1. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 Undulator Effective-K Measurements Using Angle-Integrated Spontaneous Radiation Bingxin Yang and Roger Dejus Advanced Photon Source Argonne National Lab

2. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 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 K eff with required accuracy  K/K~1.5×10 -4 Sep. 22, 2004: SLAC Commissioning workshop –Bingxin Yang: K eff 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: K eff 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  m Regular observation can monitor systematic changes in undulators –Jim Welch:

3. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 Hope for this workshop Form a consensus –Spontaneous spectral measurements can be used to measure K eff with required accuracy (  K/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. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 Features of the spontaneous spectrum and effect of beam quality: numerical calculations Average properties: e-beam divergence (  x’,  y’ ), x-ray beam divergence (   ), and energy spread (   ) 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 Outline

5. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 Spontaneous Radiation Spectrum

6. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 Angle-integrated? How large is the aperture! Pinhole (sinc) < << Angle-integrated (numeric) BXY: Large enough for the edge feature to be stable

7. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 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  K/K simulations B. X. Yang, “High-resolution undulator measurements Using angle-integrated spontaneous radiation,” PAC’05 Related publications

8. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 How large is the aperture! FEL-relevant Capture the radiation cone: 2.35 – 5 rms radius  17 – 37  rad Measured radiation spectrum is more important that calculated from field data!

9. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 Marking the location of a spectral edge We will watch how the following property changes: HALF PEAK PHOTON ENERGY

10. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 Effects of Aperture Change (Size and Center) Plot the half-peak photon energy vs. aperture size Edge position stable for 25 – 140  rad  100  rad best operation point Independent of aperture size  Independent of aperture center position

11. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 Effects of Aperture Change (Source distance) Calculate flux through an aperture satisfying: ≤ 100  rad ≤ allowed by chamber ID Plot half-peak photon energy Rectangular aperture reduces variation

12. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 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 (    ~ 0.1% or 8 eV) Photon beam divergence      rad Electron beam divergence  y’  rad

13. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 Effect of Finite Energy Resolution Edge position moves with increasing energy spread

14. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 Effects of Undulator Field Errors Electron beam parameters E = 13.640 GeV  x = 37  m  x’ = 1.2  rad    = 0.03% Detector Aperture 80  rad (H) 48  rad (V) Monte Carlo integration for 10 K particle histories.

15. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 Comparison of Perfect and Real Undulator Spectra Filename: LCL02272.ver; scaled by 0.968441 to make K eff = 3.4996 First harmonic spectrum changes little at the edge.

16. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 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. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 The following beam qualities are not problems for measuring spectrum edge: e-beam divergence (  x’,  y’ ), x-ray beam divergence (   ), energy spread (   ) 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. Summary of calculations so far

18. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 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):  = 2·  Electron trajectory angle jitter Trajectory angle (0.24  rad jitter) directly changes grazing incidence angle of the crystal monochromator Jitters and Fluctuation s Damaging effect! Use simulation to assess impact.

19. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 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  rad) Operation procedure for setting K eff Pick one reference undulator (U33) and measure a full spectrum by scanning the crystal angle (angle aperture ~ 100  rad) Position the crystal angle at the mid-edge and record n-shot (n = 10 – 100) data of the x-ray flux intensity (F REF ) with electron energy, trajectory angle, and charge Roll out reference undulator and roll in other undulator one at a time. Set slits to 100  rad or best available Adjust x-position until the n-shot x-ray flux intensity data matches F REF. Use the measured electron bunch data in real-time to correct for jitters

20. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 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. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 One Segment Simulation: Approach

22. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 Effect of electron energy “correlation” Define “Correlated Electron-Photon Energy” RMS error from simulation

23. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 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. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 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  rad steering (may be reduced if needed). Broadband monochromator (  E/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. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 Operation Procedures for setting K eff (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  rad) 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. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 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. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 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  K/K =  1.5  10 -4

28. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 Summing multi-shots improves resolution Summing difference signals over 64 bunches Distinct peaks make it possible to calculate the difference  K at the level of 10 -5. Example: Average improves resolution for  K/K =  10 -5

29. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 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  K/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. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 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. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 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  m ?!

32. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 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. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 Summary (The Main Idea) We propose to use angle-integrated spectra (through a large aperture, but radius < 1/  ) 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  K/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,  K/K =  3  10 -6 or better. It is sufficient for XFEL applications. It can also be used for routinely logging magnet degradation.

34. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 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  m in theory for now, hope to get ~ 10  m 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. Bingxin Yang Large aperture spectrum measurementsbxyang@aps.anl.gov Beam-based undulator measurement workshop, Nov. 14, 2005 Monochromator Recommendation A dedicated monochromator for undulator measurement (low cost and robust, permanently installed). Use it for  K/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.