2013/07/20
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Performance Evaluation of Shintake Monitor (IPBSM)
Americas Workshop on Linear Colliders 2014May 12-16, 2014Fermilab, IL, USA
12013/07/20
Jacqueline Yan, S. Komamiya, K. Kamiya ( The University of Tokyo )T.Okugi, T.Terunuma, T.Tauchi, K.Kubo (KEK)
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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 talkOutline of this talk
Recent Beam Recent Beam Time Status Time Status
IPBSM Performance IPBSM Performance EvaluationEvaluation Summary Summary
& Goals& Goals
IntroductionIntroduction
Signal Signal JittersJitters
• Systematic errors Systematic errors • Phase jitter studyPhase jitter study
real data analysis & simulationreal data analysis & simulation
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Beam Time Status Beam Time Status
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Spring Spring 20132013
10 consecutive scans @174°
M 〜 0.3 (S.D. 〜 7 %) σy 〜 65 nm
smaller after correct for phase jitter (?)
Best measurement stability 〜 5%
Stable contribution to e- beam focusing and studies (e.g. wakefield effects)
ICT : 0.5E9 Apr, 2014Apr, 2014
various hardware improvement to improve signal jitters/ drift
• Tune laser (profile & position/ timing stability)• detector • collimation
Dec 2013 – Mar 2014Dec 2013 – Mar 2014
• 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=10ICT : 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
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Consistency scans @174 deg mode
Again !! higher M and better stability
1st time: : 4/9 before knob tuning M = 0.29 +/- 0.04 ( S.D. ) : 15 % measurement stability ( σy = 66 +/- 4 nm (S.D)
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) )
3rd time: 4/17 (following week ): after linear/nonlinear knob tuningImproved orbit feedback and tuning knobs M =0.40 +/-0.03 (S/D. ) 7.3 % stability (σy = 57 +/- 2 nm (S.D) )
higher M and better stability
Preliminarybefore error correction
M > 0.4 reproduced at peaks of linear / nonlinear knob
ex) M : 0.3 0.45 after Y26 knob
(1) reinforcement of shielding (Pb and parafine) around detectors(2)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 IPuse 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
4/18, (30 deg )
4/11 (174 deg )
focal lens scan
-----Broad Rayleigh length 〜 4 mm
by IPBSM group@ATF2
Relaxed laser focusing
What contributed to stabilized measurements in Apr, 2014?
Changed lens setup on laser hut table reduced intensity bias in profile (Mar, 2014)
Before After: Rounder profile
laser tuning , filter exchange by Spectra Physics changed laser Q-SW trigger system improved buildup and timing stability
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comments
Laser pointing jitters(H relative position jitter)
• observed jitter (CCD) 5-10% of laser profile radius• derived “Δx” using laserwire scans : 5 〜 15% of laser radius
Phase jitter Δφ (V relative position jitter )
for Δφ = 0.5 rad , M = 0.5 : < 〜 10 %@ peak , < 〜 20%@mid
Laser power jitter < 10% from PIN-PD signal
Timing jitter 1 – 3 ns peak to peak, add < few % to signal jitters
statistical fluctuations not certain : could exceed 10% if detector not catching enough photons
Other minor factors
• BG fluctuation < 5 %, (?) recently, not important for recent high S/N
• e- beam intensity (ICT) monitor resolution
Few %
Change with beam condition
affected by collimator, detector, beam intensity
Potential Sources of Signal Jitters
observe overall sig jitter in fringe scan 〜 20-40% depend on phase drifts are hard to separate from jitters sometimes
Also a M reduction factor
Sum up ΔE/Eavg = 20 – 30 %
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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
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Apr, 2014: signal jitters reduced (?) but still an issue sometimes
30 deg174 deg
Compare θ dependence : jitters seem slightly more for 174 deg mode (?)
