1 / 50

2013/07/20

Performance Evaluation of Shintake Monitor (IPBSM) Americas Workshop on Linear Colliders 2014 May 12-16, 2014 Fermilab, IL, USA. Jacqueline Yan , S. Komamiya, K. Kamiya （ The University of Tokyo ） T.Okugi, T.Terunuma, T.Tauchi, K.Kubo (KEK). 2013/07/20. 1.

jericho-nen
Download Presentation

2013/07/20

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Performance Evaluation of Shintake Monitor (IPBSM)Americas Workshop on Linear Colliders 2014May 12-16, 2014Fermilab, IL, USA Jacqueline Yan, S. Komamiya, K. Kamiya （The University of Tokyo） T.Okugi, T.Terunuma, T.Tauchi, K.Kubo (KEK) AWLC14 2013/07/20 1

  2. IPBSM error study is essential for achieving ATF2 Goal 1 ! At the same time, reducing signal jitters/ drifts is important for both stable measurement of σy < 40 nm and error studies Outline of this talk Introduction IPBSM Performance Evaluation Summary & Goals Recent Beam Time Status Signal Jitters • Systematic errors • Phase jitter study real data analysis & simulation AWLC14

  3. Beam Time Status AWLC14

  4. Stable contribution to e- beam focusing and studies (e.g. wakefield effects) Spring 2013 • various hardware improvement to improve signal jitters/ drift • Tune laser (profile & position/ timing stability) • detector • collimation Dec 2013 – Mar 2014 Best measurement stability 〜 5% 10 consecutive scans @174° M〜0.3 (S.D.〜7 %)  σy 〜 65 nm smaller after correct for phase jitter (?) Apr, 2014 ICT : 0.5E9 • Observed improvement in signal fluctuation •  enabled effective linear / nonlinear knob tuning at 174 deg mode • observed effect from e- beam stabilization • (improvement of orbit feedback and tuning knobs) 4/17／2014, Nav=10 ICT : 0.5E9 • early Apr : Consistent measurement of M > 0.3 • mid-Apr: Consistent measurement of M > 0.35 • (σy < 61 nm) ( see next page) • High M measured at 2-8 deg , 30 deg mode • dedicated data taking for IPBSM systematic error studies AWLC14

  5. Consistency scans @174 deg mode 2nd time: 4/10 (～14 hrs later ）：　 after all linear/nonlinear knobs M =0.34 +/-0.02 (S/D. ) 7.2 % stability (σy = 62 +/- 2 nm (S.D) ) 1st time: ： 4/9 before knob tuning M = 0.29 +/- 0.04 （S.D.） : 15 % measurement stability 　（σy = 66 +/- 4 nm (S.D) Preliminary before error correction higher M and better stability M > 0.4 reproduced at peaks of linear / nonlinear knob Again !! higher M and better stability 3rd time: 4/17 (following week）：　 after linear/nonlinear knob tuning Improved orbit feedback and tuning knobs M =0.40 +/-0.03 (S/D. ) 7.3 % stability (σy = 57 +/- 2 nm (S.D) ) ex) M :0.3  0.45 after Y26 knob AWLC14

  6. What contributed to stabilized measurements in Apr, 2014? by IPBSM group@ATF2 • (1) reinforcement of shielding (Pb and parafine) around detectors • Stabilization of electron beam improved tuning multiknobs, orbit feedback showed effect in Apr run • (3) speed up DAQ software: 1 Hz  3 Hz : reduced effect from drifts (?) • (4) Improved laser profile  Reduce pointing jitter at IP • use iris on laser table to clip fluctuating outer parts of profile (round profile preserved) • Adjust reducer lens setup to reduce multi-component in profile & relax laser focusing Changed lens setup on laser hut table  reduced intensity bias in profile (Mar, 2014) 4/18, (30 deg ) After: Rounder profile Before Relaxed laser focusing focal lens scan 4/11 (174 deg ) • laser tuning , filter exchange by Spectra Physics • changed laser Q-SW trigger system •  improved buildup and timing stability ----- Broad Rayleigh length 〜 4 mm AWLC14

  7. Potential Sources of Signal Jitters Change with beam condition Also a M reduction factor affected by collimator, detector, beam intensity Sum up  ΔE/Eavg = 20 – 30 % observe overall sig jitter in fringe scan 〜 20-40% depend on phase drifts are hard to separate from jitters sometimes AWLC14

