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)

AWLC14

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

AWLC14

Beam Time Status Beam Time Status

AWLC14

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

studiesAWLC14

AWLC14

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

AWLC14

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 %

AWLC14

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

AWLC14

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 %

AWLC14

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…

AWLC14

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

AWLC14 Range of recent Clinear

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

AWLC14

AWLC14

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

AWLC14

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

AWLC14 M is corrected almost back to nominal using extracted Δφ 　　

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　

AWLC14

AWLC14

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

AWLC14

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

AWLC14

AWLC14

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,

AWLC14

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

AWLC14

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”

AWLC14

　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

AWLC14

AWLC14

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

AWLC14

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

AWLC14

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

AWLC14

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 !!

AWLC14

#2

Rotate λ/2 plate angle [deg]

AWLC14

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

AWLC14

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 %

AWLC14 Range of recent Clinear

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

AWLC14

AWLC14

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

AWLC14

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

AWLC14

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)

AWLC14

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

AWLC14

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

AWLC14

AWLC14

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

AWLC14

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

AWLC14

AWLC14

　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)

AWLC14

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)

AWLC14

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

AWLC14

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

AWLC14

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

AWLC14