Efforts to improvement laser profile & reduce jitters
Laser pointing stability : 4/9 from Nav = 50 laserwire scan @174 deg
Δx / (laser spot radius) = 12 +/- 7 %
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Contribution from σx subtracted
Assuming Gaussian laserwire profile (but not always so)
ICT: 2E9
condition seems relatively stable (improved) in April 2014However signal jitters/drifts still remains an issue stability varies for different periods
174 deg, Apr vs Mar 2014
Drift of Fitted Initial Phase in 174 deg continuous scans ( 〜 30 min)
this drift is convolution may be from laser and/or beam
Relative RMS jitter ΔE/E(φ)
power jitter < ~ 10%
Note: due to sensor size < laser spot size, part of “vertical jitter” may be pointing jitter
Timing jitter : 2-3 ns peak to peak
Timing and Power StabilityPIN-PD @hut
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 tablebecome only a little oval, but much improved from 2013AWLC14
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…
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Fitted M
Fitting error
Range of recent Clinear
Effect of Vertical Jitters on fitted M
a few % systematic M reduction in typical ranges
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 %
Input : Nav=50, 174 deg , M0 = 0.636, Δφ=0, change 1 C factor at a time, keep others 0
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Simulation: Avg of 100 random seeds
相対誤差 は低い M0 ほど大きい
2: M reduction due to Cstat (statistical fluctuation)
small M0 : 4- 6 % error
large M0 : < 1 % error
1: sudden intensity decrease(drift) Vertical jitters
In this case, M over-evaluation
ex) 50% reduction
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
Depending on the condition, nonlinear fluctuations can cause both under & over evaluation of M
Examples of SIMULATION :observe rel. M error = (Mfit – Mexp) / Mexp
3: periodically oscillating jitters
few % M over-evaluation
100% 75% 50% 75% 100%
Weak dependence on Nav
X axis: Cstat
simulation
simulation
simulation
simulation
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Focusing on IPBSM Phase Jitter (Δφ)
Simulation Input conditions: σ0y = 40 nm, M0 = 0.64, 174 deg mode
study of systematic errors (M reduction factors)
Error source M reduction factor
phase jitter(V relative position jitter )
study using simulation and analyze actual data
Fringe tilt (z, t) Optimization by “tilt scan”
Laser polarization polarization measured optimize by “ λ / 2 plate scan ”
MisalignmentLaser profile
shot-by-shot non-Gaussian fluctuation of laser profile sometimes observe 10-20% M reduction
Phase drift Negligible during typical beam tuning if drift is linear and < 100 mrad/min maybe coupled with laser position drift / jitters, e- beam drift
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Details coming up
Systematic errors : M reduction Factor
σy over evalution
M under-evaluation
Priority is to resolve signal jitters / drifts ( enable precise evaluation of M reduction factors)
dominant
Before: fitted M After correction
Phase jitter ΔφPhase jitter Δφ(relative position jitter Δy) (relative position jitter Δy)
• Hard to separate phase jitter from e- beam jitter and vertical jitters
• conditions change over time
(example)(example) ifif Δφ = 400 mrad, Δφ = 400 mrad, CΔφ CΔφ 〜 〜 90.5 % 90.5 % σσy0y0 = 40 nm = 40 nm σ σy,meas y,meas = 44 nm= 44 nm
Δφ Δφ M reduction M reduction
M reduction from Δφ
Δφ [rad]
Horizontal jitters
Small σy* especially sensitive !!
we have developed a method for extracting Δφ
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simulation
Δφ [rad]
simulationM0 = 0.636σy0 = 40 nm
Mcorr = Mmeas / CΔφ
simulation
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
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 Δφ and 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
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 (?)
