New type of a bunch compressor and generation of a short wave length coherent radiationA. Zholents (ANL) and M. Zolotorev (LBNL)

LBNL, August 06, 2010

LBNL, 08-06-2010

“Any fool with four dipoles can compress a bunch”

- anonymous

OK, but there may be a few details to consider…

P. Emma, ICFA Workshop, Sardinia, 2002

LBNL, 08-06-2010

sz0

DE/E

z

sz

under-compression

V = V0sin(wt)

RF AcceleratingVoltage

Dz = R56DE/E

Path Length-EnergyDependent Beamline

DE/E

z

sE/E

DE/E

z

‘chirp’

Courtesy P. Emma

RF Chicane

Magnetic Bunch Compression

LBNL, 08-06-2010

Some issuesDE/E

zsz

under-compression

Needs:de-chirping

De-chirping istypically done by using wake fields and/or off-crest acceleration

DE/E

zsz

under-compression

Full compression

Full compression is not good because of emittance growth due to CSR

LCLS

K. Bane et al., PRST AB, 12, 030704 (2009)

LBNL, 08-06-2010

References

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

LBNL, 08-06-2010

A schematic of the bunch compressor

BQD

QF BQD

QF B

QDQF

B B

B

QDQF

QF QFQD QD QD QF

QFQD

M+ M+D+ M- M-D-T

B

B

Variant 1

TM110 TM010TM010

Deflecting cavity

BQD

QF BQD

QF B

QDQF

B B

B

QDQF

QF QFQD QD QD QF

QFQD

I T

B

B

I I I

Focusing properties of individual sections

z →x emit. exch. x → z emit. exch.Telescope

(manipulate longitudinal phase space with ease of a transverse phase space)

LBNL, 08-06-2010

A schematic of the bunch compressor: alternative variant

QF QFQD QD QF

BQD

QF BQD

QFQD

M+ M+D+

M+ M+D+ T

BQD

QF BQD

QFQD

B

B

BVariant 2

B

TM110 TM010TM010

Deflecting cavity

LBNL, 08-06-2010

xkxEaeV

taxJEeV

rf 01

0 )cos()/(2

w

zkctEaeV

taxaxJ

EeV

x rf D 010 )sin(/

)/(2w

B B

Deflecting cavity

Courtesy: Li, Corlett

Thin cavity approximation:

In agreement withPanofsky-Wentzeltheorem

LBNL, 08-06-2010

TM110

TM110 TM010TM010

zxx

dkkdk

kkdd

16/2/010001002/1

12

1

11

d1

One can cancel unwanted energy gain using two TM010 mode side cavities

102/010001002/1

kdk

kkdd

2011

12

EeV

ad

EeV

Required energy gain in each TM010 cavity

Thick deflecting cavity:

d

LBNL, 08-06-2010

FNAL: SRF five cell prototypeEbeam = 250 MeVfRF = 3.9 GHzV0 = 4 MV (1m, 3x7 cells: Li, Corlett)V1 = 0.4 MVk = 0.013 cm-1

SLAC: copper X-band LOLAEbeam = 250 MeVfRF = 11.4 GHzV0 = 22 MV ( 0.5 m)V1 = 6.6 MVk = 0.21 cm-1

LBNL, 08-06-2010

BQD

QF B

BQD

QF BQD

QFQD

B

100010

001001

L

M

E

kk

kkMDM

00000

00000

The following constrains were used:

12/

kdL

56R

First leg of emittance exchange scheme

Complete emittance exchange scheme

zpx

x

LBNL, 08-06-2010

QF QFQD QD QFQD

T

1000010000/10000

mm

T

Telescope

Total transformation

m

mmm

kETE

000

)1(100

0010001

2

BQD

QF BQD

QF B

QDQF

B B

B

QDQF

QF QFQD QD QD QF

QFQD

I T

B

B

I I I

z →x emit. exch. x → z emit. exch.Telescope

LBNL, 08-06-2010

222

22222

)1()1(1

iif

iif

z

zz

hm

mm

mm

hm

sss

sss

Bunch length and energy spread at the end of the schemeDefine: - bunch length before compression, - uncorrelated relative energy spread before compression, and - energy chirp before compression

izs

dzEdh /)(lni

s

- bunch length after compression, - uncorrelated relative energy spread after compression

fzs

fs

Using entire mapping one obtains :

LBNL, 08-06-2010

mif zz /ss

No chirp case, e.g., h = 0

if

i

i

f

m

mmm

zz

ss

ss

s

2222

2

)1(

Case 1

mm

mi

i

zss )1( then

Case 2

mm

mi

i

zss )1( Then the compression is not yet finished

LBNL, 08-06-2010

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

0100

0010001

2

if

if

mm zz

ss

ss

1

Then, the entire mapping takes the following form:

