Simulation of Microbunching Instability in LCLS with Laser-Heater [email protected] Linac...

Laser-Heater Physics Review, March 01, 2004Laser-Heater Physics Review, March 01, 2004 Juhao Wu, SLACJuhao Wu, SLAC

Simulation of Microbunching Instability in LCLS with Laser-Simulation of Microbunching Instability in LCLS with Laser-HeaterHeater

[email protected]@SLAC.Stanford.EDU

Linac Coherent Light Source Stanford Synchrotron Radiation LaboratoryStanford Linear Accelerator Center

Simulation of Microbunching Instability in LCLS with Laser-HeaterJuhao Wu, M. Borland (ANL), P. Emma, Z. Huang, Juhao Wu, M. Borland (ANL), P. Emma, Z. Huang,

C. Limborg, G. Stupakov, J. WelchC. Limborg, G. Stupakov, J. Welch

Simulation of Microbunching Instability in LCLS with Laser-HeaterJuhao Wu, M. Borland (ANL), P. Emma, Z. Huang, Juhao Wu, M. Borland (ANL), P. Emma, Z. Huang,

C. Limborg, G. Stupakov, J. WelchC. Limborg, G. Stupakov, J. Welch

Longitudinal Space Charge (LSC) modelingLongitudinal Space Charge (LSC) modeling Drift space and Accelerator cavity as test-bed for a LSC Drift space and Accelerator cavity as test-bed for a LSC

modelmodel Implement of LSC model in ELEGANTImplement of LSC model in ELEGANT

Simulation of microbunching instability (ELEGANT)Simulation of microbunching instability (ELEGANT) Without laser-heaterWithout laser-heater With laser-heaterWith laser-heater

Longitudinal Space Charge (LSC) modelingLongitudinal Space Charge (LSC) modeling Drift space and Accelerator cavity as test-bed for a LSC Drift space and Accelerator cavity as test-bed for a LSC

modelmodel Implement of LSC model in ELEGANTImplement of LSC model in ELEGANT

Simulation of microbunching instability (ELEGANT)Simulation of microbunching instability (ELEGANT) Without laser-heaterWithout laser-heater With laser-heaterWith laser-heater





MotivationMotivationMotivationMotivation• 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





LSC Model (1-D)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;

• 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?

pancake beam

pencil beam

rb

λ





Space Charge Oscillation in a Coasting BeamSpace Charge Oscillation in a Coasting BeamSpace Charge Oscillation in a Coasting BeamSpace 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

freq. plasma 2

2/1

30

2/1

0030

pAb

LSCA

scI

I

r

ckZk

I

Ic





Two QuantitiesTwo QuantitiesTwo QuantitiesTwo Quantities

• The quantities we concern are density modulation, and energy modulation

sfedN

skb ikz ;1

);( XX

Density modulation

s

AI

kbkZIds

00 ]);([]);([

)(

Energy modulation R56

Integral equation approach

Heifets-Stupakov-Krinsky(PRST,2002); Huang-Kim(PRST,2002) (CSR)





Analytical integral equation approachAnalytical integral equation approachFind Find an effective radiusan effective radius for realistic transverse distributions and for realistic transverse distributions and use 1-D formula for LSC impedance; for parabolic & Gaussianuse 1-D formula for LSC impedance; for parabolic & Gaussian

GeneralizeGeneralize the momentum compaction function to treat the momentum compaction function to treat acceleration in LINAC, and for drift space as wellacceleration in LINAC, and for drift space as well

SimulationSimulationPARMELAPARMELAASTRAASTRAELEGANTELEGANT

Analytical integral equation approachAnalytical integral equation approachFind Find an effective radiusan effective radius for realistic transverse distributions and for realistic transverse distributions and use 1-D formula for LSC impedance; for parabolic & Gaussianuse 1-D formula for LSC impedance; for parabolic & Gaussian

GeneralizeGeneralize the momentum compaction function to treat the momentum compaction function to treat acceleration in LINAC, and for drift space as wellacceleration in LINAC, and for drift space as well

