Longitudinal-to-transverse mapping and emittance transfer

Dao Xiang, SLAC

June-10-2010

SLAC Accelerator Seminar

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Outline

Longitudinal-to-transverse mapping to break the 1 fs time barrier

Longitudinal-to-transverse emittance transfer for storage ring lasing

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Applications of ultrashort electron bunch

Generation of ultrahigh wake field

I. Blumenfeld et al, Nature, 445, 741 (2007)

E167

LCLS

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Applications of ultrashort electron bunch

Diffraction-before-Destruction

Generation of ultrashort x-ray FEL pulses

R. Neutze et al, Nature, 406, 752 (2000)

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Compact XFEL

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).

Y. Ding et al, PRL, 102, 254801 (2009)

How to measure 1 fs bunch?

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Deflecting cavity

Resolution limited by intrinsic emittance:

Bunch length measurement with a deflecting cavity

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Deflecting cavity

S band (V=10 MV, Beta=50 m)

Is it possible to overcome the fundamental resolution limit arising from the intrinsic beam divergence/emittance?

LCLS

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)

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Longitudinal-to-transverse mapping

Matrix of an isochronous non-achromatic chicane

Scheme to achieve exact mapping

D. Xiang and W. Wan, PRL, 104, 084803 (2010)

z to x’ x’ to x

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Longitudinal-to-transverse mapping

Transfer matrix of a deflecting cavity

Properly choosing the deflection strength to make

Transfer matrix of the chicane + deflecting cavity

Map z exactly to x’

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Longitudinal-to-transverse mapping

Final transfer matrix after a parallel-to-point imaging beam line

Map z exactly to x with a magnification ratio

z to x’ x’ to x

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Longitudinal-to-transverse mapping How it works?

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Longitudinal-to-transverse mapping

LCLS over-compression case

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Longitudinal-to-transverse mapping

LCLS under-compression case

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Longitudinal-to-transverse mapping

ECHO-7 puzzle

Lasers on Filter in

Turn off either laser does not kill the signal

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Longitudinal-to-transverse mapping

ECHO-7 puzzle

ECHO phase space HGHG phase space

ECHO current distribution HGHG current distriution

Mu

ltiple b

um

ps p

er wavelen

gth

On

e bu

mp

per w

aveleng

th

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Longitudinal-to-transverse mapping

ECHO-7 puzzle might be solved by measuring the current

ECHO beam profile HGHG beam profile

ECHO current distribution HGHG current distriution

Mu

ltiple b

um

ps p

er wavelen

gth

On

e bu

mp

per w

aveleng

th

17

Outline

Longitudinal-to-transverse mapping to break the 1 fs time barrier

Longitudinal-to-transverse emittance transfer for storage ring lasing

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Beam requirement in x-ray FELs

Low geometric emittance

Low energy spread

High peak current

Electron slips back by one radiation wavelength after it travels one undulator period

~1 um emittance with ~1 MeV energy spread and ~kA peak current

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Storage ring FEL

Beams in storage ring

Large energy spread & Low current

Power gain length at 1nm

PEP-X beam parameters

Low power

Poor transverse coherence

FEL at <1nm is very difficult

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Current-enhanced SASE (E-SASE) Increase peak current to increase the FEL gain

Suitable for the case when

A. Zholents, PRST-AB, 8, 040701 (2005)

current energy spread

Is it possible to increase the peak current without increasing the energy spread? Violating Liouville’s theorem?

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Laser assisted emittance tranfer Increase peak current without increasing energy spread

TEM00 laser

Schematic of the laser assisted emittance transfer

TEM01 laser

4-bend chicane Isochronous non-achromatic chicane

Increase peak current Increase peak current

Increase energy spread Increase vertical emittance

E-SASE LAET

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Laser assisted emittance tranfer

Initial distribution

phase space current

energy spread vertical emittance

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Laser assisted emittance tranfer

After interaction with the TEM01 laser

phase space current

energy spread vertical emittance

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Laser assisted emittance tranfer

Final distribution

phase space current

energy spread vertical emittance

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Laser assisted emittance tranfer

Estimated FEL performances at 1 nm

Gain length:

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

1.8 mm mrad

0.018 mm mrad5.1 MeV

300 A

35 m

~100 kW

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A technique is proposed to manipulate the beam phase space and rearrange the beam’s x distribution according to its initial z distribution

Summary

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

Thanks!

Many thanks to:

M. Borland, Y. Cai, A. Chao, Y. Ding, P. Emma, Z. Huang, G. Stupakov, M. Woodley, J. Wu and A. Zholents

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.