New type of a bunch New type of a bunch compressor and generation of a compressor and generation of a short wave length coherent short wave length coherent radiationradiationA. Zholents (ANL) and M. Zolotorev (LBNL)
SLAC, June 29, 2010SLAC, June 29, 2010
SLAC, 06-29-2010
z0z0
zz
zz
under-compression
under-compression
V = V0sin()V = V0sin()
RF AcceleratingVoltage
RF AcceleratingVoltage
z = R56z = R56
Path Length-EnergyDependent Beamline
Path Length-EnergyDependent Beamline
zz
E/EE/E
zz‘chirp’‘chirp’
Courtesy P. Emma
RF Chicane
Magnetic Bunch CompressionMagnetic Bunch Compression
SLAC, 06-29-2010
““Any fool with four dipoles can compress a bunch”Any fool with four dipoles can compress a bunch”
- anonymous- anonymous
““Any fool with four dipoles can compress a bunch”Any fool with four dipoles can compress a bunch”
- anonymous- anonymous
OK, but there may be a few details to consider…OK, but there may be a few details to consider…OK, but there may be a few details to consider…OK, but there may be a few details to consider…
P. Emma, ICFA Workshop, Sardinia, 2002P. Emma, ICFA Workshop, Sardinia, 2002
SLAC, 06-29-2010
Some issuesSome issuesSome issuesSome issues
zz
zz
under-under-compressioncompression
under-under-compressioncompression
Needs:de-chirping
Needs:de-chirping
De-chirping isDe-chirping istypically done by typically done by using wake fields using wake fields and/or off-crest and/or off-crest accelerationacceleration
zzzz
zzzz
under-under-compressioncompression
under-under-compressioncompression
Full Full compressioncompression
Full Full compressioncompression
Full compression is not good because Full compression is not good because of emittance growth due to CSRof emittance growth due to CSR
Full compression is not good because Full compression is not good because of emittance growth due to CSRof emittance growth due to CSR
LCLSLCLS
K. Bane et al., PRST K. Bane et al., PRST AB, 12, 030704 (2009) AB, 12, 030704 (2009)
SLAC, 06-29-2010
ReferencesReferences
P. Emma, Z. Huang, K.-J. Kim, P. Piot, “Transverse-to-Longitudinal Emittance Exchange to Improve Performance of High-Gain Free-Electron Lasers”, Phys. Rev. ST Accel. Beams 9, 100702 (2006).
M. Cornacchia, P. Emma, “Transverse to longitudinal emittance exchange”, Phys. Rev. ST Accel. Beams 5, 084001 (2002)
R.P. Fliller, D.A. Edwards, H.T. Edwards, T. Koeth, K.T. Harkay, K.-J. Kim, “Transverse to longitudinal emittance exchange beamline at the A0 Photoinjector”, Part. Acc. Conf., PAC07, (2007).
Results presented here use the idea of transverse to longitudinal emittance exchange
Results presented here use the idea of transverse to longitudinal emittance exchange
SLAC, 06-29-2010
A schematic of the bunch compressorA schematic of the bunch compressor
BQD
QFB
QDQF B
QDQF
B B
B
QDQF
QF QFQD QD QD QF
QFQD
M+ M+D+ M- M-D-T
B
B
Variant 1
TMTM110110 TMTM010010TMTM010010
Deflecting cavityDeflecting cavity
BQD
QFB
QDQF B
QDQF
B B
B
QDQF
QF QFQD QD QD QF
QFQD
I T
B
B
I I I
Focusing properties of individual sectionsFocusing properties of individual sections
z →x emit. exch.z →x emit. exch. x → z emit. exch.x → z emit. exch.Telescope
(manipulate longitudinal phase space with ease of a transverse phase space)
SLAC, 06-29-2010
A schematic of the bunch compressor: alternative variantA schematic of the bunch compressor: alternative variant
QF QFQD QD QF
BQD
QFB
QDQF
QD
M+ M+D+
M+ M+D+ T
BQD
QFB
QDQF
QD
B
B
BVariant 2
B
TMTM110110 TMTM010010TMTM010010
Deflecting cavity
SLAC, 06-29-2010
xkxEa
eVtaxJ
E
eVrf 0
10 )cos()/(
2
zkctEa
eVt
ax
axJ
E
eVx rf 010 )sin(
/
)/(2
B B
Deflecting cavityDeflecting cavityDeflecting cavityDeflecting cavity
Courtesy: Li, Corlett