  8. Previous Issues with signal jitter/ drifts & laser profile (〜Mar 2014) • Oscillating Compton signal jitters (period〜few min) • pointing jitters seem related to complex internal structure of laser profile at IP • non-Gaussian multi- components from Okugi-san ‘s weekly meeting slides fringe scan Efforts to improvement laser profile & reduce jitters Apr, 2014: signal jitters reduced (?) but still an issue sometimes 174 deg 30 deg Compare θ dependence : jitters seem slightly more for 174 deg mode (?) AWLC14

  9. condition seems relatively stable (improved) in April 2014 However signal jitters/drifts still remains an issuestability varies for different periods Relative RMS jitter ΔE/E(φ) Drift of Fitted Initial Phase in 174 deg continuous scans (〜 30 min) this drift is convolution may be from laser and/or beam 174 deg, Apr vs Mar 2014 Δx / (laser spot radius) = 12 +/- 7 % Laser pointing stability : 4/9 from Nav = 50 laserwire scan @174 deg Contribution from σx subtracted ICT: 2E9 AWLC14 Assuming Gaussian laserwire profile (but not always so)

  10. Timing and Power Stability PIN-PD @hut Note: due to sensor size < laser spot size, part of “vertical jitter” may be pointing jitter power jitter < ～ 10% Timing jitter : 2-3 ns peak to peak Power and Profile Measurements (4/25-30) • Measured spot size and profile •  Parallel propagation until final lenses • balanced profiles between U and L paths • Before transport: 2 X original by expander • After transport : 0.75 X original after reducer • Measured laser power at various locations • power balance (U/L path)〜 95% (174 deg mode) • loss in transport (laser hut  IP) < 7% • laser table • round profile • hot intensity spots evened out transport to vertical table become only a little oval, but much improved from 2013 AWLC14

  11. Study Effect of Vertical Jitters by Simulation • [1] assume Gaussian vertical jitters • modeled by “C factors” • [2] nonlinear instabilities • sudden jumps, drifts, oscillating jitters, etc… AWLC14

  12. Effect of Vertical Jitters on fitted M a few % systematic M reduction in typical ranges Fitted M Input : Nav=50, 174 deg , M0 = 0.636, Δφ=0, change 1 C factor at a time, keep others 0 Simulation: Avg of 100 random seeds Range of recent Clinear Fitting error Effect of Vertical jitters on relative M fitting error (ΔMfit / Mfit) ΔMstat /M < 2 % in typical ranges c.f. real data is affected by all jitter sources together  ΔMstat/M 〜 few % AWLC14 Range of recent Clinear

  13. 1: sudden intensity decrease(drift) Vertical jitters ex) 50% reduction 2: M reduction due to Cstat (statistical fluctuation) In this case, M over-evaluation 相対誤差は低いM0ほど大きい simulation simulation large M0 : < 1 % error Depending on the condition, nonlinear fluctuations can cause both under & over evaluation of M Examples of SIMULATION :observe rel. M error = (Mfit – Mexp) / Mexp small M0 : 4- 6% error 3: periodically oscillating jitters 100% 75%  50%  75%  100% X axis: Cstat simulation few % M over-evaluation Input: M0 = 0.64, σy0 = 40 nm, 174 deg mode, Nav=20, Clinear = 0.25,Cstat = 0.10, Cconst = 0.05, Δφ = 0. 588 rad simulation AWLC14 Weak dependence on Nav

  14. study of systematic errors (M reduction factors) Focusing on IPBSM Phase Jitter (Δφ) Simulation Input conditions: σ0y = 40 nm, M0 = 0.64, 174 deg mode AWLC14

  15. Systematic errors： M reduction Factor M under-evaluation σy over evalution Priority is to resolve signal jitters / drifts ( enable precise evaluation of M reduction factors) dominant Details coming up AWLC14

  16. Phase jitter Δφ (relative position jitter Δy) Δφ  M reduction Small σy* especially sensitive !! Horizontal jitters (example) ifΔφ = 400 mrad, CΔφ 〜 90.5 % σy0 = 40 nm  σy,meas = 44 nm • Hard to separate phase jitter from e- beam jitter and vertical jitters • conditions change over time we have developed a method for extracting Δφ Mcorr = Mmeas / CΔφ M reduction from Δφ simulation M0 = 0.636 σy0 = 40 nm simulation Before: fitted M After correction simulation Δφ [rad] Δφ [rad] M is corrected almost back to nominal using extracted Δφ AWLC14 16

