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James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Undulator K-Parameter Measurements at LCLSUndulator K-Parameter Measurements at LCLSJ. Welch, SLAC National Accelerator LaboratoryJ. Welch, SLAC National Accelerator Laboratory
Contributors: R. Bionta, A. Brachmann, F.-J. Decker, Y. Ding, P. Emma, A. Fisher, Z. Huang, R. Iverson, H. Loos, H.-D.
Nuhn, H. Sinn, P. Stefan, D. Ratner, J. Turner, J. Wu, D. Xiang
This work is supported by the U.S. Department of Energy, contract DE-AC02-76SF00515, and was performed under the auspices of the U.S. Department of Energy, by University of California, Lawrence Livermore National Laboratory under Contract W-7405-Eng-48, in support of the LCLS project at SLAC.
THOA05
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
TopicsTopics
IntroductionMotivation
Diagnostics
Measurements schemes
Calibrations, Checks, Errors
Results
Outlook
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Motivation for Motivation for in-situin-situ K Measurements K Measurements
The 130 m long undulator consists of 33, essentially identical, independently tunable segments.FEL gain is lost if K/K (RMS) 1.5x10-4 K Tolerance was well met, we lased right away, but…
Temperature, alignment, position, radiation, can change K.
We have a validation program, whereby segments are ocassionally removed to the laboratory and tested.
In-situ K measurements will allow timely tuning correction, and guide segment selection for removal and validation.
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
DiagnosticsDiagnostics
K monochromator passes only one x-ray energy and one angle. It is not tunable to other energies.
Si 111
W
photodiode
K-monochromator
x-rays x-ray energy [eV]
FWHM 1.2 [eV]
SSRL
Get spectrum by scanning electron beam energy.
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Basic Measurement SchemesBasic Measurement Schemes
One-segment schemeCompute K difference from spectrum shift
Two-segment scheme (FEL2006)
Match K of Test to Reference segment by minimizing the two-segment bandwidth.
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
inflection point
One-Segment MethodOne-Segment Method
First, only the REF segment is put online and a spectrum is measured. The Reference “inflection point” is determined.Next, the Ref removed and theTest segment is put online.Then, we measure a series of spectra for different horizontal positions the Test segment and find the match position.
undulator segments (33 total)
Test
RefRefTest K-mono
photodiode
Imager
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Central Ray DeterminationCentral Ray DeterminationSpectrum depends on K and observation angle .
€
λ1 =λ u
2γ 21+ K 2 /2 + γ 2θ 2( )
Statistical precision of location of Central Ray is 0.03 rad or 3 m.
Look at image just after K-monochromator with energy just below pass band energy.
Insure “Core” radiation for Ref and Test segments hits detector.
-10 MeV
-15 MeV
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
K Monochromator Transmission K Monochromator Transmission To find electron energy for transmission, aim a bit high and look at imager. Next search for the transmission angle.3 rad rotation easy to see on imager. (FWHM is ~70 rad. ) Alternately, scan angle and measure photodiode signal.
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Single Segment SpectrumSingle Segment Spectrum
3x3 mm slits for u33 -> +/- 19 rad.
core size +/-6.7 rad Beam energy jitter, 0.04% rms, typical.Data is from non-synchronous acquisition.
Simulation assumes 0.003% energy resolution based on BPM resolution and dispersion.
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
ErrorsErrors
Random Errors: RF phase jitter -> E/E = 4x10-4.
Wakefield energy loss and peak bunch current jitter Photodiode noise
Mitigation….Dogleg bends bpms provide 3x10-5 relative energy resolution and freedom from betatron motion.Bias electron energy scan to match K steps.
Systematic ErrorsSpontaneous radiation Wakefield energy loss Temperature differences Observation angle
Mitigation3000 A peak bunch current is normal for FEL operation. Can easily tune to 500 A Both bunch current jitter and wakefield energy loss per meter are reduced.
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
First Results First Results
FEL lasing at 0.15 nm means K’s are in good shape.Measurement Repeatability
1.9, 5.6, and 4.7, x 10-4.