Thin cavity approximation:
In agreement withPanofsky-Wentzeltheorem
SLAC, 06-29-2010
TMTM110110
TMTM110110 TMTM010010TMTM010010
z
x
x
dkkdk
k
kdd
16/2/
0100
010
02/1
12
1
11
d1
One can cancel unwanted energy gain using two TM010 mode side cavities
102/
0100
010
02/1
kdk
k
kdd
2
011
12
E
eV
a
d
E
eV
Required energy gain in each TM010 cavity
Thick deflecting cavity:Thick deflecting cavity:
d
SLAC, 06-29-2010
FNAL: SRF five cell prototype
Ebeam = 250 MeVfRF = 3.9 GHzV0 = 4 MV (1m, 3x7 cells: Li, Corlett)V1 = 0.4 MVk = 0.013 cm-1
SLAC: copper X-band LOLA
Ebeam = 250 MeVfRF = 11.4 GHzV0 = 22 MV ( 0.5 m)V1 = 6.6 MVk = 0.21 cm-1
SLAC, 06-29-2010
Single-Cell SC CavitySingle-Cell SC CavityFrequency 2815 MHz
QU ~109
Vt 0.4 MV
Energy 0.25 J
Rt/Q 36.4 Ohm
Epeak / Vt 83 1/m
Bpeak / Vt 200 mT / MV
Ploss < 5 W
Ibeam 200 mA
No. Cavity 10 * 2Cav. Length 128 mm
Input Coupler
LOM Damper
HOM Damper
HOM Dampers
20
2
0
rkU
V
Q
R rrt
Courtesy G. Waldschmidt
Total length = 128 mmVoltage gap = 53 mm
SLAC, 06-29-2010
BQD
QF B
BQD
QFB
QDQF
QD
B
1000
10
0010
01
L
M
E
k
k
kkMDM
000
00
00
000
The following constrains were used:
1
2/
kdL
56R
First leg of emittance exchange scheme
Complete emittance exchange scheme
z
p
x
x
SLAC, 06-29-2010
QF QFQD QD QFQD
T
1000
0100
00/10
000
m
m
T
Telescope
Total transformation
m
mmm
kETE
000
)1
(1
00
001
00012
BQD
QFB
QDQF B
QDQF
B B
B
QDQF
QF QFQD QD QD QF
QFQD
I T
B
B
I I I
z →x emit. exch.z →x emit. exch. x → z emit. exch.x → z emit. exch.Telescope
SLAC, 06-29-2010
222
22222
)1
()1
(1
iif
iif
z
zz
hm
mm
mm
hm
Bunch length and energy spread at the end of the scheme
Define: - bunch length before compression, - uncorrelated relative energy spread before compression, and - energy chirp before compression
iz
dzEdh /)(lni
- bunch length after compression, - uncorrelated relative energy spread after compression
fz
f
Using entire mapping one obtains : Using entire mapping one obtains :
SLAC, 06-29-2010
mif zz /
No chirp case, e.g., No chirp case, e.g., hh = 0 = 0
if
i
i
f
m
mmm
zz
2222
2
)1
(
Case 1
mm
mi
i
z )1
( then
Case 2
mm
mi
i
z )1
( Then the compression is not yet finished
SLAC, 06-29-2010
The last element of proposed BC is the chicane/dogleg with its R56 used to cancel the R56 accumulated upstream
)/11( 256 mR
mm
k
000
01
00
001
00012
if
if
mm zz
1
Then, the entire mapping takes the following form:
… and we obtain for the final bunch length and relative energy spread:
SLAC, 06-29-2010
… or one may prefer to wait until the electron beam gains energy from E1 to E2 and do the final compression at E2
Then R56 for the final step should be:
1
2256 )/11(
E
EmR
2
1
1
E
Em
m
if
if zz
… and we obtain for the final bunch length and relative energy spread:
Possible advantage of aPossible advantage of a Deferred CompressionDeferred Compression is reduction of the is reduction of the gain of the microbunching instability and impact of other collective gain of the microbunching instability and impact of other collective forces:forces:
a) electron bunch is not yet compressed to the shortest sizea) electron bunch is not yet compressed to the shortest sizeb) energy spread has already grown up to the final value b) energy spread has already grown up to the final value
SLAC, 06-29-2010
Because there is no need in energy chirp for compression: a) one can use BC even after the linac and obtain final
compression in a “spreader”/ “dogleg” part of the lattice leading to FEL
BCGun L1 L2 Spreader
)/11( 256 mR
Possible advantages
b) or use two BCs, one in usual location and one after the linac
BC
Possible advantages (2)
Accelerate a relatively long bunch in the re-circulating linac without a chirp and compress it in the final arc.
