Undulator Effective-K Measurements Using Angle-Integrated Spontaneous Radiation

1. Undulator Effective-K MeasurementsUsing Angle-Integrated Spontaneous Radiation Bingxin Yang and Roger Dejus Advanced Photon Source Argonne National Lab

2. Some History of the Conceptual Development • 1998 - 2002: APS Diagnostics Undulator e-beam energy measurement • Using angle-integrated undulator radiation measure stored e-beam energy change • Jan. 20, 2004: UCLA Commissioning workshop • Galayda wish list for spontaneous radiation measurements • Feb. 10, 2004: X-ray diagnostics planning meeting (John Arthur) • Roman: Not possible to measure Keff with required accuracy DK/K~1.5×10-4 • Sep. 22, 2004: SLAC Commissioning workshop • Bingxin Yang: Keff can be measured with required accuracy • Large aperture improves accuracy • Electron energy jitter is the main experimental problem • Two undulator differential measurement improves speed and accuracy over single undulator measurements. • Oct., 2004: LCLS • Jim Welch: Keff can be measured with required accuracy • Small aperture is better • Spectrometer allows fast data taking • Apr. 18, 2005: Zeuthen FEL Commissioning workshop • Bingxin Yang: Undulator mid-plane can be located within 10 mm • Regular observation can monitor systematic changes in undulators • Jim Welch:

3. Hope for this workshop • Form a consensus • Spontaneous spectral measurements can be used to measure Keff with required accuracy (DK/K~1.5×10-4) • Aperture size should not be an issue • Operational experience will decide it naturally • Make decisions on the monochromator / spectrometer issues • Monochromator (simple, low cost, robust) • Differential measurements (ultra-high resolution, dependable, other uses: vertical alignment, monitor field change / damage quickly • Spectrometer (scientific experiments) • Need to evaluate specs / cost / schedule / R & D / risk factors / operational availability / maintenance effort • Decisions may depend on other functions • My personal bias: machine diagnostics

4. Outline • Features of the spontaneous spectrum and effect of beam quality: numerical calculations • Average properties: e-beam divergence (sx’, sy’), x-ray beam divergence (sw), and energy spread (sg) • Aperture geometry: width and height, center offset, and undulator distances • Magnetic field errors • Effects of e-beam jitter: simulated experiments • Beamline Option 1: crystal monochromator with charge, energy and trajectory angle readout • Beamline Option 2: crystal monochromator with differential undulator setup • High-resolution experiment: locating magnetic mid-plane of the undulator. Dependence on beam centroid position (x, y) • Summary

5. Spontaneous Radiation Spectrum

6. Angle-integrated? How large is the aperture! Pinhole (sinc) < << Angle-integrated (numeric) BXY: Large enough for the edge feature to be stable

7. Related publications • Momentum compaction measurements • B.X. Yang, L. Emery, and M. Borland, “High Accuracy Momentum Compaction Measurement for the APS Storage Ring with Undulator Radiation,” BIW’00, Boston, May 2000, AIP Proc. 546, p. 234. • Energy spread measurements • B.X. Yang, and J. Xu, “Measurement of the APS Storage Ring Electron Beam Energy Spread Using Undulator Spectra,” PAC’01, Chicago, June 2001, p. 2338 • RF frequency / damping partition fraction manipulations • B. X. Yang, A. H. Lumpkin, ‘Visualizing Electron Beam Dynamics and Instabilities with Synchrotron Radiation at the APS,” PAC’05 • DK/K simulations • B. X. Yang, “High-resolution undulator measurements Using angle-integrated spontaneous radiation,” PAC’05

8. How large is the aperture! FEL-relevant Capture the radiation cone: 2.35 – 5 rms radius  17 – 37 mrad Measured radiation spectrum is more important that calculated from field data!

