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

2. Basic Layout Basic Scheme 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 1.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. 2.Insert one segment, adjust slit width for constant angular size, scan slit position to minimize apparent ∆ K/K, energy jitter correction on. 3.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 1.Set nominal values for reference and test segments and detector: (K’s, detector geometry, machine parameters) 2.Add random energy and beam orbit jitter 3.Calculate expected 1st harmonic photon energy averaged over detector geometry 4.Add random photon statistics noise, machine energy, and beam angle. 5.Calculate ∆K/K based on the noisy values. This becomes the “measured” value of ∆ K/K. 6.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 u 1 (0) is the theoretical on-axis resonant photon energy.

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

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

13. Photon statistics Variance of mean photon energy due to photon statistics: –Need ~10 4 counts for 10 -4 relative error in mean. –At minimum charge, there are at least 2 x 10 6 photons incident on 0.1 x 1 mm detector. Error is added to ∆ / 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 ∆ / 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.