Potential Causes for phase jitterPointing stability: angular/ pos jitter when injecting into half-mirror, mirror vibrationselectron beam jitter (ΔΦ is convolution of laser and e beam) c.f. Fringe scan piezo jitter is checked : not an issue at present
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Study of IPBSM Phase Jitter
Tested Method using Simulation
Input conditions:
σ0y = 40 nm, M0 = 0.64, 174 deg mode
test Δφ extraction precision using simulation
fix {M,φ0, Eavg, Cconst, Cstat} to jitter plot
signal jitter vs phase
STEP1: generate fringe scan try to assume “realistic” ATF2 conditions
fringe scan
vertical jitter
Jitter from Δφ
Model
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Signal energy vs phase
Input vertical jitters
input: σy0 = 40 nm, 174°mode Δφ = 0.7 mrad , 24.5 % vertical jitter
simulation
simulation
Δφ input
Δφ , Clinear (2 free parameters) fixed parameters: M, φ0, Eavg : from STEP 1 Cconst, Cstat: estimated (slight uncertainties are negligible)
STEP2: extract Δφ from fitting
Rms spread is larger for a smaller Nav
Nav = 20 vs Nav = 50
SimulationAvg and rms of 100 random seeds
In typical Δφ region (0.4-0.7 rad)Δφ error < 〜 3% 1% error for M
[2] Distribution of extracted phase jitter X: seed number Y: extracted Δφ
• error < 〜 7% for single scan • better if average over multiple
scans
large Nav scans are preferred for Δφ study
Assume a “relaistic” ATF2 conditionInput: M0 = 0.64, σy0 = 40 nm, 174 deg mode, Nav=50, Clinear = 0.25,Cstat = 0.10, Cconst = 0.05, Δφ = 0. 590 rad
Simulation
[1] Precision of extracted phase jitter X: input ΔΦY: extracted Δφ
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Mean : 1.77 +/- 0.035
Δφ_real RMS = 0.448 rad
data read out in 3 Hz (0.33 sec) intervals
Reproduced Δφ measured using phase monitor by T. Yamanaka in 2009 (beam off , old IPBSM laser)
Δφreal RMS = 0.448 radConsistent with Yamanaka-M thesis
Δφrms (real) = 0.448 rad
1. Input “Δφ_real” into fringe scan simulation
2. 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)
avg and rms of 100 random seeds
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
Extracted results for ΔΦ
Input: M0 = 0.64, σy0 = 40 nm, 174 deg Clinear = 0.25, Cconst = 0.05,
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Analysis of Δφ from real data
Phase Jitter
@ 174 deg
Using Nav=50
scans
example: 4/10
4/10 : Δφ=0.85 +/- 0.06 rad Clinear = 0.15 +/- 0.03
4/17 : Δφ=0.67 +/- 0.04 rad Clinear = 0.11 +/- 0.03
M plot
RMS jitter plot
Decrease in Δφ reflect improvement of orbit stability (feedback) ?? AWLC14
History of Phase Jitter in 2014
Mar 2014
Jan – Feb, 2014
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Apr, 2014, 30 deg
Apri, 2014
2-8 , 30 ° mode : generally Δφ = 200 - 600 mrad regardless of vertical jitters 174 ° mode: generally Δφ = 600 – 850 mrad
174 ° : σy, meas < 65 nm
-- 2-8° , 30 ° : larger σy --
RECENT
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 ??
phase jitter Δφ relative position jitter Δy Convolution of laser and e beam : difficult to separate at present
We won’t know unless we have independent measurement of e- beam jitter !! anticipate results from IPBPM
174 deg Mmeas(174)0.29 +/-0.01 σmeas = 66+/- 1 nm
Ctot(174) > 0.66
Mcorr 0.44 +/-0.02
30 deg Mmeas(30) 0.77+/-0.01 σmeas = 81+/- 2 nm
Mexp 0.82+/-0.01
Ctot,exp 0.93+/-0.01
---------------- ----------------
Ctot(30) >0.94
using data immediately before / after mode switching (174 30°)
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 before etc……
total M reduction compared to 174 °results
Ctot, exp and Ctot(30) consistent , almost no residual M reduction ??!!
