1. Simulation of Microbunching Instability in LCLS with Laser-Heater jhwu@SLAC.Stanford.EDU Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Laser-Heater Physics Review, March 01, 2004 Juhao Wu, SLAC 1 Juhao Wu, M. Borland (ANL), P. Emma, Z. Huang, C. Limborg, G. Stupakov, J. Welch 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 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. Simulation of Microbunching Instability in LCLS with Laser-Heater jhwu@SLAC.Stanford.EDU Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Laser-Heater Physics Review, March 01, 2004 Juhao Wu, SLAC 2 MotivationMotivation 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

3. Simulation of Microbunching Instability in LCLS with Laser-Heater jhwu@SLAC.Stanford.EDU Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Laser-Heater Physics Review, March 01, 2004 Juhao Wu, SLAC 3 LSC Model (1-D) Free space 1-D model: transverse uniform coasting beam with longitudinal density modulation (on-axis) where, r b is the radius of the coasting beam; For more realistic distribution  find an effective r b, and use the above impedance; Radial-dependence of the impedance will increase energy spread and enhance damping; small? pancake beam pencil beam rbrb λ

4. Simulation of Microbunching Instability in LCLS with Laser-Heater jhwu@SLAC.Stanford.EDU Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Laser-Heater Physics Review, March 01, 2004 Juhao Wu, SLAC 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. r b =0.5 mm, I 0 =100 A E = 12 MeV E = 6 MeV

5. Simulation of Microbunching Instability in LCLS with Laser-Heater jhwu@SLAC.Stanford.EDU Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Laser-Heater Physics Review, March 01, 2004 Juhao Wu, SLAC 5 Two Quantities The quantities we concern are density modulation, and energy modulation Density modulation Energy modulation R 56 Integral equation approach Heifets-Stupakov-Krinsky(PRST,2002); Huang-Kim(PRST,2002)  (CSR)

6. Simulation of Microbunching Instability in LCLS with Laser-Heater jhwu@SLAC.Stanford.EDU Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Laser-Heater Physics Review, March 01, 2004 Juhao Wu, SLAC 6 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 SimulationPARMELAASTRAELEGANT 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 SimulationPARMELAASTRAELEGANT Testing the LSC model 

7. Simulation of Microbunching Instability in LCLS with Laser-Heater jhwu@SLAC.Stanford.EDU Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Laser-Heater Physics Review, March 01, 2004 Juhao Wu, SLAC 7 Integral Equations Density modulation Energy Modulation: Applicable for both accelerator cavity and drift space Impedance for LSC

8. Simulation of Microbunching Instability in LCLS with Laser-Heater jhwu@SLAC.Stanford.EDU Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Laser-Heater Physics Review, March 01, 2004 Juhao Wu, SLAC 8 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 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 Analytical Approach – Two Limits 

9. Simulation of Microbunching Instability in LCLS with Laser-Heater jhwu@SLAC.Stanford.EDU Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Laser-Heater Physics Review, March 01, 2004 Juhao Wu, SLAC 9 3 meter drift without acceleration Analytical vs. ASTRA Analytical 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?

10. Simulation of Microbunching Instability in LCLS with Laser-Heater jhwu@SLAC.Stanford.EDU Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Laser-Heater Physics Review, March 01, 2004 Juhao Wu, SLAC 10 Analytical vs. ASTRA Analytical vs. ASTRA (density modulation) 3 meter drift without acceleration

11. Simulation of Microbunching Instability in LCLS with Laser-Heater jhwu@SLAC.Stanford.EDU Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Laser-Heater Physics Review, March 01, 2004 Juhao Wu, SLAC 11 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 simulationAnalytical approach Analytical vs. PARMELA Analytical vs. PARMELA (energy modulation) Analytical vs. PARMELA Analytical vs. PARMELA (energy modulation)

12. Simulation of Microbunching Instability in LCLS with Laser-Heater jhwu@SLAC.Stanford.EDU Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Laser-Heater Physics Review, March 01, 2004 Juhao Wu, SLAC 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) has been implementedFree 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)

13. Simulation of Microbunching Instability in LCLS with Laser-Heater jhwu@SLAC.Stanford.EDU Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Laser-Heater Physics Review, March 01, 2004 Juhao Wu, SLAC 13 Comparison with ELEGANT Free space 1-D LSC model with effective radius Example with acceleration: current modulation at different wavelength Elegant trackingAnalytical calculation --- 1 mm, --- 0.5 mm, --- 0.25 mm, --- 0.1 mm I=100 A, r b =0.5 mm, E 0 =5.5 MeV, Gradient: 7.5 MV/m

