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…