from Δφ (dominant) and alignment
M reduction derived independently using 30 deg data onlyfrom Δφ and alignment
Dedicated study of “fringe Contrast” = total M reduction factor “ Ctot”
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σcorr = 54+/- 1 nm
stable measurement and offline error study of IPBSM must go hand in hand in order to achieve ATF’s Goal 1SummarySummary
< 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 more stable performance after reduction of signal jitters / drifts by Terunuma-san and Okugi-san 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
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PlansPlans 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 σywill 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
BACKUP SLIDES
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N +
N -
[rad]
[rad]
N: no. of Compton photonsConvolution between e- beam profile and fringe intensity
Focused Beam : large M
Dilluted Beam : small M
Small σy
Large σy
29
Detector measures signal Modulation Depth “M” measurable range
determined by fringe pitch
depend on crossing angle θ (and λ )
)2/sin(2
ykd
M
d
kNN
NN
y
yy
)cos(ln2
2
)(2exp)cos( 2
M
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Crossing angle θ
174° 30° 8° 2°
Fringe pitch 266 nm 1.03 μm 3.81 μm 15.2 μm
Lower limit 20 nm 70 nm 170 nm 700 nm
Upper limit 90 nm 340 nm 1.3 μm 5.2 μm
)2/sin(2
ykd
M
dy
)cos(ln2
2
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σσyy and M and M for each θ modefor each θ mode
select appropriate mode according to beam focusing
Measures σy* = 20 nm 〜 few μm with < 10% resolution
Expected PerformanceExpected Performance
almost no M reduction due to polarization
Polarization MeasurementPolarization Measurement
P contamination : Pp/Ps < 1.5 %
Set-up
IPBSM optics designed for linear S polarization
Also measured “half mirror” reflective properties
Rs = 50.3 %, Rp = 20.1 % match catalogue value
half mirror
power ratio
confirmed “S peaks” maximize M
Beamtime : “ λ/2 plate scan
S peaks” also yields best power balance between 2 paths !!
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#2
Rotate λ/2 plate angle [deg]
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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
0 deg: S peak
45 deg: P peak
90 deg: S peak
pitch roll
Ex) if ΔΦ = 3 mrad, 〜 7 nm to σy (for σy0=60 nm)
Change in Status of IPBSM Signal Jitters /Drifts X: fringe scan phase Y: relative signal jitter = (rms jitter) / (energy) at each phase
174 deg mode data, Apr vs Mar 2014
30 deg mode data, Apr vs Mar 2014
However signal jitters/drifts still remains an issue stability varies for different periods
Drift of Fitted Initial Phase During 174 deg mode continuous scans ( 〜 30 min)
this drift is convolution may be from laser and/or beam
condition seems relatively stable (improved) in April 2014
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Fitted M
Fitting error
Range of recent Clinear
Effect of Vertical Jitters on fitted M
a few % systematic M reduction in typical ranges
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 %
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Simulation: Avg of 100 random seeds
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
M reduction due to phase jitter x: axis: input Δφ (0 – 0.9 rad ) y axis: fitted M
Nav = 10 has bias
small Nav shows larger bias Should take Nav > 50 data for “final” measurementsif evaluate syst error using extracted Δφ
Simulation: Mean & RMS (S.D.) of 100 random seeds
M reduction due to Δφ
Avg and rms of 100 random seeds
Systematic from vertical jitters
worse systematics for very small Δφ because dominated by vertical jitters
Input : M0 = 0.636, Nav=10, 174 deg mode,Cconst = 0.05, Cstat=0.15, Clinear=0.25
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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
Apr 9, 2014 Mar 11, 2014
Looking at fringe scans (Nav=10,20,50)
2/5 – 2/6 , 2014
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2/6/ 201430 deg
2/20 / 2014 6.9, 30 deg, Nav-50
2/27/2014 5.3 deg 2/25/ 2014
5.3 deg
overall signal jitter in 2-8 deg, 30 deg deg mode for Cherenkov
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Systematics on Mmeas, CstatNav=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=50Nav=20
Fitted M
Range of recent Clinear
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
Mistaken evaluation of ΔφInput Δφ = 0
If Cstat < 20%, : < 100 mrad pushed to Δφ
Change Cstat (Cconst = 0.05, Clinear = 0.25)
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average and rms/sqrt(100) of 100 random seedsinput: M0 = 0.64, σy0 = 40 nm, 174 deg mode, Nav=20, Clinear = 0.25,Cstat = 0.10, Cconst = 0.05, Δφ = 0. 588 rad
Fitted Modulation
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
Try to imitate oscillating jitters M plot
RMS jitter plot to get Δφ
25% decrease
25% decrease
50% decrease
Few % systematics
weak dependence on Nav
M expected
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Assume Comp. signal intensity suddenly decrease @ 7 – 17 rad (drift ?) Include 2 valleys , jump range < 〜 4π
Input : M0 = 0.636, Nav=10, 174 deg mode,Δφ = 470 mrad, Clinear = 0.3, Cstat = 0.1, Cconst = 0.05
Simulation :100 random seeds
Over evaluation of M in this particular case
Actually we can tell from the large chi^2 / ndf ??
