1. The Microbunching Instability in the LCLS-II Linac LCLS-II Planning Meeting October 23, 2013 A. Marinelli and Z. Huang

2. Microbunching Instability Microbunching instability Modulation induced by self-fields: -Longitudinal space- charge (Coulomb) -Wakefields -coherent Synchrotron radiation -broad-band effect -can start from shot-noise -broad-band effect -can start from shot-noise

3. Microbunching Instability Microbunching instability Modulation induced by self-fields: -Longitudinal space- charge (Coulomb) -Wakefields -coherent Synchrotron radiation -broad-band effect -can start from shot-noise -broad-band effect -can start from shot-noise

4. Microbunching in LCLS-1 Example: Recent X-TCAV measurement with FEL off. Strong microbunching due to 2- stage compression and high- current operation. Microbunches in phase-space ~ vertical: SATURATION! Ratner, Marinelli, Beherens, Ding, Turner

5. Analytical Model

6. Energy modulation induced by space-charge

7. Analytical Model Chicane Dispersion

8. Analytical Model Fourier-transform of the energy distribution: INCREASE ENERGY SPREAD TO SUPPRESS THE INSTABILITY

9. Final Energy Spread Microbunching gain is not the most meaningful quantity since it does not directly affect the FEL performance (at least for SASE and Self-Seeding). What really matters is the energy-spread induced by the instability. Simplified model: 1) Track microbuching up to the last bunch compressor

10. Final Energy Spread Microbunching gain is not the most meaningful quantity since it does not directly affect the FEL performance (at least for SASE and Self-Seeding). What really matters is the energy-spread induced by the instability. Simplified model: 2) Compute energy-spread induced by SC acting on the microbunched beam in the rest of the accelerator/transport (neglects spread induced in the early stages of the gain process)

11. Final Energy Spread Microbunching gain is not the most meaningful quantity since it does not directly affect the FEL performance (at least for SASE and Self-Seeding). What really matters is the energy-spread induced by the instability. Simplified model: SPACE-CHARGE IS THE LARGEST CONTRIBUTION TO ENERGY-SPREAD

12. Induced Energy Spread from Shot-Noise Integrate induced energy spread in the frequency domain starting from shot- noise…

13. Example LCLS1 parameters. Final peak current: Ipk = 3kA Finite mismatch between laser heater and electron beam:  r /  x = 2 Final spread computed as sum of three contributions:

14. Example LCLS1 parameters. Final peak current: Ipk = 3kA Finite mismatch between laser heater and electron beam:  r /  x = 2 Final spread computed as sum of three contributions: Heater induced spread x compression

15. Example LCLS1 parameters. Final peak current: Ipk = 3kA Finite mismatch between laser heater and electron beam:  r /  x = 2 Final spread computed as sum of three contributions: Initial gaussian spread x compression

16. Example LCLS1 parameters. Final peak current: Ipk = 3kA Finite mismatch between laser heater and electron beam:  r /  x = 2 Final spread computed as sum of three contributions: Energy- spread induced by LSC

17. Comparison with Recent X-TCAV Measurements Experimental result consistent with theory: optimum at ~12-14 keV heater induced spread Ratner, Marinelli, Beherens, Ding, Turner, Decker

18. LCLS-2 Microbunching Gain (NO HEATER) 300 eV 1000 eV 2000 eV Gain estimate assuming initial Gaussian spread G  m   initial)

19. LCLS II BC2 at 1.6 GeV BC2 at 1.6 GeV LCLS2 parameters. Final peak current: Ipk = 1kA Starting from ~12 A Finite mismatch between laser heater and electron beam:  r /  x = 2 Compression factor= 5 x 16 Energy-spread minimized at 5keV heater induced spread Assumes ~ 2500 m of transport after linac Final spread ~ 0.5 MeV

20. 20 LCLS II 25 A Initial Current LCLS-II Planning Meeting, Oct 9-11, 2013 BC2 at 1.6 GeV LCLS2 parameters. Final peak current: Ipk = 1kA Starting from ~25 A Finite mismatch between laser heater and electron beam:  r /  x = 2 Compression factor= 4 x 10 Energy-spread minimized at 5keV heater induced spread Assumes ~ 2500 m of transport after linac Final spread ~ 0.5 MeV

21. BC2 at 800 MeV LCLS2 parameters. Final peak current: Ipk = 1kA Starting from ~12 A Finite mismatch between laser heater and electron beam:  r /  x = 2 Compression factor= 5 x 16 Energy-spread minimized at 5keV heater induced spread Assumes ~ 2500 m of transport after linac Final spread ~ 0.5 MeV @ 5GeV BC2 @ 800MeV

22. Effect of Plasma Oscillations Long drift section between linac and undulators. For the lower energy cases (2-3 GeV): Ldrift ~ ½ PlasmaPeriod. Integrated impedance is effectively smaller since the collective field oscillates in time For certain frequencies Sin(k p L) ~ 0 Overall spread reduced k (rad/m) Leff (m) effective Drift-length VS wavenumber

23. 23 Conclusions LCLS-II Planning Meeting, Oct 9-11, 2013 -MBI is the largest source of energy-spread for LCLS1-2 linacs. -Microbunching instability is weaker in LCLS-2 than we are used to for LCLS1. -Heater level around ~5 keV needed to minimize energy spread. -Long drift between linac and undulators is a source of increased energy-spread but self-consistent electron response comes to our aid!

24. End LCLS-II Planning Meeting October 9, 2013 Thanks for your attention…