SimulationSimulationPARMELAPARMELAASTRAASTRAELEGANTELEGANT

Testing the LSC modelTesting the LSC modelTesting the LSC modelTesting the LSC model

s

xx

dxs

2356)(1)(

)(

xbr 7.1





Integral EquationsIntegral EquationsIntegral EquationsIntegral Equations

s

kbsKdsskbsskb00 ]);([),(]);([]);([

Density modulation

Energy Modulation:

s

AI

kbkZIds

00 ]);([]);([

)(

AI

KZIssiksK

]);([)()()(),( 56

• Applicable for both accelerator cavity and drift space

• Impedance for LSC





Analytical integral equation approach – two limitsAnalytical integral equation approach – two limitsDensity and energy modulation in a drift at distance Density and energy modulation in a drift at distance ss;;

At a very large At a very large , plasma phase advance , plasma phase advance ((s/c) << 1s/c) << 1, , “ “frozen,” energy modulation gets accumulatedfrozen,” energy modulation gets accumulated(Saldin-Schneidmiller-Yurkov, TESLA-FEL-2003-02)(Saldin-Schneidmiller-Yurkov, TESLA-FEL-2003-02)

Integral equation approach deals the general evolution of Integral equation approach deals the general evolution of the density and energy modulationthe density and energy modulation

Analytical integral equation approach – two limitsAnalytical integral equation approach – two limitsDensity and energy modulation in a drift at distance Density and energy modulation in a drift at distance ss;;

At a very large At a very large , plasma phase advance , plasma phase advance ((s/c) << 1s/c) << 1, , “ “frozen,” energy modulation gets accumulatedfrozen,” energy modulation gets accumulated(Saldin-Schneidmiller-Yurkov, TESLA-FEL-2003-02)(Saldin-Schneidmiller-Yurkov, TESLA-FEL-2003-02)

Integral equation approach deals the general evolution of Integral equation approach deals the general evolution of the density and energy modulationthe density and energy modulation

Analytical Approach – Two LimitsAnalytical Approach – Two LimitsAnalytical Approach – Two LimitsAnalytical Approach – Two Limits





• 3 meter drift without accelerationAnalytical vs. ASTRAAnalytical vs. ASTRA (energy modulation)Analytical vs. ASTRAAnalytical vs. ASTRA (energy modulation)

• 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?





Analytical vs. ASTRAAnalytical vs. ASTRA (density modulation)Analytical vs. ASTRAAnalytical vs. ASTRA (density modulation)

• 3 meter drift without acceleration





• 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

Analytical vs. PARMELA Analytical vs. PARMELA (energy modulation)

Analytical vs. PARMELA Analytical vs. PARMELA (energy modulation)





S2E SimulationS2E SimulationS2E SimulationS2E 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 has been implementedbeen 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)

pipeRk





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

wavelength

Elegant tracking Analytical calculation--- 1 mm, --- 1 mm, --- 0.5 mm,--- 0.5 mm, --- 0.25 mm, --- 0.25 mm, --- 0.1 mm --- 0.1 mm

I=100 A, rI=100 A, rbb=0.5 mm, E=0.5 mm, E00=5.5 MeV, Gradient: =5.5 MeV, Gradient: 7.5 MV/m7.5 MV/m





Halton sequence (quiet start) particle generatorHalton sequence (quiet start) particle generatorBased on PARMELA output file at E=135 MeV, with 200 k Based on PARMELA output file at E=135 MeV, with 200 k particlesparticlesLongitudinal phase space: keep correlation between t and p --- fit Longitudinal phase space: keep correlation between t and p --- fit p(t), and also local energy spread p(t), and also local energy spread pp(t)(t)

Multiply density modulation (Multiply density modulation ( 1 %) 1 %)Transverse phase space: keep projected emittanceTransverse phase space: keep projected emittance6-D Quiet start to regenerate 2 million particles6-D Quiet start to regenerate 2 million particles

Bins and Nyquist frequency --- typically choose bins to make the Bins and Nyquist frequency --- typically choose bins to make the wavelength we study to be larger than 5 Nyquist wavelengthwavelength we study to be larger than 5 Nyquist wavelength