  17. Study of Systematic errors of measured Modulation • for now , take into account : • phase jitter Δφ DOMINANT (?) extracted from fringe scan (details coming up) • alignment issues (position, profile) from laserwire scan / zscan / pointing jitter analysis • Potential Causes for phase jitter • Pointing stability: angular/ pos jitter when injecting into half-mirror, mirror vibrations • electron beam jitter (ΔΦ is convolution of laser and e beam) • c.f. Fringe scan piezo jitter is checked : not an issue at present • Results from recent 174 deg continuous scans (preliminary , need confirmation) • Apr 9-10 : about 10 nm systematic error on σy • Apr 17 : < 〜 10 nm systematic error on σy errors reduced due to improved beam stability (?) • Important to demonstrate reliability of Δφ extraction method • demonstrated acceptable precision under certain “realistic” (?) conditions • (see past slides for LCWS & ATF2 project Meeting) • tested limit of “unknown factors” using simulation • limitations from model which assumes Gaussian distr. of Δφand vertical jitters • effect from nonlinear instabilities , drifts & jumps • coupling from other instability sources • tested method by inputted real measured phase jitters into simulation • Dedicated beam time data for study of Δφ was analyzed AWLC14

  18. Study of IPBSM Phase Jitter Tested Method using Simulation Input conditions: σ0y = 40 nm, M0 = 0.64, 174 deg mode AWLC14

  19. testΔφ extraction precision using simulation STEP1: generate fringe scan try to assume “realistic” ATF2 conditions Signal energy vs phase fringe scan Δφ input Input vertical jitters simulation STEP2: extract Δφfrom fitting fix {M,φ0, Eavg, Cconst, Cstat} to jitter plot signal jitter vs phase Model Jitter from Δφ vertical jitter simulation • Δφ , Clinear (2 free parameters) • fixed parameters: • M, φ0, Eavg : from STEP 1 • Cconst, Cstat: estimated (slight uncertainties are negligible) input: σy0 = 40 nm, 174°mode Δφ = 0.7 mrad , 24.5 % vertical jitter AWLC14

  20. [1] Precision of extracted phase jitter X: input ΔΦ Y: extracted Δφ Simulation Avg and rms of 100 random seeds In typical Δφ region (0.4-0.7 rad) Δφ error <〜3%  1% error for M Nav = 20 vsNav = 50 large Nav scans are preferred for Δφ study Rms spread is larger fora smaller Nav Simulation [2] Distribution of extracted phase jitter X: seed number Y: extracted Δφ • error <〜 7% for single scan • better if average over multiple scans Assume a “relaistic” ATF2 condition Input: M0 = 0.64, σy0 = 40 nm, 174 deg mode, Nav=50, Clinear = 0.25,Cstat = 0.10, Cconst = 0.05, Δφ = 0. 590 rad AWLC14

  21. Reproduced Δφ measured using phase monitor by T. Yamanaka in 2009 (beam off , old IPBSM laser) Δφreal RMS = 0.448 rad Consistent with Yamanaka-M thesis Mean : 1.77 +/- 0.035 Δφ_real RMS = 0.448 rad data read out in 3 Hz (0.33 sec) intervals Extracted results for ΔΦ avg and rms of 100 random seeds • Input “Δφ_real” into fringe scan simulation • used my method to extract Δφ_out • Extracted results: • Δφ_out = 0.45 +/- 0.06 (rms) • close to Δφ_real RMS • OK even if move large jitters to beginning of scan • next, inputted “slow linear drift “ • OK if drift < 150 mrad/ min (similar to real drift) • precision worsen if bigger drift (> 240 mrad/min) Δφrms (real) = 0.448 rad Input: M0 = 0.64, σy0 = 40 nm, 174 deg Clinear = 0.25, Cconst = 0.05, OK even if Cstat gets large • M_meas is affected by nonlinear drifts, may be reduced more than expected from a Gaussian Δφ • Effect depends on location / length of drift : too complicated to model AWLC14