New type of a New type of a bunch compressorbunch compressor
Possible cost savingPossible cost saving
FELFEL
SLAC, 06-29-2010
ffrfrf = 12 GHz = 12 GHz
=40 cm=40 cmm=20m=20= 10 cm= 10 cmLLcavcav = 100 cm = 100 cm
32 )(8
1jitterrfjitter mkx
1 – precise calculation1 – precise calculation2 – estimation using expression:2 – estimation using expression:
)(8/1/)(2 421 yoyyyJ
Jitter studiesJitter studies
Main parametersMain parameters:
No adverse jitter effects are found in a linear approximation.No adverse jitter effects are found in a linear approximation.Timing jitter is compressed by a compression factor and Timing jitter is compressed by a compression factor and energy jitter is increased by a compression factorenergy jitter is increased by a compression factor
When exact cavity fields with Bessel, Sin and Cos functions When exact cavity fields with Bessel, Sin and Cos functions were considered the following results were obtained:were considered the following results were obtained:
Coordinate jitter after compression driven by the energy jitter Coordinate jitter after compression driven by the energy jitter before compression:before compression:
Formula can be understood via Taylor Formula can be understood via Taylor expansion of the following expression:expansion of the following expression:
SLAC, 06-29-2010
frf = 3 GHzm=20= 10 cmLcav = 100 cm
1) = 20 cm, 2) = 40 cm
1) = 20 cm, 2) = 40 cm
Same as before, but for 3 GHz rf and two sets of dispersion Same as before, but for 3 GHz rf and two sets of dispersion function:function:
Main parametersMain parameters:
Same as before, but now for Same as before, but now for an angular jitteran angular jitter
SLAC, 06-29-2010
1) = 20 cm, 2) = 40 cm Energy jitter shows ordinary Energy jitter shows ordinary increase due to compression increase due to compression with m=20with m=20
Practically no timing jitter due Practically no timing jitter due to energy jitterto energy jitter
SLAC, 06-29-2010
Timing jitter shows ordinary Timing jitter shows ordinary decrease due to compression decrease due to compression with m=20with m=20
Practically no coordinate jitter Practically no coordinate jitter due to timing jitterdue to timing jitter
SLAC, 06-29-2010
Practically no energy jitter due Practically no energy jitter due to coordinate jitterto coordinate jitter
Practically no timing jitter due Practically no timing jitter due to coordinate jitterto coordinate jitter
SLAC, 06-29-2010
Practically no energy jitter due Practically no energy jitter due to angular jitterto angular jitter
Practically no timing jitter due Practically no timing jitter due to angular jitterto angular jitter
SLAC, 06-29-2010
Second rf cavity is set approximately at 0.5% high value to reduce jitter in x.Second rf cavity is set approximately at 0.5% high value to reduce jitter in x. Conditions Conditions kk1111=-1 and =-1 and kk2222=-1 are observed.=-1 are observed.
1) = 20 cm, 2) = 40 cm
Reduction of the coordinate jitter driven by energy jitterReduction of the coordinate jitter driven by energy jitter
1) = 20 cm, 2) = 40 cm
SLAC, 06-29-2010
In the following numerical example we use: fRF = 2.85 GHz k=0.05 cm-1
cavity length = 1 m
At Eb = 250 MeV this corresponds to:V0 = 21 MVV1 = -8.7 MV
IllustrationIllustration
SLAC, 06-29-2010
Lattice functions for a bunch compressor with a telescopic factor m=15.Lattice functions for a bunch compressor with a telescopic factor m=15.Note, matching of the vertical beta-function was not pursued. Note, matching of the vertical beta-function was not pursued.
Illustration: compression by a factor of 15Illustration: compression by a factor of 15--II --II --II --IITT
tcavtcav tcavtcav B2B2B1B2B2B1
Magnets:Magnets:B1B1= 0.10= 0.10
B2B2= 0.0445= 0.0445
Length=0.3 mLength=0.3 m
xx=56 m=56 mxx=0.25 m=0.25 m
SLAC, 06-29-2010
BQD
QFB
QDQF B
QDQF
B B
B
QDQF
QF QFQD QD QD QF
QFQD
B
B
1
2 34 5
6 7
8
Numerical values of beam sizes at key locationsNumerical values of beam sizes at key locations
m=15
Eb=250 MeVx=0.5 m=10-4
E0=25 keVz0= 160 m
Deferred compression 42 m -> 10 m
Input parameters
SLAC, 06-29-2010
Eb=250 MeVx=0.5 m=2x10-5
E0=5 keVz0= 160 m
m=15
Same as before, but with a reduced energy spread to 5 keVSame as before, but with a reduced energy spread to 5 keV
SLAC, 06-29-2010
Eb=100 MeVx=0.5 m=5x10-5
E0=5 keVz0= 160 m
m=15
Same as before, but with a reduced beam energy to 100 MeVSame as before, but with a reduced beam energy to 100 MeVThis may eliminate a need in the laser heaterThis may eliminate a need in the laser heater
SLAC, 06-29-2010
Same as before, but with increased bunch length to 640 Same as before, but with increased bunch length to 640 mm