Not implemented in this data
synchronous acquisitionenergy biasingtwo-segment method
Test Segment Reference Segment K (Test-Ref/Ref)x104 X match [mm]
4 5 0.5 -0.07
5 6 2.3 -0.34
6 7 -3.8 0.57
7 8 1 -0.15
8 9 -1.5 0.23
9 10 -0.7 0.11
10 11 0 0
11 12 -1.1 0.17
12 13 -4.7 0.71
13 14 -1.3 0.20
14 15 -2.7 0.40
15 16 -0.3 -0.33
31 32 2 -0.3
32 33 1.9 -0.28
Meas. Ave -0.6Design -0.5
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
OutlookOutlook
Early results from in-situ measurement of K-parameters are
promissing, though somewhat noisy.
Signal levels are good, simulation and measurements are in good
general agreement.
Noise reduction techniques were not fully implemented but are
ready.
Measurement parameters (step size, slit settings, gains,
integration times, energy range, harmonic, etc. ) still need to be
optimized.
Two-segment method needs implementation.
Systematic effects are small and well in hand.
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Theory of Two Segment SpectrumTheory of Two Segment Spectrum
Spectral intensity depends on relative detuning and phase difference
Detuning parameters, 1,2
Phase difference, Angle parameter, Spectral intensity, IIncludes angle energy correlation
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λ1 =λ u
2γ 21+ K 2 /2 + γ 2θ 2( )
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Theory - Angle IntegrationTheory - Angle Integration
Two identical segments
Most signal comes from first 7-8 rad
20 rad is max angle for 1st segment (chamber limit
Maximum negative slope for K measurement doesn’t depend on angle of integration much for angles ≈ 7-8 rad or more.
Steepest (negative) slope
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Theory - Angle Integrated, 2 Detuned Theory - Angle Integrated, 2 Detuned SegmentsSegments
Detuning segments produces slight slope/linewidth change
3% slope change for 0.1% K change
Steepest negative slope will be used to track K.
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Radiation Spectrum from Two UndulatorsRadiation Spectrum from Two Undulators
Pinhole SpectrumDependence on K
Dependence on N
Dependence on ∆K between 2 segments
Dependence of phase error between 2 segments
Angle Integrated Spectrum
Dependence on angle of integration
Dependence on K
Dependence on N
Dependence on ∆K/K between 2 segments
Dependence of phase error between 2 segments
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Measure All Segments: ‘Leap Frogging’Measure All Segments: ‘Leap Frogging’
Phase difference introduced by skipping segments can be adjusted using a closed orbit bump (if 2 or more segments are skipped).
rms(K1 - K33) ≈ rms(K1-K2) x √33
rms(K1 - K33) ≈ rms(K1-K4) x √11
MeasureAdjacent Pairs
Skip 2BetweenPairs
. . .
. . .
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Theory - Pinhole, 2 Segments with Phase Theory - Pinhole, 2 Segments with Phase DifferenceDifference
No detuning
Slight shift and asymmetric distortion of curve
Max negative slope change 0.7%.
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Real vs Ideal Undulator FieldsReal vs Ideal Undulator Fields
Two identical segments, with a simulated
magnetic field equal to the measured field in
the LCLS prototype, were modeled.
A systematic error of 0.008% was found but is
not understood.
Still within required tolerance 0.015%
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Theory - Pinhole, 2 Detuned SegmentsTheory - Pinhole, 2 Detuned Segments
0.1% K detune, no
phase error
-0.09% shift and
slight broadening.
4% decrease in
max. negative slope
Steepest (negative)slope
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Method Method
Roll out all but two nearby segmentsVerify pointing angles using slit scanning to maximize photon energy.Precisely measure electron beam energy jitter, pulse to pulseDetect xrays around the first harmonic using narrow bandwidth crystal spectrometerConstruct the xray spectrum by correlating the no. of detected photons with the measured energy jitter.
Change K of second segment a known amount by shifting horizontally.Obtain another spectrum and move again (≈ 9 X). Find steepest slope of each spectrum. Fit steepest slopes vs K data to find position where K’s are matched. Advance to next pair of segmentsRepeat until all segments are measured.