  22. Analysis of Δφ from real data AWLC14

  23. 4/17 : Δφ=0.67 +/- 0.04 rad Clinear = 0.11 +/- 0.03 4/10 : Δφ=0.85 +/- 0.06 rad Clinear = 0.15 +/- 0.03 example: 4/10 Phase Jitter @ 174 deg Using Nav=50 scans M plot Decrease in Δφ reflect improvement of orbit stability (feedback) ?? RMS jitter plot AWLC14

  24. History of Phase Jitter in 2014 phase jitter Δφ  relative position jitter Δy Convolution of laser and e beam : difficult to separate at present 174 °： σy, meas < 65 nm Mar 2014 Apri, 2014 Jan – Feb, 2014 RECENT Apr, 2014, 30 deg -- 2-8° , 30 ° : larger σy -- Δφ very different for 30 deg and 174 deg Δy / σymeas similar for 30 and 174 deg (50-60%) Indicate e beam jitter is dominant ?? 2-8 , 30 ° mode： generally Δφ = 200 - 600 mrad regardless of vertical jitters 174 ° mode: generally Δφ= 600 – 850 mrad We won’t know unless we have independent measurement of e- beam jitter !! anticipate results from IPBPM AWLC14

  25. Dedicated study of “fringe Contrast” = total M reduction factor “ Ctot” using data immediately before / after mode switching (174  30°) from Δφ (dominant) and alignment  σcorr = 54+/- 1 nm total M reduction compared to 174 °results M reduction derived independently using 30 deg data only from Δφ and alignment Ctot, exp and Ctot(30) consistent , almost no residual M reduction ??!! • Difference in ΔΦ maybe due to : • Effect of laser pointing jitter : path length after 50% beamsplitter is longer for 174 °than 30 ° • Effect of electron beam jitter • Characteristics of data taken in Apr 2014: • stability and jitters improved in Apr, 2014 that’s why this study is possible !! • total M reduction for 30 °, (esp Δφ) is less than beforeetc…… AWLC14

  26. Summary < Status > • multiple sets of continuous scans ＠174° in Apr, 2013 • M〜0.3 before multiknob tuning @174° • effective implementation of linear/non-linear knobs reproducibility of M > 0.4 • e.g. 4/17 : 11 scans M = 0.40 +/- 0.03 (S.D.) 〜 7 % measurement stability • more stable performance after reduction of signal jitters / drifts by Terunuma-san and Okugi-san • σy measurement status also reflects improvement of e- beam stabilization and tuning methods • < error studies> • Dedicated beam time for IPBSM systematic error studies • preliminary analysis conducted (reliability of method need confirmation ) • Phase jitter ΔΦ may be dominant M reduction factor , 〜10 nm systematic error(?) to σy@174° • Δφ show some θ dependence  maybe explained by laser pointing jitters and e beam jitter • simulation study on effect of vertical jitters, jumps, oscillating jitters stable measurement and offline error study of IPBSM must go hand in hand in order to achieve ATF’s Goal 1 AWLC14

  27. Plans • Continue to identify and suppress sources for jitters / drifts • essential for ATF2 Goal 1 • Personal tasks: • analyze data to evaluate effect of hardware upgrades • Use simulation to study the effect on Mmeas and error analysis precision from various instabilities • Improve precision of error analysis • Final Goal: evaluate precise systematic error for measured σy • will be summarized in J.Y’s D thesis (〜Jan 2015) • based on σy measurement @ 174° in Apr 9-17 • study of jitters/ drifts and M reduction factors (simulation & real data analysis) • TIPP2014 (Jun 2-6) : talk on IPBSM performance • peer-reviewed proceedings will be published by Proceedings of Science (〜6/20) • will quote beam size results from Kubo-san’s IPAC proceedings This priority should be achieved for precise M reduction evaluation AWLC14

  28. BACKUP SLIDES AWLC14

  29. Focused Beam ： large M N + Small σy N - [rad] N: no. of Compton photons Convolution between e- beam profile and fringe intensity Dilluted Beam ： small M Large σy [rad] 29 Detector measures signal Modulation Depth “M” measurable range determined by fringe pitch depend on crossing angle θ (and λ )　 AWLC14

  30. Expected Performance Measures σy* = 20 nm 〜few μm with < 10% resolution σy and M for each θ mode select appropriate mode according to beam focusing AWLC14

