS with Laser-Heater
Juhao Wu, SLAC
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
Comparison with ELEGANT
• Free space 1-D LSC model with effective radius
• Example with acceleration: current modulation at different
I=100 A, rb=0.5 mm, E0=5.5 MeV, Gradient: 7.5 MV/m
wavelength
Elegant tracking
--- 1 mm, --- 0.5 mm, --- 0.25 mm, --- 0.1 mm
Laser-Heater Physics Review, March 01, 2004
13
Simulation of Microbunching Instability in LCLS with Laser-Heater
Analytical calculation
Juhao Wu, SLAC
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
Simulation Details
Halton sequence (quiet start) particle generator
Based on PARMELA output file at E=135 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
Laser-Heater Physics Review, March 01, 2004
14
Simulation of Microbunching Instability in LCLS with Laser-Heater
Juhao Wu, SLAC
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
Simulation Details
Wake
W (t )  IFFT[FFT[ I (t )] f ( ) Z ( )]
Current form-factor
Low-pass filter
Impedance
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
Laser-Heater Physics Review, March 01, 2004
15
Simulation of Microbunching Instability in LCLS with Laser-Heater
Juhao Wu, SLAC
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
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
Laser-Heater Physics Review, March 01, 2004
16
Simulation of Microbunching Instability in LCLS with Laser-Heater
Juhao Wu, SLAC
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
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
Laser-Heater Physics Review, March 01, 2004
17
Simulation of Microbunching Instability in LCLS with Laser-Heater
Juhao Wu, SLAC
[email protected]
E/E
E/E
5105
5105
time (sec)
30 m
1%
injector output (135 MeV)
LCLS
l0 = 30 m
time (sec)
NO HEATER
E/E
E/E
5105
5105
time (sec)
30 m
after DL1 dog-leg (135 MeV)
LCLS
l0 = 30 m
time (sec)
NO HEATER
1103
E/E
E/E
1103
time (sec)
30 m
before BC1 chicane (250 MeV)
LCLS
l0 = 30 m
time (sec)
NO HEATER
E/E
E/E
1103
1103
time (sec)
30/4.3 m
after BC1 chicane (250 MeV)
LCLS
l0 = 30 m
time (sec)
NO HEATER
E/E
E/E
5104
5104
time (sec)
30/4.3 m
before BC2 chicane (4.5 GeV)
LCLS
l0 = 30 m
time (sec)
NO HEATER
E/E
E/E
2103
2103
time (sec)
30/30 m
after BC2 chicane (4.5 GeV)
LCLS
l0 = 30 m
time (sec)
NO HEATER
E/E
E/E
1103
1103
0.09 % rms
time (sec)
30/30 m
before undulator (14 GeV)
LCLS
l0 = 30 m
time (sec)
NO HEATER
E/E
E/E
5105
5105
time (sec)
30 m
1%
injector output (135 MeV)
LCLS
l0 = 30 m
time (sec)
MATCHED HEATER
E/E
E/E
5104
5104
time (sec)
30 m
just after heater (135 MeV)
LCLS
l0 = 30 m
time (sec)
MATCHED HEATER
E/E
E/E
5104
5104
time (sec)
30 m
after DL1 dog-leg (135 MeV)
LCLS
l0 = 30 m
time (sec)
MATCHED HEATER
1103
E/E
E/E
1103
time (sec)
30 m
before BC1 chicane (250 MeV)
LCLS
l0 = 30 m
time (sec)
MATCHED HEATER
E/E
E/E
2103
2103
time (sec)
30/4.3 m
after BC1 chicane (250 MeV)
LCLS
l0 = 30 m
time (sec)
MATCHED HEATER
E/E
E/E
5104
5104
time (sec)
30/4.3 m
before BC2 chicane (4.5 GeV)
LCLS
l0 = 30 m
time (sec)
MATCHED HEATER
E/E
E/E
5104
5104
time (sec)
30/30 m
after BC2 chicane (4.5 GeV)
LCLS
l0 = 30 m
time (sec)
MATCHED HEATER
E/E
E/E
2104
2104
0.01% rms
time (sec)
30/30 m
before undulator (14 GeV)
LCLS
l0 = 30 m
time (sec)
MATCHED HEATER
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
LCLS gain and slice energy spread
End of BC2
Nonlinear region
/ Saturation
1%, 30m
Undulator entrance
Laser-Heater Physics Review, March 01, 2004
33
Simulation of Microbunching Instability in LCLS with Laser-Heater
Juhao Wu, SLAC
[email protected]
Linac Coherent Light Source
Stanford Synchrotron Radiation Laboratory
Stanford Linear Accelerator Center
Discussion and Conclusion
Instability not tolerable without laser-heater for l < 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.
Limborg’s talk)
Laser-Heater Physics Review, March 01, 2004
34
Simulation of Microbunching Instability in LCLS with Laser-Heater
Juhao Wu, SLAC
[email protected]