Report

The Microbunching Instability in the LCLS-II Linac LCLS-II Planning Meeting October 23, 2013 A. Marinelli and Z. Huang Microbunching Instability Microbunching instability Modulation induced by self-fields: -Longitudinal spacecharge (Coulomb) -Wakefields -coherent Synchrotron radiation -broad-band effect -can start from shot-noise Microbunching Instability Microbunching instability Modulation induced by self-fields: -Longitudinal spacecharge (Coulomb) -Wakefields -coherent Synchrotron radiation -broad-band effect -can start from shot-noise Microbunching in LCLS-1 Example: 20 Recent X-TCAV measurement with FEL off. 40 Strong microbunching due to 2stage compression and highcurrent operation. 60 80 100 120 50 100 150 200 250 Ratner, Marinelli, Beherens, Ding, Turner 300 Microbunches in phase-space ~ vertical: SATURATION! Analytical Model Analytical Model Energy modulation induced by space-charge Analytical Model Chicane Dispersion Analytical Model Fourier-transform of the energy distribution: INCREASE ENERGY SPREAD TO SUPPRESS THE INSTABILITY 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 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. 2) Compute energy-spread induced by SC acting on the microbunched beam in the rest Simplified model: of the accelerator/transport (neglects spread induced in the early stages of the gain process) 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. SPACE-CHARGE IS THE LARGEST CONTRIBUTION Simplified model: TO ENERGY-SPREAD Induced Energy Spread from Shot-Noise Integrate induced energy spread in the frequency domain starting from shotnoiseâ€¦ 1 s g ,IND = 2p nz 2 dk | G(k)D g (k) | ò f Ip 4p Z(k, s) Dg f (k) = ò ds IA Z0 Example LCLS1 parameters. Final peak current: Ipk = 3kA Finite mismatch between laser heater and electron beam: sr/sx = 2 Final spread computed as sum of three contributions: s g ,tot = (Cs lh )2 + (Cs g ,0 )2 + s g2,IND Example LCLS1 parameters. Final peak current: Ipk = 3kA Finite mismatch between laser heater and electron beam: sr/sx = 2 Final spread computed as sum of three contributions: s g ,tot = (Cs lh )2 + (Cs g ,0 )2 + s g2,IND Heater induced spread x compression Example LCLS1 parameters. Final peak current: Ipk = 3kA Finite mismatch between laser heater and electron beam: sr/sx = 2 Final spread computed as sum of three contributions: s g ,tot = (Cs lh )2 + (Cs g ,0 )2 + s g2,IND Initial gaussian spread x compression Example LCLS1 parameters. Final peak current: Ipk = 3kA Finite mismatch between laser heater and electron beam: sr/sx = 2 Final spread computed as sum of three contributions: s g ,tot = (Cs lh )2 + (Cs g ,0 )2 + s g2,IND Energyspread induced by LSC Comparison with Recent X-TCAV Measurements Ratner, Marinelli, Beherens, Ding, Turner, Decker Experimental result consistent with theory: optimum at ~12-14 keV heater induced spread LCLS-2 Microbunching Gain (NO HEATER) 300 eV 1000 eV 2000 eV 1000 Gain estimate assuming initial Gaussian spread G 10 0.1 0.00000 0.00005 0.00010 0.00015 0.00020 l(m) (initial) 0.00025 0.00030 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: sr/sx = 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 LCLS II 25 A Initial Current BC2 at 1.6 GeV LCLS2 parameters. Final peak current: Ipk = 1kA Starting from ~25 A Finite mismatch between laser heater and electron beam: sr/sx = 2 Compression factor= 4 x 10 Energy-spread minimized at 5keV heater induced spread Assumes ~ 2500 m of transport after linac LCLS-II Planning Meeting, Oct 9-11, 2013 Final spread ~ 0.5 MeV 20 BC2 at 800 MeV LCLS2 parameters. Final peak current: Ipk = 1kA Starting from ~12 A Finite mismatch between laser heater and electron beam: sr/sx = 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 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 effective Drift-length VS wavenumber Ip 4p Z(k, s0 ) Dg f (k) = ò ds cos(k p s) IA Z0 Leff (m) k (rad/m) For certain frequencies Sin(kp L) ~ 0 Overall spread reduced Conclusions -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! LCLS-II Planning Meeting, Oct 9-11, 2013 23 End Thanks for your attentionâ€¦ LCLS-II Planning Meeting October 9, 2013