LSC in drifts Simulations for Injector Case of 100 m modulation

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Technical Review, March 1st, 2004Technical Review, March 1st, 2004 CCéécile Limborg-Déprey, SLACcile Limborg-Déprey, SLAC

Injector RequirementsInjector Requirements Limborg@slac.stanford.eduLimborg@slac.stanford.edu

Linac Coherent Light Source Stanford Linear Accelerator Center

Simulations of LSC in the LCLS Injector

Cécile Limborg-Déprey, P. Emma, Z. Huang, Juhao Wu March 1st, 2003

Simulations of LSC in the LCLS Injector

Cécile Limborg-Déprey, P. Emma, Z. Huang, Juhao Wu March 1st, 2003

LSC in driftsLSC in drifts

Simulations for Injector Simulations for Injector Case of 100 Case of 100 m modulationm modulation Other wavelengths [ 50 ,150 ,200 , 300] Other wavelengths [ 50 ,150 ,200 , 300] mm

ConclusionConclusion

LSC in driftsLSC in drifts

Simulations for Injector Simulations for Injector Case of 100 Case of 100 m modulationm modulation Other wavelengths [ 50 ,150 ,200 , 300] Other wavelengths [ 50 ,150 ,200 , 300] mm

Simulations of LSC in driftsSimulations of LSC in driftsSimulations of LSC in driftsSimulations of LSC in drifts

Simulations descriptionSimulations description40k/200k particles 40k/200k particles

Distribution generated using the Halton sequence of numbers Distribution generated using the Halton sequence of numbers

Longitudinal distributionLongitudinal distribution

2.65 m of drift2.65 m of drift

With 3 cases studied With 3 cases studied 6MeV, 1nC6MeV, 1nC

6 MeV , 2nC6 MeV , 2nC

12 MeV, 1nC12 MeV, 1nC

Simulations descriptionSimulations description40k/200k particles 40k/200k particles

Distribution generated using the Halton sequence of numbers Distribution generated using the Halton sequence of numbers

Longitudinal distributionLongitudinal distribution

2.65 m of drift2.65 m of drift

With 3 cases studied With 3 cases studied 6MeV, 1nC6MeV, 1nC

6 MeV , 2nC6 MeV , 2nC

12 MeV, 1nC12 MeV, 1nC

44 4/)cos(1 ozzekzA

+/- 5%

Summary 100mSummary 100mComparison with theoryComparison with theoryComparison with theoryComparison with theory

• Transverse beam size evolution along beamline taken into account

(Radial variation of green’s function for 2D )

• Evolution of peak current NOT taken into account yet

• Absence of dip in 6MeV curve :

• “Coasting beam “ against “bunched beam” with edge effects

• Intrinsic energy spread

Nominal Tuning Nominal Tuning 10 ps pulse (rise/fall time 1ps ) 10 ps pulse (rise/fall time 1ps )

1 nC 1 nC

Nominal Tuning Nominal Tuning 10 ps pulse (rise/fall time 1ps ) 10 ps pulse (rise/fall time 1ps )

1 nC 1 nC

Laser + Gun

Linac0-1 Linac0-2

6MeV0MeV 60MeV 150MeV

ASTRA Simulations of LSC along Injector BeamlineASTRA Simulations of LSC along Injector BeamlineASTRA Simulations of LSC along Injector BeamlineASTRA Simulations of LSC along Injector Beamline

ASTRA Simulations for modulation of 100 mASTRA Simulations for modulation of 100 m

Modulation Wavelength = 100 Modulation Wavelength = 100 m , with m , with 8% amplitude peak-to-peak8% amplitude peak-to-peak

““Noise of Noise of 8% amplitude around flat top is likely to be present “ P.Bolton 8% amplitude around flat top is likely to be present “ P.Bolton

FWHM = 3mmFWHM = 3mm

Longitudinal bining = 200 points (~ more than 6 bins per period) Longitudinal bining = 200 points (~ more than 6 bins per period)