9. Marking the location of a spectral edge We will watch how the following property changes: • HALF PEAK PHOTON ENERGY

10. Effects of Aperture Change (Size and Center) • Plot the half-peak photon energy vs. aperture size • Edge position stable for 25 – 140 mrad  100 mrad best operation point • Independent of aperture size  Independent of aperture center position

11. Effects of Aperture Change (Source distance) • Calculate flux through an aperture satisfying: • ≤ 100 mrad • ≤ allowed by chamber ID • Plot half-peak photon energy • Rectangular aperture reduces variation

12. Effects of Finite Energy Resolution • Four factors contribute to photon energy resolution • Electron beam energy spread (0.03% RMS  X-ray energy width = 11.7 eV FWHM) • Monochromator resolution (DwM/w ~ 0.1% or 8 eV) • Photon beam divergence Dqw ~ 2.35/gN1/2 ~ 8 mrad • Electron beam divergence sy’ ~ 1.2 mrad

13. Effect of Finite Energy Resolution • Edge position moves with increasing energy spread

14. Effects of Undulator Field Errors Monte Carlo integration for 10 K particle histories. Electron beam parameters E = 13.640 GeV sx = 37 mm sx’ = 1.2 mrad sg/g = 0.03% Detector Aperture 80 mrad (H) 48 mrad (V)

15. Comparison of Perfect and Real Undulator SpectraFilename: LCL02272.ver; scaled by 0.968441 to make Keff = 3.4996 • First harmonic spectrum changes little at the edge.

16. Comparison of Perfect and Real Undulator Spectra • Changes in the third harmonic spectrum is more pronounced. But the edge region appears to be usable. • Changes in the fifth harmonic spectrum is significant. Not sure whether we can use even the edge region.

17. Summary of calculations so far • The following beam qualities are not problems for measuring spectrum edge: • e-beam divergence (sx’, sy’), • x-ray beam divergence (Dqw ), • energy spread (sg) and monochromator resolution, • aperture width and height, center offset, and • undulator distances • Magnetic field errors • Preliminary results show that the first harmonic edge is usable. Third harmonic edge may also be usable. • How to define effective K in the presence of error is not a trivial issue. I need to learn more to understand it (BXY). • Next we move on jitter simulations.

18. Jitters and Fluctuations • Bunch charge jitter • X-ray intensity is proportional to electron bunch charge (0.05% fluctuation). • Electron energy jitter • Location of the spectrum edge is very sensitive to e-beam energy change (10-5 noise): Dw/w = 2·Dg/g • Electron trajectory angle jitter • Trajectory angle (0.24 mrad jitter) directly changes grazing incidence angle of the crystal monochromator Damaging effect! Use simulation to assess impact.

19. Beamline Option 1: Poor man’s solution • One reference undulator • One flat crystal monochromator (asymmetrically cut preferred) • One flux intensity detector • One hard x-ray imaging detector • Beamline slits (get close to 100 mrad) Operation procedure for setting Keff • Pick one reference undulator (U33) and measure a full spectrum by scanning the crystal angle (angle aperture ~ 100 mrad) • Position the crystal angle at the mid-edge and record n-shot (n = 10 –100) data of the x-ray flux intensity (FREF) with electron energy, trajectory angle, and charge • Roll out reference undulator and roll in other undulator one at a time. • Set slits to 100 mrad or best available • Adjust x-position until the n-shot x-ray flux intensity data matches FREF. • Use the measured electron bunch data in real-time to correct for jitters

20. Measure fluctuating variables • Charge monitor: bunch charge • OTR screen / BPM at dispersive point: energy centroid • Hard x-ray imaging detector: electron trajectory angle (new proposal)

21. One Segment Simulation: Approach

22. Effect of electron energy “correlation” Define “Correlated Electron-Photon Energy” RMS error from simulation

23. Summary of 1-undulator simulations(charge normalized and energy-corrected) • Applying correction with electron charge, energy and trajectory angle data shot-by-shot greatly improves the quality of data analysis at the spectral edge. • Full spectrum measurement for one undulator segment (reference) • The minimum integration time to resolve effective-K changes is 10 – 100 shots with other undulator segment (data processing required) • As a bonus, the dispersion at the flag / BPM can be measured fairly accurately. • Not fully satisfied: • Rely heavily on correction calibration of the instrument • No buffer for “unknown-unknowns” • Non-Gaussian beam energy distribution ???