  31. #2 IPBSM optics designed for linear S polarization Polarization Measurement Set-up P contamination : Pp/Ps < 1.5 % power ratio Beamtime ： “λ/2 plate scan almost no M reduction due to polarization Also measured “half mirror” reflective properties Rs = 50.3 %, Rp = 20.1 %  match catalogue value half mirror Rotate λ/2 plate angle [deg] S peaks” also yields best power balance between 2 paths !! confirmed “S peaks” maximize M AWLC14

  32. Other IPBSM Data “tilt scan” confirm (almost) no M reduction from relative tilt between fringe and beam tilt scan takes very long time (few hrs) effected by rifts not sure if this represent condition at time of actual beam size measurement should not have been much M reduction due to fringe tilt pitch roll 0 deg: S peak 90 deg: S peak Ex) if ΔΦ = 3 mrad, 〜7 nm to σy (for σy0=60 nm) 45 deg: P peak AWLC14

  33. Change in Status of IPBSM Signal Jitters /Drifts X: fringe scan phase Y: relative signal jitter = (rms jitter) / (energy) at each phase condition seems relatively stable (improved) in April 2014 174 deg mode data, Apr vs Mar 2014 30 deg mode data, Apr vs Mar 2014 Drift of Fitted Initial Phase During 174 deg mode continuous scans (〜 30 min) However signal jitters/drifts still remains an issue stability varies for different periods this drift is convolution may be from laser and/or beam AWLC14

  34. Effect of Vertical Jitters on fitted M a few % systematic M reduction in typical ranges Fitted M Input : Nav=50, 174 deg , M0 = 0.636, Δφ=0, change 1 C factor at a time, keep others to default : Cconst = 0.05, Cstat = 0.15,Clinear= 0.25 Simulation: Avg of 100 random seeds Range of recent Clinear Fitting error Effect of Vertical jitters on relative M fitting error (ΔMfit / Mfit) ΔMstat /M < 2.5 % in typical ranges c.f. real data is affected by all jitter sources together  ΔMstat/M 〜 few % AWLC14 Range of recent Clinear

  35. M reduction due to phase jitter x: axis: input Δφ (0 – 0.9 rad ) y axis: fitted M small Nav shows larger bias Should take Nav > 50 data for “final” measurements if evaluate syst error using extracted Δφ M reduction due to Δφ Systematic from vertical jitters Nav = 10 has bias worse systematics for very small Δφ because dominated by vertical jitters Avg and rms of 100 random seeds Input : M0 = 0.636, Nav=10, 174 deg mode, Cconst = 0.05, Cstat=0.15, Clinear=0.25 AWLC14 Simulation: Mean & RMS (S.D.) of 100 random seeds

  36. Apr 9, 2014 Mar 11, 2014 compare relative signal jitter of Apr 9, 2014 with Mar 2014 (blue) Recent condition at least as stable as last year Mar 2013 (??) many setups have changed within this year AWLC14

  37. 2/27/2014 5.3 deg 2/25/ 2014 5.3 deg Looking at fringe scans (Nav=10,20,50) 2/5 – 2/6 , 2014 overall signal jitter in 2-8 deg, 30 deg deg mode for Cherenkov 2/20 / 2014 6.9, 30 deg, Nav-50 2/6/ 2014 30 deg AWLC14

  38. Systematics on Mmeas, Cstat Nav=20, 50 Δφ = 0 effect is slightly stronger for smaller Nav 〜 5 % systematics from vertical jitters (under-evaluation) Change Cstat (Cconst = 0.05, Clinear = 0.25) Nav=50 Nav=20 Fitted M Effect of Clinear on fitted M < 5 % systematic M reduction expected from Clinear Input : 100 random seeds, Nav=10, 174 deg mode, M0 = 0.636, Cconst = 0.05, Cstat = 0.1, Δφ = 470 mrad Range of recent Clinear AWLC14

  39. Mistaken evaluation of Δφ Input Δφ = 0 Change Cstat (Cconst = 0.05, Clinear = 0.25) If Cstat < 20%, : < 100 mrad pushed to Δφ AWLC14

  40. Try to imitate oscillating jitters M plot Jitter period 〜 few min  close to length of fringe scan type 1: light case: normal  85%  65%  85%  normal type 2: heavy case: normal  75%  50%  75%  normal 25% decrease 25% decrease Fitted Modulation 50% decrease Few % systematics weak dependence on Nav RMS jitter plot to get Δφ M expected average and rms/sqrt(100) of 100 random seeds input: M0 = 0.64, σy0 = 40 nm, 174 deg mode, Nav=20, Clinear = 0.25,Cstat = 0.10, Cconst = 0.05, Δφ = 0. 588 rad AWLC14

