“Pinhole Measurement” Approach to K Measurements using Spontaneous Radiation

1. “Pinhole Measurement” Approach to K Measurements using Spontaneous Radiation November 14, 2005 J. Welch, R. Bionta, S. Reiche

2. Basic Scheme Basic Layout Slit width must be small to get clean signal. 2 mm shown. Useg #1 is worst case

3. Fundamental Measurements • Relative energy deviation of 1st harmonic photons • Relative energy deviation of electron beam

4. Derived Quantities • Electron beam angles x´, y´ • ∆K / K: the relative difference between a given segment K and that of a reference segment

5. Experimental Procedure to Measure K • All segments out, flatten orbit to “a few times BBA quality”. Need orbit angles less than 10 micro-radians to avoid scraping 1st harmonic SR on vacuum chamber. • Insert one segment, adjust slit width for constant angular size, scan slit position to minimize apparent ∆ K/K , energy jitter correction on. • Remove segment, repeat with different segment. The difference in K is calculated from the difference in measured ∆ K/K for the two segments.

6. Simulation Procedure • Set nominal values for reference and test segments and detector: (K’s, detector geometry, machine parameters) • Add random energy and beam orbit jitter • Calculate expected 1st harmonic photon energy averaged over detector geometry • Add random photon statistics noise, machine energy, and beam angle. • Calculate ∆K/K based on the noisy values. This becomes the “measured” value of ∆ K/K. • Repeat one shot at a time.

7. Flux Spectrum in Simulation • Shifted interference function at constant flux • Valid for 1st harmonic photons over + /- 10 micro-radian range

8. Spectrum Verification: Reiche/Ott Calculation • Essentially same agreement result for off axis radiation and radiation produced by detuned segments

9. Spectrum Verification: line outs • Reich/Ott photons from 8000-8500 eV, from -1 mm to 1 mm at 145 m from source. Y line out is very similar.

10. Geometry Effects • Effect of finite detector size and offset • u1(0) is the theoretical on-axis resonant photon energy.

11. ∆K/K Calculation • ∆K/K = beam energy term + photon energy term + geometry term Minimize Measure

12. Aligning the Pinhole Scan range + / - 1 mm X and Y Actual beam Axis 0.5, 0.5 • Simple 2D scan, one shot per data point, 0.1 mm steps, no multi-shot averaging • Error is added to geometry term. “Measured” Beam axis 0.33, 0.34

13. Photon statistics • Variance of mean photon energy due to photon statistics: • Need ~104 counts for 10-4 relative error in mean. • At minimum charge, there are at least 2 x 106 photons incident on 0.1 x 1 mm detector. • Error is added to ∆<u>/<u> term.

14. Simulated K Measurement

15. Simulation values used • Detector Model • Efficiency 1% • Energy Sensitivity ~1 eV / 8.275 keV • Size 0.1mm x 1.0 mm • Beam Model • Orbit jitter 25% sigma, position and angle • Energy jitter, 0.1%; energy uncertainty 3x10-5. • Beam size, 36 micron sigma, beta = 30 m. • Minimum charge, 0.2 nC. • Segment Model • Design values for K and positions, 113 periods

16. Detector Requirements • ∆<u>/<u> sensitivity ~ 1 x 10-4 • Energy window ~ 8000 - 8500 eV; enough to include the 1st harmonic bandwidth and beam energy jitter effect. • Precisely movable slits with adjustable width. • Scan range of a few mm, x,y. Slit width range 0 to a few mm. • Efficiency (counts per photon) ~ 1% or better.

17. Global Alignment Tool? • ∆ can be measured to better than 1 micro-radian with pinhole scan, globally! • x, y can then be integrated from slope, similar to method of autocollimator measurement for straightness.