Longitudinal-to-transverse
mapping and emittance transfer
Dao Xiang, SLAC
June-10-2010
SLAC Accelerator Seminar
 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
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LCLS
I. Blumenfeld et al, Nature, 445, 741 (2007)
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 Applications of ultrashort electron bunch
 Generation of ultrashort x-ray FEL pulses
Diffraction-before-Destruction
R. Neutze et al, Nature, 406, 752 (2000)
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 Compact XFEL
Y. Ding et al, 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?
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 Deflecting cavity
Bunch length measurement with a deflecting cavity
Resolution limited by intrinsic emittance:
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 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?
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 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)
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 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’
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 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
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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 current distribution
HGHG phase space
One bump per wavelength
Multiple bumps per wavelength
ECHO phase space
HGHG current distriution
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 Longitudinal-to-transverse mapping
 ECHO-7 puzzle might be solved by measuring the current
ECHO current distribution
HGHG beam profile
One bump per wavelength
Multiple bumps per wavelength
ECHO beam profile
HGHG current distriution
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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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 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
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 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
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 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?
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 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
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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
1.8 mm mrad
0.018 mm mrad
5.1 MeV
300 A
Gain length:
35 m
Peak power:
~100 kW
 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
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 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!
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