Fitted M, Nav=10
Fitted M, Nav=50
M expected from ΔφSudden decreaseE’ / E = 0.5
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input: M0 = 0.64, σy0 = 40 nm, 174 deg mode, Nav=20, Clinear = 0.25, Cconst = 0.05, Δφ = 0. 588 rad
If fix Cstat as real (input) Cstat
average and rms/sqrt(100) of 100 random seeds
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 Δφreal (input) Cstat is 0.07
Δφ is over-evaluated if fixed Cstat is too small 0.07 even if real (input) Cstat is larger
Δφ extraction precision looks good
average and rms/sqrt(100) of 100 random seedsinput: M0 = 0.64, σy0 = 40 nm, 174 deg mode, Nav=20, Clinear = 0.25,Cstat = 0.10, Cconst = 0.05, Δφ = 0. 588 rad
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
Try to imitate oscillating jitters
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Extracted Δφ
Extracted Clinear
Δφ extraction not much affected in this particular case (?)
Clinear is over-evaluated
Beam intensity about 0.5E9
Signal trend: Cherenkov (top) vs CsI (bottom) , during Zscan
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
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actual data (blue)Nav = 20 fringe scan(Mar 11 2014) @ 174 deg mode
RMS signal jitter (green)
vsEnergy at each phase
Sig jitter due to phase jitter (red) is larger at fringe mid point and smaller at fringe peak(compare with bottom plot)
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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
Reproduced CH1 dataRead out in 3 Hz (0.33 sec) intervals
Δφmeasured by T. Yamanaka in 2009Using phase monitor (beam off , old laser)
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input: M0 = 0.64, σy0 = 40 nm, 174 deg mode, Nav=20, Clinear = 0.25, Cconst = 0.05, Δφ = 0. 588 rad
If fix Cstat as real (input) Cstat
average and rms/sqrt(100) of 100 random seeds
Clinear is under-evaluated if fix too large CstatClinear is over-evaluated if Cstat is fixed to a too small 0.07 even if real (input) Cstat is larger
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Very large & consistent M,meas before switching to 30 deg M reduction studies
Nav=5
Nav=10
Nav=10
Nav=50
summary of consistency scan140220_221459
data M Δφ Clinear Nav221459 0.925 5221736 0.842 0.35 0.23 10222119 0.925 0.27 0.23 10222459 0.842 0.42 0.26 50 Avg 0.88 0.35 0.24 ERR=STD/sqrt(N-1) 0.03 0.05 0.01
summary of consistency scan140220_221459
data M Δφ Clinear Nav
35100 0.761 0.549 0.17 50
40832 0.848 0.34 0.22 50
41849 0.776 0.51 0.17 50
Avg 0.80 0.47 0.19
ERR=STD/sqrt(N-1) 0.03 0.08 0.02
2/20 , 6.9 deg , M = 0.88 /- 0.03
2/27 5.3 deg , M = 0.80 /- 0.03
All are Nav=50
ΔφNav = 10
ClinearNav = 100
ClinearNav = 10
ΔφNav = 100
Simulation test : Mean & RMS (S.D.) of 100 random seeds
Little systematics on fitted center value RMS increase for large Δφ and small Nav
Input Clinear = 0.23
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Proposal by Kubo-san on more accurate fitting function for signal jitters
before, I used just E = Eavg*(1+ M*cos(φ+φ0))
Vertical jitters
Signal jitter due to phase jitter
Convolution of phase jitter and vertical jitters
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