1 Million particles1 Million particles

Modulation Wavelength = 100 Modulation Wavelength = 100 m , with m , with 8% amplitude peak-to-peak8% amplitude peak-to-peak

““Noise of Noise of 8% amplitude around flat top is likely to be present “ P.Bolton 8% amplitude around flat top is likely to be present “ P.Bolton

FWHM = 3mmFWHM = 3mm

Longitudinal bining = 200 points (~ more than 6 bins per period) Longitudinal bining = 200 points (~ more than 6 bins per period)

1 Million particles1 Million particles

Current

density

with modulation = 100 m with modulation = 100 m Region of interestRegion of interest Fourier AnalysisFourier Analysis

Position (mm)Position (mm) Position (mm)Position (mm) Cycles per mmCycles per mm

Longitudinal Phase Space Longitudinal Phase Space

After removal of correlation up to order 5

Energy

Current

Fourier transform

Fit up to 3rd order

Substract and Fit

Amplitude + rms

w.r.t reference level

z = 0.15 m

E = 6MeV

Gun Exit

E = 0 → 0.35 keV

Current modulation = 5.65% → 3%

Energy

Current

Fourier transform

z = 1.4 m

E = 6MeV

Entrance L01

E = 0.35 keV → 1 keV

Current modulation = 3% → 1.5%

Exit L01

Energy

Current

Fourier transform

z = 4.4 m

E = 60MeV

Exit L01

E = 1 keV → 3 keV

Current modulation = 1.5 % → 1.5%

Exit L02

Energy

Current

Fourier transform

z = 8.4 m

E = 150MeV

Exit L02

E = 3 keV → 3.9 keV

Current modulation = 1.5 % → 1.6%

Summary 100mSummary 100m

Summary 50,100,150,300mSummary 50,100,150,300m

Attenuation by factor

More than 5 for <100m

~ 5 for >100m

At end LCLS injector beamline:At end LCLS injector beamline:

Current density modulation strongly attenuated residual energy oscillation has

amplitude between 2 keV and 4 keV for wavelengths [50 m, 500 m]

Impedance defined by

At end LCLS injector beamline:At end LCLS injector beamline:

Current density modulation strongly attenuated residual energy oscillation has

amplitude between 2 keV and 4 keV for wavelengths [50 m, 500 m]

Impedance defined by i

kzIzI io cos1

Same results with PARMELASame results with PARMELA

Good agreement Simulations / Theory for drift and AccelerationSolutions to handle Numerical Problems

Noise Problem ( high number of particles)Shorter wavelengths (new option in ASTRA)

Clear “Attenuation” in gun makes situation less critical than first thought But not enough attenuation :

for wavelengths >100 m : attenuation line density modulation by factor of~5 for wavelengths <100 m : attenuation line density modulation by factor of more than 5 To reach less than 0.1% at end of beamline requires less than 0.4% rms on laser so +/- 0.56% = far beyond what is achievable by laser

Also large energy modulation in all cases (“large” = of the order or more than intrinsic energy spread)

Heater is required as microstructure present in all wavelengths cases and in particular those < 100 m

Good agreement Simulations / Theory for drift and AccelerationSolutions to handle Numerical Problems

Noise Problem ( high number of particles)Shorter wavelengths (new option in ASTRA)

Clear “Attenuation” in gun makes situation less critical than first thought But not enough attenuation :

for wavelengths >100 m : attenuation line density modulation by factor of~5 for wavelengths <100 m : attenuation line density modulation by factor of more than 5 To reach less than 0.1% at end of beamline requires less than 0.4% rms on laser so +/- 0.56% = far beyond what is achievable by laser

Also large energy modulation in all cases (“large” = of the order or more than intrinsic energy spread)

Heater is required as microstructure present in all wavelengths cases and in particular those < 100 m

LSC in drifts Simulations for Injector Case of 100 m modulation

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