Transcript Spontaneous Radiation at LCLS Sven Reiche UCLA - 09/22/04 General Properties  Resonant wavelength:  u (1  0 cos( )) 0 u K2  2 (1    2

Spontaneous Radiation at LCLS
Sven Reiche
UCLA - 09/22/04
General Properties
 Resonant wavelength:

u
(1  0 cos( ))
0
u
K2
 2 (1 
  2 2 )
2
2
 Maximum signal when directions of observation and
trajectory are parallel
with a characteristic opening angle

of 
 Maximum angle in electron trajectory is K/
 Effective solid angle of radiation is  = 1/ x K/
The Signal in Time Domain
trajectory
For larger angle in x the
uni-polar signals move closer
together, merging into a bipolar signal for >K/
Above plane of oscillation
Angular distribution (Far Field)
 Only odd harmonics are visible on-axis
 All harmonics are present for off-axis angles.
 The nth harmonic has n-1 knots in the yz-plane.
fundamental
2nd harmonic
3rd harmonic
Intensity Spectrum
 LCLS-lattice with super period. Detector 113 behind exit
of undulator.
 Rich harmonic content on-axis.
 Wider spikes for off-axis radiation due to red shift
 Reduced harmonic content for off-axis emission.
Full Spectrum
 Summing over all emission angles, the full spectrum
resembles that of a bend dipole.
Simplified LCLS lattice (far field)
Power Consideration
 The total power is
cZ0Ie
P
Nuku 2K 2
6
 For LCLS the total power is 75 GW, 10x larger than the
FEL signal at 1.5 Å.
 The effective solid angle is 1/2 =1.5•10-9 rad2, 3 orders of

magnitude
larger than for the FEL signal (~10-12 rad2)
At saturation the FEL intensity is about 100 larger
than the spontaneous background signal
Intensity Distribution
 Angular distribution, 113 m behind undulator exit, using
real LCLS lattice:
The peak intensity
is 73 kW/mm2
The distribution is
almost like in the far
field zone.
Total energy 75 GW
Spectral Power Cut
 The opening angle for a single frequency is:
K
 
2
1
Nu
 For LCLS the angle is  = 1.5 rad.
 The emitted power at the fundamental is about 1 MW per

0.1% bandwidth (the full FEL signal of about 10 GW falls
within this bandwidth).
 Higher harmonics contribute less than 5% to the total
background signal and are most likely filtered out by
spatial apertures.
Spatial Power Cut
 Array detectors (e.g. X-ray CCD cameras) or spatial
collimator improve the signal to noise ratio.
 For LCLS, any cut below 1 mm2 at the first detector
position (113 m behind undulator) would reduce also the
FEL signal.
Signal-Noise (Full Undulator)
Case
1.5 Å
1.5 nm
FEL power
8 GW
4 GW
Spontaneous
Radiation
75 GW
7.5 GW
Spectral Cut: 0.1%
1 MW
100 kW
Spectral Cut: 1.0%
10 MW
1 MW
Spatial Cut: 1 mm2
0.9 GW
9 MW
Spatial Cut: 4 mm2
3 GW
30 MW
The noise signal for spatial cuts can be lower,
depending on the spectral response of the detector.
Detecting the FEL Signal
Solid - electron beam mis-steered
Dashed - undulator modules removed
Spectral Cut: 0.1%
Spectral Cut: 1.0%
Spatial Cut: 1 mm2
Spatial Cut: 4 mm2
FEL Signal
Detecting the FEL Signal
 For LCLS no information can be obtained from the FEL
signal for the first 20 m with respect to undulator
alignment and field quality.
 Operating at longer wavelength reduces the distance but
makes the FEL signal less sensitive to the field quality.
 Short pulse operation of the FEL (e.g. two-stage pulse
slicing or slit in dispersive section) reduces the signalnoise ration by 1-2 orders of magnitude.
 Information on undulator modules can be obtained by the
spectrum of the spontaneous radiation.
Module Detuning Tolerance
 Detuned modules yield a ‘local’ phase slippage of the
radiation field with respect to electron beam, yield a
degradation in the synchronization of the resonance
condition.
 Simulations yield tolerance of K=9.10-4
Undulator Module Tuning
 Possible method to tune undulator modules with the
spontaneous radiation.
 Following method, proposed by TESLA (thanks to Markus
Tischer, Kai Tiedke - HASYLAB, DESY)
 Prerequisite set-up: Non-destructive measurement of X-ray
path (e.g. X-ray BPM, resolution < 1 mm)
Gas
+ + +
+
+
+
+
+
+
X-ray beam
Pick-up line
 To measure changes in K of 9.10-4 the orbit of the photon
beam has to be stable by about 2.1 rad.
Single Module Spectrum
 Bandwidth of 1/Nu~1%
 Angular distribution
after monochromator
At 5th harmonic
Ideal case of zero energy
spread and emittance
Detuned Module
 Monochromator selects frequency slightly above 5th
harmonic (shift of about 6.10-4)
K/K = 10-4
Same at 1st harmonic
 Variation in detected power and width of distribution
 Works best for monochromator tuned to the half value
point of the high-frequency side of the spectrum
Emittance and Energy Spread
 Line width and distribution size are dominated by
emittance (energy spread is negligible) for the 10th or
higher harmonics.
 At 5th harmonic no degradation by emittance and energy
spread.
 No benefits by going to higher harmonics
K/K = 10-4
1st
5th
10th
20th
Machine Jitter
 Energy jitter of 0.1% has same wavelength shift as
detuning of K/K=10-4, but can be eliminated by statistic
 Same argument applies to charge jitter
 Alternatively the radiation measurement can be binned by
measuring charge and energy of the spent beam.
 Jitter in beam angle (0.12-0.24 rad) is sufficiently small
for the measurement. Transferred jitter on the radiation
beam might be detectable if a X-ray BPM is installed.
 Other machine jitter not of relevance for tuning the
modules.
Tuning the Undulator
 After BBA the orbit must be straight enough to have a
beam divergence less than 1 rad.
 X-ray BPM are complimentary measurement of the orbit
straightness. Improvement in resolution when installed in
far hall, but not necessary when BBA is successful.
 Tuning works only for one module per time. If tuned
modules remain in beam line than line width and
distribution are determined by emittance and change in
signal is too weak.
 Emittance effects can be slightly suppressed by increasing
the beta-function for tuning.
Micro-Taper
 The energy loss due to spontaneous energy radiation
requires to taper the undulator.
 The required taper is K=1.7•10-4 per module.
 Defines the required precision for undulator alignment.
 Denies module detuning at lower energy.
Ideal Case
Tapered
Not tapered
Coherent Radiation
 Coherent radiation arises from
 Undulator radiation, emitted under large angles
 Transition undulator radiation in the forward direction
 The coherently emitted energy of 40.5 J for CUR and 1.3
J for CTUR are negligible with respect to the
incoherently emitted radiation.
 Although CTUR emits although at the resonant
wavelength and is proportional to the bunching factor, the
emission is strongly suppressed due to the finite extend of
the electron bunch.
Conclusion
 Strong background signal from spontaneous undulator
radiation. Requires some spatial and/or spectral cut to
select FEL signal.
 No information on the undulator quality can be obtained
from the FEL signal for the first section of the undulator.
 Individual undulator modules can be tuned by spectral
analysis of the 5th (or 3rd) harmonics.
 Tuning for multiple modules in the beam line somehow
limited by emittance