The Microbunching Instability in the LCLS-II Linac
LCLS-II Planning MeetingOctober 23, 2013
A. Marinelli and Z. Huang
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
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
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
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.
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)
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
Induced Energy Spread from Shot-Noise
Integrate induced energy spread in the frequency domain starting from shot-noise…
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:
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:
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:
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:
Energy-spread induced by LSC
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
LCLS-2 Microbunching Gain (NO HEATER)
300 eV1000 eV2000 eV
Gain estimateassuming initial Gaussian spread
G
l(m) (initial)
LCLS II BC2 at 1.6 GeV
BC2 at 1.6 GeV
LCLS2 parameters. Final peak current:Ipk = 1kAStarting 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
20LCLS-II Planning Meeting, Oct 9-11, 2013
LCLS II 25 A Initial Current
BC2 at 1.6 GeV
LCLS2 parameters. Final peak current:Ipk = 1kAStarting 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
Final spread ~ 0.5 MeV
BC2 at 800 MeV
LCLS2 parameters. Final peak current:Ipk = 1kAStarting 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
For certain frequencies
Sin(kp L) ~ 0Overall spread reduced
k (rad/m)
Leff(m)
effective Drift-length VS wavenumber
23LCLS-II Planning Meeting, Oct 9-11, 2013
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!
End
LCLS-II Planning MeetingOctober 9, 2013
Thanks for your attention…