Self-seeding Free Electron Lasers
J. Wu
FEL Physics Group
Beam Physics Department
Oct. 26, 2010
Accelerator Research Division Status Meeting
Outline
Brief description of a Self-Amplified Spontaneous
Emission (SASE) Free Electron Laser (FEL) as LCLS
Schemes to improve the longitudinal coherence
– Self-seeding as one of the possibilities
Monochromator
– Crystals for hard x-ray
– Variable Line Spacing Gratings for soft x-ray
Issues
– Electron bunch centroid energy jitter
– Electron bunch energy profile imperfectness
October 26, 2010
ARD Status meeting
jhwu@slac.stanford.edu
J. Wu, FEL Physics Group
2
What is a laser
A laser (standing for Light Amplification by Stimulated
Emission of Radiation) is a device which produces
electromagnetic radiation, often visible light, using the
process of optical amplification based on the stimulated
emission of photons within a so-called gain medium.
The emitted laser light is notable for its high degree of spatial
and temporal coherence, unattainable using other
technologies.
– Spatial coherence typically is expressed through the output being
a narrow beam which is diffraction-limited, often a so-called
"pencil beam."
– Temporal (or longitudinal) coherence implies a polarized wave at
a single frequency whose phase is correlated over a relatively
large distance (the coherence length) along the beam.
October 26, 2010
ARD Status meeting
jhwu@slac.stanford.edu
J. Wu, FEL Physics Group
Conceptual physics, Paul Hewitt, 2002
3
SASE FEL
SASE FEL
SASE FEL
– Starts from undulator Spontaneous Emission random
startup from shot noise  intrinsically a chaotic
polarized light, e.g., in the linear exponential growth
regime, the FEL energy fluctuation distribution falls on a
g-distribution function
Collective effects
– Self-Amplified Spontaneous Emission (SASE)
– Guided mode  mode selection  transverse coherence
– Slippage  temporal coherent within slippage distance
 coherent spike
SASE FEL—Transverse Coherence
Gain guiding—mode selection for LCLS
courtesy S. Reiche
SASE FEL—Temporal Coherence
Photon slips (advances) over electron bunch,
the electrons being swept by the same photon
wavepacket (which is also growing due to
bunching) will radiate coherently  coherent
length  coherent spike
Speed of light = c
Speed of electron < c
– Spike duration on order of N wFEL / c . For
LCLS, less than 1 fs (0.3 mm) at saturation
6
LCLS 1.5 Å SASE FEL Performance
FEL power along the undulator
Instability:
saturation
Instability:
exponential growth
Saturation early with
power on order of GW
7
LCLS 1.5 Å SASE FEL Performance
FEL bandwidth along the undulator
Bandwidth on order of 1E-3
Bandwidth
decreases as 1/z1/2
8
LCLS 1.5 Å SASE FEL Performance
FEL temporal profile at 60 m
9
LCLS 1.5 Å SASE FEL Performance
FEL spectrum at 60 m
10
Temporal Coherence
Reason for wide bandwidth: coherent length
shorter than the entire pulse length
– Decrease the entire pulse length  low
LCLS low charge operation mode
charge, single spike [Y. Ding et al., PRL, 2009]
– Increase the coherent length  seeding
with coherent length to be about the entire
pulse length
11
FEL Types: Amplifiers & Oscillators
SASE and seeded FEL
SASE Amplifier
Laser or HHG
Seeded Amplifier
(external seeding)
Modulator
Buncher
Radiator
in/n
Harmonic Generation
EEHG, HGHG, etc.
(external seeding)
Oscillator (self-seeding)
Mirror
Mirror
J.B. Murphy and J. Wu, The Physics of FELs, US Particle Accelerator School, Winter, 2009
13
Schematics of Self-Seeded FEL
Originally proposed at DESY [J. Feldhaus, E.L. Saldin,
J.R. Schneider, E.A. Schneidmiller, M.V. Yurkov, Optics
Communications, V.140, p.341 (1997) .]
– Chicane & monochromator for electron and photon
chicane
1st undulator
2nd undulator
FEL
SASE FEL
electron
monochromator
Seeded FEL
electron
dump
Transform Limited Pulses
14
For a transform limited Gaussian photon beam
sw  1/2s t   wFWHMs t  2 ln 2  1.18
– For flat top wFWHMs t  1.61
– Gaussian pulse, at 1.5 Å, if Ipk= 3 kA, Q = 250 pC, sz  10
mm, then transform limit is: sw/w0  10-6
– LCLS normal operation bandwidth on order of 10-3
Improve longitudinal coherence, and reduce the
bandwidth improve the spectral brightness
The coherent seed after the monochromator should
be longer than the electron bunch; otherwise SASE
will mix with Seeded FEL
15
Single Spike vs Self-Seeding
Reaching a single coherent spike?
– Low charge might reach this, but bandwidth will be broad
Narrow band, “relatively long” pulse  Self-Seeding.
