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

1. Undulator K-Parameter Measurements at LCLSJ. 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

2. Introduction Motivation Diagnostics Measurements schemes Calibrations, Checks, Errors Results Outlook Topics

3. The 130 m long undulator consists of 33, essentially identical, independently tunable segments. FEL gain is lost if dK/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. Motivation for in-situ K Measurements

4. K monochromator passes only one x-ray energy and one angle. It is not tunable to other energies. FWHM 1.2 [eV] SSRL x-ray energy [eV] Diagnostics x-rays W photodiode Si 111 Get spectrum by scanning electron beam energy. K-monochromator

5. One-segment scheme Compute K difference from spectrum shift Two-segment scheme (FEL2006) Match K of Test to Reference segment by minimizing the two-segment bandwidth. Basic Measurement Schemes

6. 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. inflectionpoint Test Test Ref Ref One-Segment Method Imager undulator segments (33 total) K-mono photodiode

7. Spectrum depends on K and observation angle . -15 MeV -10 MeV Central Ray Determination Insure “Core” radiation for Ref and Test segments hits detector. Look at image just after K-monochromator with energy just below pass band energy. Statistical precision of location of Central Ray is 0.03 mrad or 3 mm.

8. To find electron energy for transmission, aim a bit high and look at imager. Next search for the transmission angle. 3 mrad rotation easy to see on imager. (FWHM is ~70 mrad. ) Alternately, scan angle and measure photodiode signal. K Monochromator Transmission

9. 3x3 mm slits for u33 -> +/- 19 mrad. core size +/-6.7 mrad Beam energy jitter, 0.04% rms, typical. Data is from non-synchronous acquisition. Single Segment Spectrum Simulation assumes 0.003% energy resolution based on BPM resolution and dispersion.

10. Random Errors: RF phase jitter -> dE/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 Errors Spontaneous radiation Wakefield energy loss Temperature differences Observation angle Mitigation 3000 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. Errors

11. 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 acquisition energy biasing two-segment method First Results Meas. Ave -0.6 Design -0.5

12. 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. Outlook

13. Spectral intensity depends on relative detuning and phase difference Theory of Two Segment Spectrum Detuning parameters,1,2 Phase difference,  Angle parameter,  Spectral intensity, I Includes angle energy correlation

14. 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. Theory - Angle Integration Steepest (negative) slope

15. Detuning segments produces slight slope/linewidth change 3% slope change for 0.1% K change Steepest negative slope will be used to track K. Theory - Angle Integrated, 2 Detuned Segments

16. Pinhole Spectrum Dependence 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 Radiation Spectrum from Two Undulators

17. Phase difference introduced by skipping segments can be adjusted using a closed orbit bump (if 2 or more segments are skipped). Measure All Segments: ‘Leap Frogging’ . . . Measure Adjacent Pairs rms(K1 - K33) ≈ rms(K1-K2) x √33 . . . Skip 2 Between Pairs rms(K1 - K33) ≈ rms(K1-K4) x √11

18. No detuning Slight shift and asymmetric distortion of curve Max negative slope change 0.7%. Theory - Pinhole, 2 Segments with Phase Difference

19. 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% Real vs Ideal Undulator Fields

20. Theory - 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

21. Roll out all but two nearby segments Verify pointing angles using slit scanning to maximize photon energy. Precisely measure electron beam energy jitter, pulse to pulse Detect xrays around the first harmonic using narrow bandwidth crystal spectrometer Construct 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 segments Repeat until all segments are measured. Method

22. Energy Jitter Measurement (x0, x'0, d) R = I x2=R11 x0 + R12 x'0 - d BPM-1 BPM-2 x1=R11 x0 +R12 x'0 +d Take BPM reading difference: x1 - x2 =2d Get clean relative energy signal:  = (x1 - x2) / 2 Error, sd , is BPM resolution, sx :  = x ⁄ √2  = 125 mm, x ≈ 5 m   ≈ 3 x 10-5

23. 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. Phase Difference Effect of 70 degrees of phase difference between segments. (LCLS spec. is max of 20 degrees)

24. One segment K dependence Simple frequency (photon energy) shift of spectrum Higher K means lower frequency Observation angle  can only shift spectrum lower Theory - Pinhole

25. Noise effects that add error to the number of detected photons or the frequency --> Detector

26. 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 Finding ∆K=0

27. Steepest slope depends on K difference, but not on spectrum absolute shift Third order polynomial fit to truncated spectrum data easily yields steepest slope Inflection Point Determination

28. Good general agreement with simulation Way too little slope compared with one-segment Again, excess noise some amplitude noise Two-Segment Spectrum Makes No sense! Measurement Simulation

29. Beam energy jitter, 0.1% rms. Detector is assumed to be narrow bandwidth ( << 1/N), high efficiency, Si crystal, Bragg diffraction Measure each pulse to 3x10-5 and use to reconstruct the spectrum Natural beam energy jitter is sufficient to sample region of steepest slope. Phase differences between segments Shown to be neglible Alignment/Pointing errors More than about 8 rad beam angle will scrape core SR on the vacuum chamber and distort the high energy edge of the measured spectrum. Error sources

30. All measurements are preliminary - not credible. Only <1 shift of reasonable looking data was obtained No verification using Two-segment technique More Disclaimer

31. Measure energy deviation of each pulse in dispersive region. Dogleg bends bpms provide 3x10-5 relative energy resolution and freedom from betatron motion. Random Error Mitigation • 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.

32. 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. 2-Segment Scheme 2-Segment intial results are too erratic to report here undulator segments (33 total) Test Ref

33. Effective K varies linearly with horizontal position, DK/K = -2.68x10-3 mm-1 K Adjustment Mechanism Horizontal Slides Segment Canted Poles

34. Alignment of Central Rays K-monochromator transmission angle and energy One-segment spectrum Measurement details Calibrations and Checks

35. 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.) Inflection Point Measurement Details Real Data