1. Longitudinal-to-transverse mapping and emittance transfer
Dao Xiang, SLAC
June
SLAC Accelerator Seminar

2. Outline
Longitudinal-to-transverse mapping to break the 1 fs time barrier
Longitudinal-to-transverse emittance transfer for storage ring lasing

3. Applications of ultrashort electron bunch
Generation of ultrahigh wake field
E167
LCLS
I. Blumenfeld et al, Nature, 445, 741 (2007)

4. Applications of ultrashort electron bunch
Generation of ultrashort x-ray FEL pulses
Diffraction-before-Destruction
R. Neutze et al, Nature, 406, 752 (2000)

5. Compact XFEL
Y. Ding et al, PRL, 102, (2009)
Recent success of using 20 pC electron beam to drive an x-ray FEL at the LCLS has stimulated world-wide interests in using low charge beam (1~20pC) to drive a compact XFEL which delivers ultrashort x-ray pulses (0.1 fs~10 fs).
How to measure 1 fs bunch?

6. Deflecting cavity Bunch length measurement with a deflecting cavity
Resolution limited by intrinsic emittance:

7. Deflecting cavity LCLS NLCTA
S band (V=10 MV, Beta=50 m)
X band (V=20 MV)
NLCTA
Beam (E=120 MV, Beta=10 m, emittance=8 mm mrad)
X band (V=5 MV, f = GHz)
Is it possible to overcome the fundamental resolution limit arising from the intrinsic beam divergence/emittance?

8. Longitudinal-to-transverse mapping
z to x’
x’ to x
Scheme to achieve exact mapping
Matrix of an isochronous non-achromatic chicane
D. Xiang and W. Wan, PRL, 104, (2010)

9. Longitudinal-to-transverse mapping
Transfer matrix of a deflecting cavity
Transfer matrix of the chicane + deflecting cavity
Properly choosing the deflection strength to make
Map z exactly to x’

10. Longitudinal-to-transverse mapping
Final transfer matrix after a parallel-to-point imaging beam line
z to x’
x’ to x
Map z exactly to x with a magnification ratio

11. Longitudinal-to-transverse mapping
How it works?

12. Longitudinal-to-transverse mapping
LCLS over-compression case

13. Longitudinal-to-transverse mapping
LCLS under-compression case

14. Longitudinal-to-transverse mapping
ECHO-7 puzzle
Lasers on
Filter in
Turn off either laser does not kill the signal

15. Longitudinal-to-transverse mapping
ECHO-7 puzzle
ECHO phase space
HGHG phase space
One bump per wavelength
Multiple bumps per wavelength
ECHO current distribution
HGHG current distriution

16. Longitudinal-to-transverse mapping
ECHO-7 puzzle might be solved by measuring the current
ECHO beam profile
HGHG beam profile
One bump per wavelength
Multiple bumps per wavelength
ECHO current distribution
HGHG current distriution 16

17. Outline
Longitudinal-to-transverse mapping to break the 1 fs time barrier
Longitudinal-to-transverse emittance transfer for storage ring lasing

18. Beam requirement in x-ray FELs
Electron slips back by one radiation wavelength after it travels one undulator period
Low geometric emittance
Low energy spread
High peak current
~1 um emittance with ~1 MeV energy spread and ~kA peak current 18

19. Storage ring FEL Beams in storage ring PEP-X beam parameters Low power
Large energy spread & Low current
PEP-X beam parameters
Low power
Poor transverse coherence
FEL at <1nm is very difficult
Power gain length at 1nm 19

20. Current-enhanced SASE (E-SASE)
Increase peak current to increase the FEL gain
Suitable for the case when
current
energy spread
A. Zholents, PRST-AB, 8, (2005)
Is it possible to increase the peak current without increasing the energy spread? Violating Liouville’s theorem? 20

21. Laser assisted emittance tranfer
Increase peak current without increasing energy spread
Schematic of the laser assisted emittance transfer
E-SASE
LAET
TEM00 laser
TEM01 laser
4-bend chicane
Isochronous non-achromatic chicane
Increase peak current
Increase peak current
Increase energy spread
Increase vertical emittance 21

22. Laser assisted emittance tranfer
Initial distribution
phase space
current
energy spread
vertical emittance 22

23. Laser assisted emittance tranfer
After interaction with the TEM01 laser
phase space
current
energy spread
vertical emittance 23

24. Laser assisted emittance tranfer
Final distribution
phase space
current
energy spread
vertical emittance 24

25. Laser assisted emittance tranfer
Estimated FEL performances at 1 nm
1.8 mm mrad
0.018 mm mrad
5.1 MeV
300 A
35 m
Gain length:
~100 kW
Peak power:
Limitation
The duration of the current bump is shorter than the slippage length and one needs to frequently use isochronous chicane to shift the radiation to the upstream bumps to sustain the effective interaction 25

26. Summary
A technique is proposed to manipulate the beam phase space and rearrange the beam’s x distribution according to its initial z distribution
The longitudinal-to-transverse mapping technique may allow one to break the 1 fs time barrier in ultrashort bunch length measurement
A technique is proposed to significantly increase the beam current without greatly increasing the energy spread
The laser assisted emittance transfer technique can be used to repartitioning the emittance in 6-D phase space so that one might be able to use the beam from a large storage ring to drive a high-gain FEL.
Many thanks to:
M. Borland, Y. Cai, A. Chao, Y. Ding, P. Emma, Z. Huang, G. Stupakov, M. Woodley, J. Wu and A. Zholents
Thanks!