1. Analysis of ATF EXT/FF Orbit Jitter and extrapolation to IP (Data of 2014.11.18) ATF2 Project Meeting 2015. 2 K. Kubo

2. Data taking Data taken in November 18 (2014) swing shift. After IP beam size tuning, observing modulation with IPBSM 174 degree mode. (10x1 optics) – Positions of the BPM reference cavity and OTR2 chanber were optimized. Data of EXT/FF BPM are saved with several conditions. (See Log Note) This report used data of – One file (2000 pulses) with bunch intensity intentionally changed by hand. – 3 files (1000 pulses), each is for fixed bunch intensity setting. (N~8.5E9, 4.9E9, 1.8E9)

3. BPM reading vs, pulse number (MQD10BFF: Large beta_y) In horizontal, drift is larger compare with pulse to pulse jitter. In vertical, pulse to pulse jitter is more significant. (It may be only in this particular case. (?))

4. Analysis using SVD W: Diagonal matrix of singular values U_ij represents amplitude of mode j in pulse i V_kl represents response of monitor l to mode k pulse monitor (Average is subtracted for each monitor) (Data far from average (>5-sigma) removed. BPM noise, etc.)

5. Result of SVD: First 4 modes vs. BPM x,y Circles: amplitude at each BPM, Lines: Fitting by injection orbit + dispersion (model) Dispersion

6. Result of SVD: other 2 modes vs. BPM x,y Intensity dependence Only seen in data with large intensity change y position at IP phase

7. Standard deviation at each BPM in EXT/FF (not from SVD) Horizontal: ~20% of beam size (emittance 2 nm assumed) Vertical: ~40% of beam size (emittance 12 pm assumed) (High intensity N~8.5E9)

8. Effect to IP position of some first modes -1 3 Different intensities (about 1000 pulses for each) – All BPMs used for fitting ModeVertical Jitter propagation to IP (nm) N~8.5E9N~4.9E9N~1.8E9 13.912.517.3 216.69.47.1 31.14.42.0 86.17.36.6 40.50.80.1 Total of mode 1 - 1018.117.920.3 No intensity dependence.

9. Effect to IP position of some first 10 modes -2 Compared Using All BPMs Using only downstream BPMs Used BPMVertical Jitter propagation to IP (nm) N changedN~8.5E9N~4.9E9N~1.8E9 All19.918.117.920.3 From QD10AFF1272125810981139 From QF7FF1000974863882 Extrapolated to IP Too large jitter using downstream BPMs only  check waist shift (May be from optics error???)

10. Fitted orbit around IP (s=0) s (m) Y (microm) s (m) Y (microm) All BPMs used BPM from MQD10AFF used There is waist shift. (Note different scales)

11. Effect to position at waist of first 10 modes Using All BPMs Using only downstream BPMs Used BPMVertical Jitter propagation to IP (nm) N changedN~8.5E9N~4.9E9N~1.8E9 All8.56.49.18.0 From QD10AFF233283184183 From QF7FF251213208210 Extrapolated to waist (not exactly IP) Still large using BPMs only in downstream region

12. Simulation of SVD analysis Create sets of EXT-FF BPM data – Orbit jitter is given At the beginning of the extraction line (injection error) Or position jitter of QD10BFF magnet Or position jitter of All Q-magnets – Beam position at every BPM is calculated by SAD – BPM resolution assumed 1 micron, or 100 nm for cavity BPMs 10 micron for stlipline BPMs Apply the same analysis program for the real data. – Look at evaluated (extrapolated) y position jitter at IP by SVD – Compare with “real” jitter at IP

13. Simulation result of SVD analysis -1 injection jitter Evaluated jitter (all BPMs used) vs. Real jitter at IP Real jitter was changed by changing amplitude of injection jitter. Evaluated jitter include 10 SVD modes Good resolution for injection jitter, using all BPMs Resolution CavBPM: 1 um Stlipline: 10 um

14. Simulation result of SVD analysis -2 jitter induced at QD10BFF Evaluated jitter vs. Real jitter at IP “Real” jitter amplitude was changed by changing position jitter amplitude of QD10BFF. Evaluated jitter include 10 SVD modes 6 cases of used BPMs (and resolution) Use All BPMs from QD10AFF (1 um and 100 nm) from QF7FF (1 um and 100 nm) Good estimation using BPMs downstream of jitter source only 100 nm BPM resolution: good estimation 1 um BPM resolution: over estimate jitter at IP by several x 10 nm.

15. Simulation result of SVD analysis -3 jitter induced at all Quads Evaluated jitter vs. Real jitter at IP “Real” jitter amplitude was changed by changing position jitter amplitude of all Quads in EXT-FF. Evaluated jitter include 10 SVD modes Use All BPMs and use from MQD10AFF CavBPM resolution 100 nm and 1 um Always underestimate jitter at IP Bad BPM resolution makes estimated jitter large

16. Fitted jitter depends on BPM resolution jitter induced at all Quads BPM resolution about 5 um may explain the large fitted jitter using BPMs in downstream part of FF line only. (about 200 nm at waist)

17. Extrapolated position jitter at IP About 20 nm (RMS) vertical jitter at IP using all BPMs (57% of beam size) Using BPMs in downstream part of FF line only, large extrapolated position jitter (about 1 um at IP, 200 nm at waist) – Orbit jitter induced in FF line so large? (But measured beam size was ~60nm a few hours before these data taken.) – Or, misunderstood BPM data, or assumed wrong optics in FF,,,,,,? Simulations were performed to check the analysis. – If BPMs downstream of jitter source are used, the analysis can reproduce jitter at IP. – Including BPMs upstream of jitter source, the analysis tends to underestimate jitter at IP. (This is reasonable.) – Bad BPM resolution overestimate jitter at IP (This is reasonable too.) 200 nm jitter from the analysis of the experimental data may be explained if BPM resolution is about 5 um. But it seems too large. No clear conclusion on jitter induced in the beam line

18. NOTE: BPMs in downstream FF line is not so sensitive to Position-at-IP phase orbit Using IPBPM will be probably necessary for reliable estimation of orbit difference induced in the FF line.

19. SUMMARY Data of EXT/FF BPM taken in November 18 (2014) swing shift were analyzed using Singular Value Decomposition method. Vertical jitter at FF line BPMs (angle-at-IP phase) is a bout 40% of beam size. Position jitter at IP (or waist) estimated extrapolating orbits calculated from SVD modes. – About 20 nm jitter from injection (or from upstream part of EXT) jitter. – No intensity dependence. – Estimation of jitter induced in FF beam line was tried without any clear results. With more data, better optics information and careful BPM calibration, some improved results may be possible. But, Using IPBPM is simple for reliable estimation of position jitter at IP.