… and we obtain for the final bunch length and relative energy spread:

LBNL, 08-06-2010

… 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(

EEmR

2

1

1

EEm

m

if

if zz

ss

ss

… and we obtain for the final bunch length and relative energy spread:

Possible advantage of a Deferred Compression is reduction of the gain of the microbunching instability and impact of other collective forces:

a) electron bunch is not yet compressed to the shortest sizeb) energy spread has already grown up to the final value

LBNL, 08-06-2010

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 bunch compressor

Possible cost saving

FEL

LBNL, 08-06-2010

Jitter studies

No adverse jitter effects are found:Timing jitter is compressed by a compression factor and energy jitter is increased by a compression factor:

mEEmttDD

DD /

LBNL, 08-06-2010

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

Illustration

LBNL, 08-06-2010

Lattice functions for a bunch compressor with a telescopic factor m=15.Note, matching of the vertical beta-function was not pursued.

Illustration: compression by a factor of 15-I -I -I -IT

tcav tcav B2B2B1B2B2B1

Magnets:jB1= 0.10jB2= 0.0445Length=0.3 m

bx=56 mbx=0.25 m

LBNL, 08-06-2010

BQD

QF BQD

QF 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 locations

m=15

Eb=250 MeVex=0.5 mms0=10-4

sE0=25 keVsz0= 160 mm

Deferred compression 42 mm -> 10 mm

Input parameters

LBNL, 08-06-2010

Eb=100 MeVex=0.5 mms0=5x10-5

sE0=5 keVsz0= 160 mm

m=15

Same as before, but with a reduced beam energy to 100 MeVThis may eliminate a need in the laser heater

LBNL, 08-06-2010

Compression of the laser induced energy modulation for microbunching at a shorter wave length

Laser e-beam interaction

BC

Plots of longitudinal phase space at various locations

z/l

DE/s

E

Initial modulation

DE/s

E

DE/s

E

z/l

z/l

Compression factor, m=20

Compressed modulation

Bunching efficiency at m-th harmonic of modulating frequency:

laser

HGHG:EEHG:

This method: 0

3/1

21 2

mbE

mb

eb

m

Em

Em

m

E

D

D

s

s

LBNL, 08-06-2010

Compression of the laser induced energy modulation can also be made at the end of the linac

z/l

DE/s

E

Laser e-beam interaction

BCLinac

Laser e-beam interaction

BCLinac

Spreader

… or be deferred to a “spreader”/“dogleg”

LBNL, 08-06-2010

Compression of the Echo induced microbunching

BC

z/l

DE/s

E

z/l

Compression factor, m=5

LBNL, 08-06-2010

0.2

Compression of the Echo induced microbunching (2)

Peak current after compression, kA

z/l

z/l

zoom on one peak1

0.8

0.6

0.4

LBNL, 08-06-2010

BCGun L1 L2

SpreaderBCtraditional BC new type BC, m=10

Echo:harmonic number = 20

Producing 1 nm seeding beginning from 200 nm laser modulation

Ipeak=100 A Ipeak=1 kA

Total harmonic number = 20x10 = 200 !

Echo

LBNL, 08-06-2010

Other uses

BQD

QF BQD

QF B

QDQF

B B

B

QDQF

QF QFQD QD QDQF

QFQD

B

B

z →x emit. exch. x → z emit. exch.FODO

collimator

It is often desirable to get rid off the tails in longitudinal distribution and proposed scheme can be used as efficient tail cutter

SLAC, 06-29-2010

Other uses (2)

BQD

QF BQD

QF B

QDQF

B B

B

QDQF

QF QFQD QD QDQF

QFQD

B

B

z →x emit. exch. x → z emit. exch.Telescope

Collimator with slits

It is possible to create a sequence of a tightly spaced microbunches using a sequence of slits

Using demagnification of the beam size before slits and magnification after the slits can help to obtain a real tight spacing of microbunches

LBNL, 08-06-2010

Other uses (3)

BQD

QF BQD

QF B

QDQF

B B

B

QDQF

QF QFQD QD QDQF

QFQD

B

B

z →x emit. exch. x → z emit. exch.Telescope

x- px tomography here

Longitudinal phase space tomography

is - z tomography there

LBNL, 08-06-2010

Summary

1. Efficient electron bunch manipulation in the longitudinal phase space can be accomplished by first exchanging longitudinal and transverse emittances, manipulating electrons in the transverse phase space and finally exchanging emittances back to their original state.

2. One application is bunch compressor that does not need energy chirp• This can also be used for a compression of any features

introduced to the electron bunch, like, for example energy modulation produced in interaction with the laser.

3. Proposed techniques for a bunch compression allows deferred compression that might be useful to mitigate possible adverse effects caused by collective forces.