Eb=100 MeVx=0.5 m=5x10-5
E0=5 keVz0= 640 m
m=15
SLAC, 06-29-2010
Emittance degradationEmittance degradation
Concern:Concern:space charge induced energy modulation in the telescope section can space charge induced energy modulation in the telescope section can transfer into the coordinate space and be seen as emittance degradationtransfer into the coordinate space and be seen as emittance degradation
z
E
z
xx
px
z
x = 0.5 m
E0 =5 keVz0= 160 m m
0= 0.25 m1= 10 mInside telescopeIpeak=3 kA
No emittance degradation is expected No emittance degradation is expected
Eb=250 MeV
m15.0 xpz
assume: px=px/100 1
2
zx
Eb=100 MeV
SLAC, 06-29-2010
Compression of the laser induced energy modulation for microbunching at a shorter wave length
Compression of the laser induced energy modulation for microbunching at a shorter wave length
Laser e-beam Laser e-beam interactioninteraction
BCBC
Plots of longitudinal phase space at various locations Plots of longitudinal phase space at various locations Plots of longitudinal phase space at various locations Plots of longitudinal phase space at various locations
z/
E/
E
Initial modulation
E/
E
E/
E
z/
z/
Compression factor, m=20
Compression factor, m=20
Compressed modulation
Bunching efficiency at m-th harmonic of modulating Bunching efficiency at m-th harmonic of modulating frequency:frequency:
laserlaser
HGHG:HGHG:
EEHG:EEHG:
This method:This method: 0
3/1
2
12
mb
Emb
eb
m
Em
E
m
m
E
SLAC, 06-29-2010
Compression of the laser induced energy modulation can also be made at the end of the linac
Compression of the laser induced energy modulation can also be made at the end of the linac
z/
E/
E
Laser e-beam interaction
BCLinac
Laser e-beam interaction
BCLinac
Spreader
… or be deferred to a “spreader”/“dogleg”
… or be deferred to a “spreader”/“dogleg”
SLAC, 06-29-2010
Compression of the Echo induced microbunching
Compression of the Echo induced microbunching
BC
z/
E/
E
z/
Compression factor, m=5Compression factor, m=5
SLAC, 06-29-2010
0.2
Compression of the Echo induced microbunching (2)
Compression of the Echo induced microbunching (2)
Peak current after compression, kAPeak current after compression, kA
z/
z/
zoom on one peak1
0.8
0.6
0.4
SLAC, 06-29-2010
BCGun L1 L2
SpreaderBC
traditional BC new type BC, m=10
Echo:harmonic number = 20
Producing 1 nm seeding beginning from 200 nm laser modulation
Producing 1 nm seeding beginning from 200 nm laser modulation
Ipeak=100 A Ipeak=1 kA
Total harmonic number = 20x10 = 200 !
EchoEchoEchoEcho
SLAC, 06-29-2010
Other usesOther uses
BQD
QFB
QDQF B
QDQF
B B
B
QDQF
QF QFQD QD QDQF
QFQD
B
B
z →x emit. exch.z →x emit. exch. x → z emit. exch.x → z emit. exch.FODO
collimator
It is often desirable to get rid off the tails in longitudinal distribution It is often desirable to get rid off the tails in longitudinal distribution and proposed scheme can be used as efficient tail cutterand proposed scheme can be used as efficient tail cutter
SLAC, 06-29-2010
Other uses (3)Other uses (3)
BQD
QFB
QDQF B
QDQF
B B
B
QDQF
QF QFQD QD QDQF
QFQD
B
B
z →x emit. exch.z →x emit. exch. x → z emit. exch.x → z emit. exch.Telescope
x- px- px x tomography heretomography here
Longitudinal phase space tomographyLongitudinal phase space tomography
is is - z- z tomography theretomography there
SLAC, 06-29-2010
SummarySummary
1.1. Efficient electron bunch manipulation in the longitudinal phase space Efficient electron bunch manipulation in the longitudinal phase space
can be accomplished by first exchanging longitudinal and transverse can be accomplished by first exchanging longitudinal and transverse
emittances, manipulating electrons in the transverse phase space and emittances, manipulating electrons in the transverse phase space and
finally exchanging emittances back to their original state.finally exchanging emittances back to their original state.
2.2. One application is bunch compressor that does not need energy chirpOne application is bunch compressor that does not need energy chirp
• This can also be used for a compression of any features This can also be used for a compression of any features
introduced to the electron bunch, like, for example energy introduced to the electron bunch, like, for example energy
modulation produced in interaction with the laser. modulation produced in interaction with the laser.
3.3. Proposed techniques for a bunch compression allows Proposed techniques for a bunch compression allows deferred deferred
compressioncompression that might be useful to mitigate possible adverse effects that might be useful to mitigate possible adverse effects
caused by collective forces.caused by collective forces.