  41. Assume Comp. signal intensity suddenly decrease @ 7 – 17 rad (drift ?) Include 2 valleys , jump range < 〜 4π Fitted M, Nav=50 Fitted M, Nav=10 Over evaluation of M in this particular case Actually we can tell from the large chi^2 / ndf ?? M expected from Δφ Sudden decrease E’ / E = 0.5 Simulation :100 random seeds Input : M0 = 0.636, Nav=10, 174 deg mode, Δφ = 470 mrad, Clinear = 0.3, Cstat = 0.1, Cconst = 0.05 AWLC14

  42. If fix Cstat as real (input) Cstat Δφ extraction precision looks good average and rms/sqrt(100) of 100 random seeds input: M0 = 0.64, σy0 = 40 nm, 174 deg mode, Nav=20, Clinear = 0.25, Cconst = 0.05, Δφ = 0. 588 rad Δφ is over-evaluated if fixed Cstat is too small 0.07 even if real (input) Cstat is larger Δφ is under-evaluated if fix too large Cstat ex) if real Cstat is 0.15, but Cstat fixed to 0.07, about 10% over-evaluation of Δφ real (input) Cstat is 0.07 AWLC14

  43. Try to imitate oscillating jitters Extracted Δφ Jitter period 〜 few min  close to length of fringe scan type 1: light case: normal  85%  65%  85%  normal type 2: heavy case: normal  75%  50%  75%  normal Δφ extraction not much affected in this particular case (?) Extracted Clinear average and rms/sqrt(100) of 100 random seeds input: M0 = 0.64, σy0 = 40 nm, 174 deg mode, Nav=20, Clinear = 0.25,Cstat = 0.10, Cconst = 0.05, Δφ = 0. 588 rad Clinear is over-evaluated AWLC14

  44. Signal trend: Cherenkov (top) vsCsI (bottom) , during Zscan Beam intensity about 0.5E9 • At low beam intensity, smaller jitter for CsI than Cherenkov • Cherenkov mainly dominated by statistic errors i.e. Amount of Compton signal • - better fitting and smaller ΔMsyst for CsI , esp for smaller M at 174 deg mode AWLC14

  45. actual data (blue) Nav = 20 fringe scan(Mar 11 2014) @ 174 deg mode Sig jitter due to phase jitter (red) is larger at fringe mid point and smaller at fringe peak (compare with bottom plot) RMS signal jitter (green) vs Energy at each phase AWLC14

  46. Include slow linear drift over long time scale Input : M0 = 0.64, σy0 = 40 nm, 174 deg Clinear = 0.25 , Cstat = 0.15 , Cconst = 0.05 Δφmeasured by T. Yamanaka in 2009 Using phase monitor (beam off , old laser) Reproduced CH1 data Read out in 3 Hz (0.33 sec) intervals AWLC14

  47. If fix Cstat as real (input) Cstat average and rms/sqrt(100) of 100 random seeds input: M0 = 0.64, σy0 = 40 nm, 174 deg mode, Nav=20, Clinear = 0.25, Cconst = 0.05, Δφ = 0. 588 rad Clinear is over-evaluated if Cstat is fixed to a too small 0.07 even if real (input) Cstat is larger Clinear is under-evaluated if fix too large Cstat AWLC14

  48. Very large & consistent M,meas before switching to 30 deg M reduction studies Nav=5 Nav=50 Nav=10 2/20 , 6.9 deg , M = 0.88 /- 0.03 Nav=10 All are Nav=50 2/27 5.3 deg , M = 0.80 /- 0.03 AWLC14

  49. Simulation test : Mean & RMS (S.D.) of 100 random seeds Δφ Nav = 10 Δφ Nav = 100 Little systematics on fitted center value RMS increase for large Δφ and small Nav Clinear Nav = 10 Clinear Nav = 100 Input Clinear = 0.23 AWLC14

  50. Proposal by Kubo-san on more accurate fitting function for signal jitters Convolution of phase jitter and vertical jitters Signal jitter due to phase jitter Vertical jitters before, I used just E = Eavg*(1+ M*cos(φ+φ0)) AWLC14

More Related