Longitudinal-to-transverse mapping and emittance transfer

1. Longitudinal-to-transverse mapping and emittance transfer Dao Xiang, SLAC June-10-2010 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 etal, PRL, 102, 254801 (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 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 = 11.424 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, 084803 (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 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, 040701 (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 TEM01 laser TEM00 laser Isochronous non-achromatic chicane 4-bend chicane Increase peak current Increase peak current Increase vertical emittance Increase energy spread 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!