2000 bins for initial 11.6 ps bunch2000 bins for initial 11.6 ps bunchNyquist wavelength is 3.48 Nyquist wavelength is 3.48 mmWe study wavelength longer than 20 We study wavelength longer than 20 mm

Halton sequence (quiet start) particle generatorHalton sequence (quiet start) particle generatorBased on PARMELA output file at E=135 MeV, with 200 k Based on PARMELA output file at E=135 MeV, with 200 k particlesparticlesLongitudinal phase space: keep correlation between t and p --- fit Longitudinal phase space: keep correlation between t and p --- fit p(t), and also local energy spread p(t), and also local energy spread pp(t)(t)

Multiply density modulation (Multiply density modulation ( 1 %) 1 %)Transverse phase space: keep projected emittanceTransverse phase space: keep projected emittance6-D Quiet start to regenerate 2 million particles6-D Quiet start to regenerate 2 million particles

Bins and Nyquist frequency --- typically choose bins to make the Bins and Nyquist frequency --- typically choose bins to make the wavelength we study to be larger than 5 Nyquist wavelengthwavelength we study to be larger than 5 Nyquist wavelength

2000 bins for initial 11.6 ps bunch2000 bins for initial 11.6 ps bunchNyquist wavelength is 3.48 Nyquist wavelength is 3.48 mmWe study wavelength longer than 20 We study wavelength longer than 20 mm

Simulation DetailsSimulation DetailsSimulation DetailsSimulation Details





WakeWake

Low-pass filter is essential to get stable resultsLow-pass filter is essential to get stable resultsSmoothing algorithms (e.g. Savitzky-Golay) is not helpfulSmoothing algorithms (e.g. Savitzky-Golay) is not helpful

Non-linear regionNon-linear regionSynchrotron oscillation Synchrotron oscillation rollover rollover harmonics harmonicsLow-pass filter is set to just Low-pass filter is set to just allowallow the second harmonic the second harmonic

WakeWake

Low-pass filter is essential to get stable resultsLow-pass filter is essential to get stable resultsSmoothing algorithms (e.g. Savitzky-Golay) is not helpfulSmoothing algorithms (e.g. Savitzky-Golay) is not helpful

Non-linear regionNon-linear regionSynchrotron oscillation Synchrotron oscillation rollover rollover harmonics harmonicsLow-pass filter is set to just Low-pass filter is set to just allowallow the second harmonic the second harmonic


)]()()]([FFT[IFFT)( ZftItW

Low-pass filter

Current form-factor

Impedance





Gain calculation (linear region)Gain calculation (linear region)Choose the central portion to do the analysisChoose the central portion to do the analysisUse polynomial fit to remove any gross variationUse polynomial fit to remove any gross variationUse NAFF to find the modulation wavelength and the amplitudeUse NAFF to find the modulation wavelength and the amplitude

Gain calculation (linear region)Gain calculation (linear region)Choose the central portion to do the analysisChoose the central portion to do the analysisUse polynomial fit to remove any gross variationUse polynomial fit to remove any gross variationUse NAFF to find the modulation wavelength and the amplitudeUse NAFF to find the modulation wavelength and the amplitude






Without laser-heater (Without laser-heater ( 1% initial density modulation at 30 1% initial density modulation at 30 m )m )Really badReally bad

With matched laser-heater (With matched laser-heater ( 1% initial density modulation at 30 1% initial density modulation at 30 m )m )Microbunching is effectively dampedMicrobunching is effectively damped

Without laser-heater (Without laser-heater ( 1% initial density modulation at 30 1% initial density modulation at 30 m )m )Really badReally bad

With matched laser-heater (With matched laser-heater ( 1% initial density modulation at 30 1% initial density modulation at 30 m )m )Microbunching is effectively dampedMicrobunching is effectively damped

Phase space evolution along the beam linePhase space evolution along the beam linePhase space evolution along the beam linePhase space evolution along the beam line

30 m

5105

EE

EE

time (sec)

injector output (135 MeV)

