Undulator K-Parameter Measurements at LCLS J. Welch, SLAC National Accelerator Laboratory

James [email protected]

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



TopicsTopics

IntroductionMotivation

Diagnostics

Measurements schemes

Calibrations, Checks, Errors

Results

Outlook



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.



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.



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.



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



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



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.



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.



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.



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



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.



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

€

λ1 =λ u

2γ 21+ K 2 /2 + γ 2θ 2( )



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



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.



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



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

. . .

. . .



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%.



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%



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



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.



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



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)



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( )



Detector Detector

Noise effects that add

error to the number of

detected photons or the

frequency -->



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



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



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



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.



More DisclaimerMore Disclaimer

All measurements are preliminary - not credible.Only <1 shift of reasonable looking data was obtainedNo verification using Two-segment technique



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.



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



K Adjustment MechanismK Adjustment Mechanism

Segment

Canted Poles

Horizontal SlidesEffective K varies linearly with horizontal position, K/K = -2.68x10-3 mm-1



Calibrations and ChecksCalibrations and Checks

Alignment of Central Rays

K-monochromator transmission angle

and energy

One-segment spectrum

Measurement details



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

Documents

Undulator K-Parameter Measurements at LCLS J. Welch, SLAC National Accelerator Laboratory