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 shotnoise…
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 attention…
LCLS-II Planning Meeting
October 9, 2013