24. Beamline Option 2: Ultra-high Resolution • Reference Undulator (U33) • Period length and B-field same as other segments • Zero cant angle • Field characterized with high accuracy • Upstream corrector capable of 200 mrad steering (may be reduced if needed). • Broadband monochromator (DE/E ~ 0.03%) • Improves photon statistics • Suppress coherent intensity fluctuations • Big area, large dynamic range, uniform, linear detector • Hard x-ray imaging detector (trajectory angle)

25. Operation Procedures for setting Keff (BL2) • Steer the beam to be away from the axis in the reference undulator (U33) and measure a full spectrum by scanning the crystal angle (angle aperture ~ 100 mrad) • Position the crystal angle at the mid-edge • Roll in other undulator one at a time (test undulator). • Adjust the x-position of the test undulator until the x-ray intensities of the two undulator matches (difference < threshold). • Use the measured electron beam angle data in real-time to correct for angle jitters if necessary

26. Differential Measurements of Two Undulators • Insert only two segments in for the entire undulator. • Steer the e-beam to separate the x-rays Use one mono to pick the same x-ray energy Use two detectors to detect the x-ray flux separately Use differential electronics to get the difference in flux

27. Signal of Differential Measurements • Select x-ray energy at the edge (Point A). • Record difference in flux from two undulators. • Make histogram to analyze signal quality • Signals are statistically significant when peaks are distinctly resolved DK/K =  1.5  10-4

28. Summing multi-shots improves resolution • Summing difference signals over 64 bunches • Distinct peaks make it possible to calculate the difference DK at the level of 10-5. Example: Average improves resolution for DK/K =  10-5

29. Differential Measurement Recap • Use one reference undulator to test another undulator simulataneously • Set monochromator energy at the spectral edge • Measure the difference of the two undulator intensity Simulation gives approximately: • To get RMS error DK/K < 0.710-4, we need only a single shot (0.2 nC)! • We can use it to periodically to log minor magnetic field changes, for radiation damage. • Any other uses?

30. Other application of the techniques:Search for the neutral magnetic plane • Set the monochromator at mid-edge (Point A). • Insert only one test segment in. • Move the undulator segment up and down, or move electron beam up and down with a local bump. • When going through the plane of minimum field (neutral plane), the spectrum edge is highest in energy. Hence the photon flux peaks. • After the undulator is roughly positioned, taking turns to scan one end at a time, up and down, to level it.

31. Simulation of undulator vertical scan • Charge normalization only: ~ 20K shots / point • Charge-normalized and electron-energy corrected: ~ 512 shots / point • Differential measurements (two undulators): ~ 16 shots /point gives us RMS error ~ 1.0 mm ?!

32. Conclusion for Locating Magnetic Neutral Plane • Both techniques can be used to search the magnetic neutral plane, each has its own advantages and disadvantages: • Single undulator measurement (with charge-normalization and e-beam energy correction) can get required S/N ratio after averaging. • Differential measurement has best sensitivity, need shortest time (keep up with mechanical scan), but required more hardware. • Finite beam sizes and centroid offset (in undulator) shift spontaneous spectrum: the apparent K is given by

33. Summary (The Main Idea) • We propose to use angle-integrated spectra (through a large aperture, but radius < 1/g) for high-resolution measurements of undulator field. • Expected to be robust against undulator field errors and electron beam jitters. • Simulation shows that we have sufficient resolution to obtain DK/K <  10-4 using charge normalization. Correlation of undulator spectra and electron beam energy data further improves measurement quality. • A Differential technique with very high resolution was proposed: It is based on comparison of flux intensities from a test undulator with that from a reference undulator. • Within a perfect undulator approximation, the resolution is extremely high, DK/K =  3  10-6 or better. It is sufficient for XFEL applications. • It can also be used for routinely logging magnet degradation.

34. Summary (Continued) • Either beamline option can be used for searching for the effective neutral magnetic plane and for positioning undulator vertically. The simulation results are encouraging (resolution ~1 mm in theory for now, hope to get ~ 10 mm in reality). What’s next • Sources of error need to be further studied. Experimental tests need to be done. • More calculation and understanding of realistic field • Longitudinal wake field effect, • Experimental test in the APS 35ID • More?

35. Monochromator Recommendation • A dedicated monochromator for undulator measurement (low cost and robust, permanently installed). • Use it for DK/K measurements • Use it for regular vertical alignment check • Use it for routine magnetic field measurements at regular intervals (after routine BBA operation). • Logging magnetic field changes to see trend of damage, identify sources / mechanism for damage • Look for most damaged undulator segments for service for next shutdown • Location of the monochromator • Front end  easy to service. Too crowded? • In tunnel OK. • Differential measurement strongly recommended • But steering magnet can be added later as an upgrade. • Differential measurement saves time, improves accuracy. • Spectrometer will be easily justified by the science it supports.