In the following, we focus on 250-pC case with a
“relatively” long bunch, and look for “narrower”
bandwidth and “good” temporal coherence
For shorter wavelength (< 1 nm), single spike is not easy to
reach, but self-seeding is still possible
16
Two-Stage FEL with Monochromator
Seeding the second undulator (vs. single undulator
followed by x-ray optics)
– Power loss in monochromator is recovered in the second
undulator (FEL amplifier)
– Peak power after first undulator is less than saturation
power  damage to optics is reduced
With the same saturated peak power, but with two-orders of
magnitude bandwidth reduction, the peak brightness is increased
by two-orders of magnitude
Hard x-ray self-seeding Monochromator
17
For hard x-ray, crystals working in the Bragg
geometry can serve as the monochromator
– Original proposal invokes 4 crystals to form the photon
monochromator, which introduces a large optical delay
 a large chicane has to introduce for the electron to
have the same amount of delay  is not favored.
– Two electron bunch scheme Y. Ding et al., 2010; G. Geloni et al., 2010
– More recent proposal uses single diamond crystal  the
monochromatized wake as a coherent seed
G. Geloni et al., 2010
LCLS: Two-bunch HXR Self-seeding
~4m
SASE
U1
U2
Si (113)
Before U2
18
After U2
Seeded
Si (113)
Spectrum
Y. Ding, Z. Huang, R. Ruth, PRSTAB 13, 060703 (2010)
G.Geloni et al., DESY 10-033 (2010),
Single diamond crystal proposal
G. Geloni et al., 2010
Single diamond crystal proposal
G. Geloni et al., 2010
Power distribution after the
SASE undulator (11 cells).
6 GW
Spectrum
after the
diamond
crystal
10-5
Power
distribution
after diamond
crystal
FWHM
6.7  10-5
G. Geloni et al., 2010
Soft x-ray self-seeding monochromator
Optical components (assuming dispersion in vertical plane)
– (horizontal) Cylindrical focusing M1: Focusing at re-entrant point
– (rotational) Planar pre-mirror M2: Varying incident angle to
grating G
– (rotational) Planar variable-line-spacing grating G: Focusing at
exit slit
– Adjustable/translatable exit slit S
– (vertical) Spherical collimation mirror M3: Re-collimate at reentrant point
e-beam
1st undulator
source
point
M3
M1
g
M2
2nd undulator
re-entrant
point
h
G
Y. Feng, J. Hastings, P. Heimann, M. Rowen, J. Krzywinski, J. Wu, FEL2010 Proceedings. (2010)
22
23
6-Å Case: Electron Bunch
Peak current ~3 kA
Undulator period 5 cm, Betatron function 4 m
For 250 pC case, assuming a step function current
profile, sz  7 mm.
Gain length ~ 2.1 m
SASE spikes ~ 160
24
6-Å SASE FEL Parameters
6-Å FEL power along the first undulator
saturation around 32 m
with power ~10 GW
LCLS-II uses about 40 meter long undulators
25
6 Å SASE FEL Properties
6 Å FEL temporal profile at 30 m in the first
undulator: challenge
26
6 Å SASE FEL Properties
6 Å FEL spectrum at 30 m in the first undulator
– Spiky spectrum: challenge
27
6-Å Case - Requirement on Seed Power
Effective SASE start up power is 1.3 kW.
Use small start up seed power 100 kW.
– Monochromator efficiency ~ 0.2 % (at 6 Å)
– Phase space conservation: bandwidth decreases 1 to 2orders of magnitude (~ 160 spikes)
– Take total efficiency 5.010-5 Need 2 GW on
monochromator to seed with 0.1 MW in 2nd und.
2 GW
0.1 MW
28
6-Å Self-Seeded FEL Performance
Temporal profile at ~25 m in the 2nd undulator for
seed of 100 kW
~12 mm
29
6-Å Self-Seeded FEL Performance
FEL spectrum at ~25 m in the 2nd undulator for
seed of 100 kW
FWHM 5.210-5
6-Å case — transform limited
Effective pulse duration 12 mm, sz ~ 3.5 mm
Transform limited Gaussian pulse  bandwidth is
3.210-5 FWHM.
(For uniform pulse  4.410-5 FWHM)
The seeded FEL bandwidth (5.210-5 FWHM) is
close to the transform limited bandwidth
30
Self-Seeding Summary at 6 nm and 6 Å
Parameter
Emittance
Peak Current
Pulse length rms
6 nm
0.6
1
35
6Å
0.6
3
12
unit
mm
kA
fs
Bandwidth FWHM
Limited Bandwidth
Seed Power
24
15
100
5.2
4.4
100
10-5
10-5
kW
Power on Mono
Mono Efficiency
Over all Efficiency
50
10
20
2000
0.2
0.5
MW
%
10-4
Sat. Power
Sat. Length
Brightness Increment
5
30
50
10
35
150
GW
m
J. Wu, P. Emma, Y. Feng, J. Hastings, C. Pellegrini, FEL2010 Proceedings. (2010)
31
Issues
Electron centroid energy jitter can lead to both
timing jitter and also a detuning effect
– Take 6 nm as example, FEL parameter r ~ 1.2 ×10-3
– R56 ~ 3 mm
– Timing jitter 12 fs
– FEL detuning
theory; positive
detune  longer
gain length, higher
saturation power;
negative detune 
longer gain length,
lower saturation
X.J. Wang et al., Appl. Phys.
power
October 26, 2010
ARD Status meeting
Lett. 91, 181115 (2007).
jhwu@slac.stanford.edu
J. Wu, FEL Physics Group
32
Issues
The previous slide shows the power fluctuation due
to centroid energy jitter, the spectrum bandwidth
seems to be less affected.