= 30 = 30 mm

5105

NO HEATERNO HEATER

1% LCLS

time (sec)

30 m

EE

EE

after DL1 dog-leg (135 MeV)

= 30 = 30 mm

5105

5105

NO HEATERNO HEATER

LCLS

time (sec)

time (sec)

30 m

EE

EE

before BC1 chicane (250 MeV)

= 30 = 30 mm

11031103

NO HEATERNO HEATER

LCLS

time (sec)

time (sec)

30/4.3 m

EE

EE

after BC1 chicane (250 MeV)

= 30 = 30 mm

1103

1103

NO HEATERNO HEATER

LCLS

time (sec)

time (sec)

30/4.3 m

EE

EE

before BC2 chicane (4.5 GeV)

= 30 = 30 mm

5104

5104

NO HEATERNO HEATER

LCLS

time (sec)

time (sec)

30/30 m

EE

EE

after BC2 chicane (4.5 GeV)

= 30 = 30 mm

21032103

NO HEATERNO HEATER

LCLS

time (sec)

time (sec)

30/30 m

EE

EE

before undulator (14 GeV)

= 30 = 30 mm

11031103

NO HEATERNO HEATER

0.09 % rms

LCLS

time (sec)

time (sec)

30 m

5105

EE

EE

injector output (135 MeV)

= 30 = 30 mm

5105

MATCHEDMATCHED HEATER HEATER

1% LCLS

time (sec)

time (sec)

30 m

EE

EE

just after heater (135 MeV)

= 30 = 30 mm

510455101044


LCLS

time (sec)

time (sec)

30 m

EE

EE

after DL1 dog-leg (135 MeV)

= 30 = 30 mm

510455101044


LCLS

time (sec)

time (sec)

30 m

EE

EE

before BC1 chicane (250 MeV)

= 30 = 30 mm

11031103


LCLS

time (sec)

time (sec)

30/4.3 m

EE

EE

after BC1 chicane (250 MeV)

= 30 = 30 mm

2103


2103

LCLS

time (sec)

time (sec)

30/4.3 m

EE

EE

before BC2 chicane (4.5 GeV)

= 30 = 30 mm

5104 5104


LCLS

time (sec)

time (sec)

30/30 m

EE

EE

after BC2 chicane (4.5 GeV)

= 30 = 30 mm

5104

5104


LCLS

time (sec)

time (sec)

30/30 m

EE

EE

before undulator (14 GeV)

= 30 = 30 mm

2104

2104


0.01% rms

LCLS

time (sec)

time (sec)





End of BC2

Undulator entrance

Nonlinear region / Saturation

LCLS gain and slice energy spreadLCLS gain and slice energy spreadLCLS gain and slice energy spreadLCLS gain and slice energy spread

1%, 301%, 30mm





Discussion and ConclusionDiscussion and ConclusionDiscussion and ConclusionDiscussion and Conclusion

Instability not tolerable without laser-heater for Instability not tolerable without laser-heater for < 200 -- < 200 -- 300 300 m with about m with about 1% density modulation after 1% density modulation after injector;injector;

Laser-heater is quite effective and a fairly simple and Laser-heater is quite effective and a fairly simple and prudent addition to LCLS;prudent addition to LCLS;

Injector modulation study also important, no large Injector modulation study also important, no large damping is found to confidently eliminate heater. (damping is found to confidently eliminate heater. (see C.

Limborg’s talk) )

Instability not tolerable without laser-heater for Instability not tolerable without laser-heater for < 200 -- < 200 -- 300 300 m with about m with about 1% density modulation after 1% density modulation after injector;injector;

Laser-heater is quite effective and a fairly simple and Laser-heater is quite effective and a fairly simple and prudent addition to LCLS;prudent addition to LCLS;

Injector modulation study also important, no large Injector modulation study also important, no large damping is found to confidently eliminate heater. (damping is found to confidently eliminate heater. (see C.

Limborg’s talk) )

Simulation of Microbunching Instability in LCLS with Laser-Heater [email protected] Linac...

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