14. Simulation of Microbunching Instability in LCLS with Laser-Heater jhwu@SLAC.Stanford.EDU Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Laser-Heater Physics Review, March 01, 2004 Juhao Wu, SLAC 14 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 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 Simulation Details

15. Simulation of Microbunching Instability in LCLS with Laser-Heater jhwu@SLAC.Stanford.EDU Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Laser-Heater Physics Review, March 01, 2004 Juhao Wu, SLAC 15 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 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 Simulation Details Low-pass filter Current form-factor Impedance

16. Simulation of Microbunching Instability in LCLS with Laser-Heater jhwu@SLAC.Stanford.EDU Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Laser-Heater Physics Review, March 01, 2004 Juhao Wu, SLAC 16 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 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 Simulation Details

17. Simulation of Microbunching Instability in LCLS with Laser-Heater jhwu@SLAC.Stanford.EDU Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Laser-Heater Physics Review, March 01, 2004 Juhao Wu, SLAC 17 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 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 Phase space evolution along the beam line

18. 30  m 5  10  5 EEEE EEEE time (sec) injector output (135 MeV)  = 30  m  = 30  m 5  10  5 NO HEATER  1% LCLS time (sec)

19. 30  m EEEE EEEE after DL1 dog-leg (135 MeV)  = 30  m  = 30  m 5  10  5 NO HEATER LCLS time (sec)

20. 30  m EEEE EEEE before BC1 chicane (250 MeV)  = 30  m  = 30  m 1  10  3 NO HEATER LCLS time (sec)

21. 30/4.3  m EEEE EEEE after BC1 chicane (250 MeV)  = 30  m  = 30  m 1  10  3 NO HEATER LCLS time (sec)

22. 30/4.3  m EEEE EEEE before BC2 chicane (4.5 GeV)  = 30  m  = 30  m 5  10  4 NO HEATER LCLS time (sec)

23. 30/30  m EEEE EEEE after BC2 chicane (4.5 GeV)  = 30  m  = 30  m 2  10  3 NO HEATER LCLS time (sec)

24. 30/30  m EEEE EEEE before undulator (14 GeV)  = 30  m  = 30  m 1  10  3 NO HEATER 0.09 % rms LCLS time (sec)

25. 30  m 5  10  5 EEEE EEEE injector output (135 MeV)  = 30  m  = 30  m 5  10  5 MATCHED HEATER  1% LCLS time (sec)

26. 30  m EEEE EEEE just after heater (135 MeV)  = 30  m  = 30  m 5  10  4 MATCHED HEATER LCLS time (sec)

27. 30  m EEEE EEEE after DL1 dog-leg (135 MeV)  = 30  m  = 30  m 5  10  4 MATCHED HEATER LCLS time (sec)

28. 30  m EEEE EEEE before BC1 chicane (250 MeV)  = 30  m  = 30  m 1  10  3 MATCHED HEATER LCLS time (sec)

29. 30/4.3  m EEEE EEEE after BC1 chicane (250 MeV)  = 30  m  = 30  m 2  10  3 MATCHED HEATER 2  10  3 LCLS time (sec)

30. 30/4.3  m EEEE EEEE before BC2 chicane (4.5 GeV)  = 30  m  = 30  m 5  10  4 MATCHED HEATER LCLS time (sec)

31. 30/30  m EEEE EEEE after BC2 chicane (4.5 GeV)  = 30  m  = 30  m 5  10  4 MATCHED HEATER LCLS time (sec)

32. 30/30  m EEEE EEEE before undulator (14 GeV)  = 30  m  = 30  m 2  10  4 MATCHED HEATER 0.01% rms LCLS time (sec)

33. Simulation of Microbunching Instability in LCLS with Laser-Heater jhwu@SLAC.Stanford.EDU Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Laser-Heater Physics Review, March 01, 2004 Juhao Wu, SLAC 33 End of BC2 Undulator entrance Nonlinear region / Saturation LCLS gain and slice energy spread  1%, 30  m

34. Simulation of Microbunching Instability in LCLS with Laser-Heater jhwu@SLAC.Stanford.EDU Linac Coherent Light Source Stanford Synchrotron Radiation Laboratory Stanford Linear Accelerator Center Laser-Heater Physics Review, March 01, 2004 Juhao Wu, SLAC 34 Discussion and Conclusion Instability not tolerable without laser-heater for < 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. ( ) Injector modulation study also important, no large damping is found to confidently eliminate heater. ( see C. Limborg’s talk ) Instability not tolerable without laser-heater for < 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. ( ) Injector modulation study also important, no large damping is found to confidently eliminate heater. ( see C. Limborg’s talk )