1. A. Zholents (ANL) and M. Zolotorev (LBNL)
New type of a bunch compressor and generation of a short wave length coherent radiation
A. Zholents (ANL) and M. Zolotorev (LBNL)
LBNL, August 06, 2010

2. “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

3. Magnetic Bunch Compression
Courtesy P. Emma
DE/E z
DE/E z
‘chirp’
DE/E
under-compression
sz0
sE/E z sz RF
Chicane
V = V0sin(wt)
RF Accelerating
Voltage
Dz = R56DE/E
Path Length-Energy
Dependent Beamline

4. Some issues DE/E z sz DE/E z sz Needs: de-chirping De-chirping is
typically done by using wake fields and/or off-crest acceleration
under-compression z sz
LCLS
K. Bane et al., PRST AB, 12, (2009)
DE/E z sz
under-compression
Full compression
Full compression is not good because of emittance growth due to CSR

5. References
Results presented here use the idea of transverse to longitudinal emittance exchange
M. Cornacchia, P. Emma, “Transverse to longitudinal emittance exchange”, Phys. Rev. ST Accel. Beams 5, (2002)
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, (2006).
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).

6. A schematic of the bunch compressor
(manipulate longitudinal phase space with ease of a transverse phase space) B QD QF M+ D+ M- D- T
Variant 1
TM110
TM010
Deflecting cavity
Focusing properties of individual sections I I T I I QD QF QD QF QD QF QD QF B B QF QD QF QD B B B B QF QD B
z →x emit. exch.
Telescope
x → z emit. exch. QD QF B

7. A schematic of the bunch compressor: alternative variantQF QD B M+ D+ T
Variant 2
TM110
TM010
Deflecting cavity

8. Deflecting cavity Thin cavity approximation: B Courtesy: Li, Corlett
In agreement with
Panofsky-Wentzel
theorem

9. One can cancel unwanted energy gain using two TM010 mode side cavities
Thick deflecting cavity: d1
TM110
One can cancel unwanted energy gain using two TM010 mode side cavities d
TM010
TM110
TM010
Required energy gain in each TM010 cavity

10. FNAL: SRF five cell prototype
Ebeam = 250 MeV
fRF = 3.9 GHz
V0 = 4 MV (1m, 3x7 cells: Li, Corlett)
V1 = 0.4 MV
k = cm-1
SLAC: copper X-band LOLA
Ebeam = 250 MeV
fRF = 11.4 GHz
V0 = 22 MV ( 0.5 m)
V1 = 6.6 MV
k = 0.21 cm-1

11. First leg of emittance exchange schemeB QF QD B
Complete emittance exchange scheme QD QF QD B B QF QD B
The following constrains were used:

12. Total transformation Telescope z →x emit. exch. TelescopeQF QD T
Total transformation B QD QF I T
z →x emit. exch.
x → z emit. exch.
Telescope

13. 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
- bunch length after compression,
- uncorrelated relative energy spread after compression
Using entire mapping one obtains :

14. No chirp case, e.g., h = 0 Case 1 then Case 2
Then the compression is not yet finished

15. The last element of proposed BC is the chicane/dogleg with its R56 used to cancel the R56 accumulated upstream
Then, the entire mapping takes the following form:
… and we obtain for the final bunch length and relative energy spread:

16. … 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:
… 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 size
b) energy spread has already grown up to the final value

17. Possible advantages
Because there is no need in energy chirp for compression:
one can use BC even after the linac and obtain final compression in a “spreader”/ “dogleg” part of the lattice leading to FEL
Gun L1 L2
Spreader BC BC
b) or use two BCs, one in usual location and one after the linac

18. Possible advantages (2)
Accelerate a relatively long bunch in the re-circulating linac without a chirp and compress it in the final arc.
FEL
New type of a bunch compressor
Possible cost saving

19. 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:

20. Illustration 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 MV
V1 = -8.7 MV

21. Illustration: compression by a factor of 15
tcav B2 B1 B2
tcav B2
Magnets:
jB1= 0.10
jB2=
Length=0.3 m
bx=0.25 m
bx=56 m
Lattice functions for a bunch compressor with a telescopic factor m=15.
Note, matching of the vertical beta-function was not pursued.

22. Numerical values of beam sizes at key locationsQD QF 1 2 3 4 5 6 7 8
Deferred compression
42 mm -> 10 mm
m=15
Input parameters
Eb=250 MeV
ex=0.5 mm
sd0=10-4
sE0=25 keV
sz0= 160 mm

23. Same as before, but with a reduced beam energy to 100 MeV
This may eliminate a need in the laser heater
m=15
Eb=100 MeV
ex=0.5 mm
sd0=5x10-5
sE0=5 keV
sz0= 160 mm

24. Compression of the laser induced energy modulation for microbunching at a shorter wave length
Compression factor, m=20
laser BC
Laser e-beam interaction
Initial modulation
DE/sE
DE/sE
Compressed modulation
z/l
z/l
Bunching efficiency at m-th harmonic of modulating frequency:
HGHG:
EEHG:
This method:
DE/sE
z/l
Plots of longitudinal phase space at various locations

25. … or be deferred to a “spreader”/“dogleg”
Compression of the laser induced energy modulation can also be made at the end of the linac BC
Laser e-beam interaction
Linac
z/l
DE/sE
Laser e-beam interaction BC
Linac
Spreader
… or be deferred to a “spreader”/“dogleg”

26. Compression of the Echo induced microbunchingBC
Compression factor, m=5
DE/sE
z/l
z/l

27. Compression of the Echo induced microbunching (2)
Peak current after compression, kA
z/l
zoom on one peak 1
0.8
0.6
0.4
0.2
z/l

28. Producing 1 nm seeding beginning from 200 nm laser modulation
Echo:
harmonic number = 20
traditional BC
new type BC, m=10
Gun L1 L2 BC
Echo BC
Spreader
Ipeak=100 A
Ipeak=1 kA
Total harmonic number = 20x10 = 200 !

29. Other uses
It is often desirable to get rid off the tails in longitudinal distribution and proposed scheme can be used as efficient tail cutter
collimator QD QF QD QF QD QF QD QF B B QD QF QF QD B B B B QF QD
x → z emit. exch. QD QF B
z →x emit. exch.
FODO B

30. Other uses (2)
It is possible to create a sequence of a tightly spaced microbunches using a sequence of slits
Collimator with slits QD QF QD QF QD QF QD QF B B QD QF QF QD B B B B QF QD QD QF B
z →x emit. exch.
Telescope
x → z emit. exch. B
Using demagnification of the beam size before slits and magnification after the slits can help to obtain a real tight spacing of microbunches

31. Other uses (3) Longitudinal phase space tomography
x- px tomography here
is d- z tomography there QD QF QD QF QD QF QD QF B B QD QF QF QD B B B B QF QD
x → z emit. exch. QD QF B
z →x emit. exch.
Telescope B

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