High-Resolution Measurements of Effective K Using Spontaneous Undulator Radiation

1. High-Resolution Effective K MeasurementsUsing Spontaneous Undulator Radiation Bingxin Yang Advanced Photon Source Argonne National Lab

2. Two Essential Elements for Far-Field Measurements (Adapted from x-ray diagnostics planning meeting, Feb. 2004, SLAC) • Roll away undulators Spontaneous radiation is most useful when background is clean, with each undulator rolled in individually. • Adequate Far-field X-ray Diagnostics extracts the beam / undulator information • Electron trajectory inside the undulator (mm / mrad accuracy) • Undulator K-value (DK/K ~ 1.5 × 10-4) • Relative phase of undulators (Df ~ 10°) • X-ray intensity measurements (DE/E ~ 0.1%, z-dependent) • Micro-bunching measurements (z-dependent)

3. Scope Relative measurements of undulator effective K using far-field spontaneous radiation (8 keV, 40 m to 60 m from undulator exit). Bonus: Wide bandwidth monochromator for z-dependent x-ray intensity measurement (DE/E ~ 0.1%). • Introduction: A simple feature of the spontaneous spectrum • Effect of beam quality: emittance, energy spread… • Simulated experiments (DK/K ~ 10-6?!) • Key components • Final remarks (conditional conclusion) Contents

4. Main Tools • Analytical work (back of an envelope) • Numerical simulations (MathCAD) • Undulator Radiation Modeling (XOP) • Angle integrated spectra: XOP/XUS • Undulator radiation intensity profile: XOP/XURGENT • Reference: M. Sanchez del Rio and R. J. Dejus "XOP: Recent Developments," SPIE proceedings Vol. 3448, pp.340-345, 1998.

5. Spontaneous Radiation Spectrum

6. A Closer Look at the Spectral Edge • Monitor the edge of angle-integrated spectrum • Shifts DE/E ~ – 2DK/K. • 50 – 100 data points, 5 – 15 minutes to acquire a spectrum! • Monitor the intensity at fundamental photon energy • Change DF/F ~ 400 DK/K  < 6% intensity change needed • Takes 1 – 2 seconds to acquire data?

7. Impact of Aperture Change (Size and Center) • Lower energy photons come in larger angles. • Spectra independent ofaperture size / location as long as the beam is fully contained. • Spectra independent of emittance for adequate aperture.

8. Impact of Finite Energy Resolution • Electron beam energy spread (0.06% RMS) • X-ray energy spread = 25 eV FWHM • Monochromator resolution (DE/E ~ 0.1% or 8 eV) Small effect on 70-eV wide edge!

9. Impact of Electron Bunch Charge Fluctuation Impact of Electron Energy Jitter • X-ray intensity is proportional to electron bunch charge. Current monitor data (20% fluctuation) can be used to normalize the x-ray intensity data. • Location of the spectrum edge is very sensitive to e-beam energy change (0.1% jitter): Dw/w = 2·Dg/g Most damaging instrument effect!

10. A Simulation: Input and Approach

11. A look at the output intensity jitter Intensity distribution depends strongly on photon energy!

12. Effect of multi-shots integration An acceptable spectrum needs integration of 256 – 1024 shots, resulting scan time = 7 – 18 minutes @ 120 Hz.

13. Summary of One-Undulator Simulations • Intensity noise (jitter) at the spectrum edge is largely due to electron beam energy jitter. • With sufficient integration time, the measured spectrum is accurate enough to resolve effective K change at a level of DK/K ~ 1.5 × 10-4. • Average will take longer if LINAC jitter has time structure. • A faster and more accurate technique is desirable.

14. Electricity 101 • DV/V ~ 0.001, DI/I ~ 0.001, R = 3.50xxx? • Compare two passive devices: (R-R0)/R ~ I

15. Differential Measurements of Two Undulators • Insert only two segments in for the entire undulator. • Kick 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

16. Differential Measurements: Signal • 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

17. Summing multi-shots improves resolution • Summing difference signals over 64 bunches (0.5 sec.) • 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

18. Simulation II Recap • Use one perfect reference undulator to test another perfect undulator (two Perfect Periodic Undulators) • Set monochromator energy at the spectral edge • Accumulate difference count from the two undulators for ~64 bunches (0.5 second). The signal is statistically significant in resolving undulators with DK/K =  3  10-6 Is it still meaningful? Can we detect minor radiation damage?

19. Key Component: Reference Undulator • Last segment in the undulator • Period length and B-field same as other segments • Zero cant angle • Field characterized with high accuracy • Upstream corrector capable of 400 mrad kicks.

20. Key Component: Monochromator • Large acceptance aperture (30 mm  15 mm) • Wide bandwidth (DE/E = 0.1%) • Asymmetrically cut Ge(111) crystals (2 – 8 keV) • Multilayer reflectors (0.8 – 2.5 keV) • Low power only • Large dynamic range detector(s) • Low noise amplifier and 16-bit digitizers

21. Asymmetrically Cut Ge(111)

22. Final Remarks • We proposed a differential measurement technique for effective K. It is based on comparison of angle-integrated flux intensity from a test undulator with that from a reference undulator. • Within the perfect undulator approximation, its potential resolution, DK/K =  3  10-6 or better, is sufficient for LCLS applications. • It is essential to have remotely controlled roll away undulators for this technique to be practical. • For not so perfect undulators, we need to extend the definition of Keff, or define a new figure of merit. The limitation of this proposed technique will need to be re-examined in that context.