October 26, 2010
ARD Status meeting
jhwu@slac.stanford.edu
J. Wu, FEL Physics Group
33
Issues
Electron bunch energy profile imperfectness
– In the second undulator, with the injection of
monochromatized coherent seed, the FEL process is
essentially a seeded FEL
– Study a linear energy chirp on the electron bunch first,
m
   2s w2 ,GF ( z ) 
s w , s , f ( z )  s w , s 1  

2
18
216
s

w ,s 

– The FEL bandwidth
where
mk z
 w
r
2 dg
g 0ws dt
and
3 3r ws2
s w ,GF ( z ) 
kw z
J. Wu, P.R. Bolton, J.B. Murphy, K. Wang, Optics Express 15, 12749 (2007);
J. Wu, J.B. Murphy, P.J. Emma et al., J. Opt. Soc. Am. A 24, 484 (2007).
October 26, 2010
ARD Status meeting
jhwu@slac.stanford.edu
J. Wu, FEL Physics Group
34
Issues
Take 1.5 Å as example
– Initial coherent seed bandwidth 10-5;
– The electron energy chirp is taken for four cases: over
the rms bunch length, the rms correlated relative energy
spread is 0.5 r (green), r (purple), 2.5 r (blue), and 5 r
(red)
October 26, 2010
ARD Status meeting
jhwu@slac.stanford.edu
J. Wu, FEL Physics Group
35
LCLS Self-Seeded FEL Performance
Start with 10-6 bandwidth, 10 MW seed, well cover
the entire electron bunch the FEL power along the
undulator
Saturation early with
power on order of GW
36
LCLS Self-Seeded FEL Performance
FEL temporal profile at 40 m
37
LCLS Self-Seeded FEL Performance
FEL spectrum at 40 m
FWHM 10-5
The nonuniform energy profile affects the bandwidth
October 26, 2010
ARD Status meeting
jhwu@slac.stanford.edu
J. Wu, FEL Physics Group
38
Issues
Electron bunch energy profile imperfectness
– Study a linear energy chirp together with a second order
curvature on the electron bunch,
s w2 ,ˆ ,ˆ ( z)  s w2 ,GF ( z)1     2 
where
2 dg
m
g 0w s dt
ˆ  -
d 2g
 g 0w s2 dt 2
2
t 0
m
2r 2
ˆ 
t 0

2r 3
A.A. Lutman, G. Penco, P. Craievich, J. Wu, J. Phys. A: Math. Theor. 42, 045202 (2009);
A.A. Lutman, G. Penco, P. Craievich, J. Wu, J. Phys. A: Math. Theor. 42, 085405 (2009);
October 26, 2010
ARD Status meeting
jhwu@slac.stanford.edu
J. Wu, FEL Physics Group
39
Issues
Electron bunch energy profile imperfectness
– Electron bunch can have an energy modulation,
J. Wu, A.W. Chao, J.J. Bisognano, LINAC2008 Proceedings, p. 509 (2008);
B. Jia, Y.K. Wu, J.J. Bisognano, A.W. Chao, J. Wu, Phys. Rev. ST Accel. Beams 13, 060701 (2010);
J. Wu, J.J. Welch, R.A. Bosch, B. Jia, A.A. Lutman, FEL2010 proceedings. (2010).
October 26, 2010
ARD Status meeting
jhwu@slac.stanford.edu
J. Wu, FEL Physics Group
40
Summary
LCLS excellent electron beam quality leads to short
gain length, early saturation. This makes possible to
add more functions
Two-stage FEL with monochromator reduces the
bandwidth by 2 order of magnitude with similar
peak power  increases the brightness by 2 order
of magnitude
Some details about electron energy centroid jitter
and energy profile imperfectness has been looked
into
41
Thanks for your attention!
Thanks to Y. Cai for providing this chance!
Special thanks to:
P. Emma, Z. Huang, J. Arthur, U. Bergmann, Y.
Ding, Y. Feng, J. Galayda, J. Hastings, C.-C. Kao,
J. Krzywinski, A.A. Lutman, H.-D. Nuhn, T.O.
Raubenheimer, M. Rowen, P. Stefan, J.J. Welch
of SLAC, W. Fawley, Ph. Heimann of LBL, B.
Kuske of HZB, J.B. Murphy, X.J. Wang of BNL, C.
Pellegrini of UCLA, and J. Schneider of DESY for
fruitful discussions. ……
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