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Energy Jitter MeasurementEnergy Jitter Measurement
BPM- BPM-
RR = = II
Take BPM reading difference:
Get clean relative energy signal:
Error, , is BPM resolution, x :
(x0, x'0, )
x1=R11 x0 +R12 x'0 +
x2=R11 x0 + R12 x'0 -
x1 - x2 = 2
= (x1 - x2) / 2
= x ⁄ √2
= 125 mm, x ≈ 5 m ≈ 3 x 10-5
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Phase DifferencePhase Difference
Phase difference between
segments distorts shape of
spectrum.
Effect is easy to identify
and if necessary data can
be excluded from fit for
steepest slope
determination.Effect of 70 degrees of phase
difference between segments. (LCLS
spec. is max of 20 degrees)
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Theory - PinholeTheory - Pinhole
One segment K dependence
Simple frequency (photon
energy) shift of spectrum Higher K means lower frequency
Observation angle can only shift spectrum lower
€
λ1 =λ u
2γ 21+ K 2 /2 + γ 2θ 2( )
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Detector Detector
Noise effects that add
error to the number of
detected photons or the
frequency -->
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Finding ∆K=0Finding ∆K=0
Scan K of one segment and find value that maximizes the steepest slope
Neglecting small energy loss between segments, the extremum value is when the segment K values are identical.
Simulation shows resolution of ∆K /K of 0.004% rms
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Inflection Point DeterminationInflection Point Determination
Steepest slope depends on K
difference, but not on
spectrum absolute shift
Third order polynomial fit to
truncated spectrum data
easily yields steepest slope
€
N = N0 + a(Δω /ω) + b(Δω /ω)2 + c(Δω /ω)3
dN
(Δω /ω)
⎛
⎝ ⎜
⎞
⎠ ⎟max
= a −b2
3c
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Two-Segment Spectrum Makes No sense!Two-Segment Spectrum Makes No sense!
Good general agreement with simulationWay too little slope compared with one-segmentAgain, excess noise
some amplitude noise
Measurement
Simulation
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Error sources Error sources Beam energy jitter, 0.1% rms.
Detector is assumed to be narrow bandwidth ( << 1/N), high efficiency, Si crystal, Bragg diffractionMeasure each pulse to 3x10-5 and use to reconstruct the spectrumNatural beam energy jitter is sufficient to sample region of steepest slope.
Phase differences between segmentsShown to be neglible
Alignment/Pointing errorsMore than about 8 rad beam angle will scrape core SR on the vacuum chamber and distort the high energy edge of the measured spectrum.
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
More DisclaimerMore Disclaimer
All measurements are preliminary - not credible.Only <1 shift of reasonable looking data was obtainedNo verification using Two-segment technique
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Random Error MitigationRandom Error Mitigation
Measure energy deviation of each pulse in dispersive region.
Dogleg bends bpms provide 3x10-5 relative energy resolution and freedom from betatron motion.
Run at low bunch 3000 A peak bunch current is normal for FEL operation. Can easily tune to 500 A (longer bunch).Both bunch current jitter and wakefield energy loss per meter are reduced.
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
2-Segment Scheme2-Segment Scheme
Measure synchrotron radiation spectrum produced by two undulator segments, and scan K of one segment
Other schemes compare spectra from individual segments. (Pinhole technique, angle-integrated edge measurement, reference undulator)
K’s are matched when spectrum has the steepest slope on high energy side of 1st harmonic peak.
Match segments pairwise until all segments are measured.
undulator segments (33 total)
2-Segment intial
results are too erratic
to report here
RefTest
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
K Adjustment MechanismK Adjustment Mechanism
Segment
Canted Poles
Horizontal SlidesEffective K varies linearly with horizontal position, K/K = -2.68x10-3 mm-1
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Calibrations and ChecksCalibrations and Checks
Alignment of Central Rays
K-monochromator transmission angle
and energy
One-segment spectrum
Measurement details
James Welchwelch@slac.stanford.edu
August 27,2009FEL 2009
Measurement DetailsMeasurement Details
Inflection point can be sensitive to range of data used for fit when data is noisy.Biasing the electron energy scan range avoid biasing the fit.One measurement takes about 5 minutes. (Slow stage travel.)
Real Data
Inflection Point