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Sci Fi PerformanceSci Fi Performance

Malcolm EllisMalcolm Ellis

MICE Collaboration MeetingMICE Collaboration Meeting

Feburary 11Feburary 11thth 2005 2005

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OutlineOutline Reconstruction statusReconstruction status Data production since last collaboration Data production since last collaboration

meetingmeeting Miscellaneous studies:Miscellaneous studies:

Momentum resolution vs Magnetic FieldMomentum resolution vs Magnetic Field Helium gas versus VacuumHelium gas versus Vacuum

Emittance calculation and correctionEmittance calculation and correction Tracker performanceTracker performance

Resolution (X,PResolution (X,PXX, etc...), etc...) Transverse (4D) Emittance resolutionTransverse (4D) Emittance resolution Longitudinal (2D) Emittance resolutionLongitudinal (2D) Emittance resolution

ConclusionsConclusions

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Reconstruction StatusReconstruction Status Problems were found in the field map Problems were found in the field map

implemented since November meeting. For implemented since November meeting. For the moment, the field is still assumed to be the moment, the field is still assumed to be constant in the Reconstruction.constant in the Reconstruction.

Navigation bug in Kalman found and Navigation bug in Kalman found and temporary fix applied to remove error in temporary fix applied to remove error in calculation of MCS covariance matrix.calculation of MCS covariance matrix.

dE/dx model tuned, but still far from optimal.dE/dx model tuned, but still far from optimal. Results presented are from a stable, tested Results presented are from a stable, tested

version, but do not represent the ultimate version, but do not represent the ultimate physics performance possible, hence show physics performance possible, hence show the worst-case. Future improvements will the worst-case. Future improvements will likely improve the performance by a small likely improve the performance by a small amount.amount.

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Data ProductionData Production

One large and numerous smaller One large and numerous smaller productions run since November:productions run since November: 10 million events – matched beams (narrow P10 million events – matched beams (narrow PZZ) )

transverse emittance between 0.5 and 9.5 transverse emittance between 0.5 and 9.5 mm mm rad.rad.

1 million events – matched 2.5 1 million events – matched 2.5 mm rad beam, mm rad beam, with 510 ns and 25 MeV RMS longitudinally – with 510 ns and 25 MeV RMS longitudinally – used for tracker performance and longitudinal used for tracker performance and longitudinal emittance studies.emittance studies.

0.5 million events – various matched beams at 0.5 million events – various matched beams at different tracker solenoid fieldsdifferent tracker solenoid fields

~250k – studies for global PID and matching, He ~250k – studies for global PID and matching, He gas vs vacuum, varying physics processes to gas vs vacuum, varying physics processes to study pulls, etc...study pulls, etc...

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Momentum Resolution vs BMomentum Resolution vs B Prediction by John Cobb that for a matched Prediction by John Cobb that for a matched

beam, the resolution in P would go beam, the resolution in P would go approximately as 1/sqrt(B).approximately as 1/sqrt(B).

Two separate beams were simulated each Two separate beams were simulated each at 2T, 3T, 4T, 5T and 6T:at 2T, 3T, 4T, 5T and 6T: One beam matched for the particular field (red One beam matched for the particular field (red

points)points) Another beam that is matched at 4T (blue Another beam that is matched at 4T (blue

points).points). In both cases the beam is 2.5 In both cases the beam is 2.5 mm rad. mm rad.

Conclusion:Conclusion: No strong effect in PNo strong effect in PTT resolution, however P resolution, however PZZ

resolution does improve with increasing B...resolution does improve with increasing B...

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Beams vs BBeams vs B

Red points : beams matched to the particular magnetic field 2T, 3T, etc.Blue points : beams matched for 4T but simulated going through 2T, 3T, etc.

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Resolution vs BResolution vs B

Red points : beams matched to the particular magnetic field 2T, 3T, etc.Blue points : beams matched for 4T but simulated going through 2T, 3T, etc.

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Tracker Performance SpecificationTracker Performance Specification

In order to determine if a given tracker can In order to determine if a given tracker can measure the emittance with sufficient measure the emittance with sufficient precision, a figure of merit has been precision, a figure of merit has been determined based on the resolution of the determined based on the resolution of the tracker in each measured parameter and the tracker in each measured parameter and the RMS of the true parameter.RMS of the true parameter.

If, in the iIf, in the ithth variable, the RMS spread of the variable, the RMS spread of the beam is beam is ii

truetrue and the RMS resolution of the and the RMS resolution of the tracker is tracker is ii

resres. The RMS spread of the . The RMS spread of the measured distribution is then given by:measured distribution is then given by: 2res2true2meas

iii

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Specification continuedSpecification continued

The uncertainty in the measurement The uncertainty in the measurement causes a bias in the measured width causes a bias in the measured width of the beam.of the beam.

To estimate the size of this bias, the To estimate the size of this bias, the previous equation can be re-previous equation can be re-arranged, and using the binomial arranged, and using the binomial expansion:expansion:

2

true

res

21true

2

true

restruemeas 11

i

ii

i

iii

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Specification from BiasSpecification from Bias In order that the bias induced by the In order that the bias induced by the

measurement error be less than 1%, it follows measurement error be less than 1%, it follows that:that:

The figure of merit chosen, that the ratio The figure of merit chosen, that the ratio above be less than 10%, thus satisfies this above be less than 10%, thus satisfies this condition.condition.

In this analysis, correlations between In this analysis, correlations between measurement uncertainties and the measured measurement uncertainties and the measured values have been ignored as have correlations values have been ignored as have correlations between the measured parameters between the measured parameters themselves.themselves.

%147

1true

res

i

i

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Correcting the EmittanceCorrecting the Emittance A measurement of emittance will always be A measurement of emittance will always be

biased by the measurement error, the amount biased by the measurement error, the amount depending on the resolution of the tracker.depending on the resolution of the tracker.

In 2 x n dimensions, the true normalised In 2 x n dimensions, the true normalised emittance is given by:emittance is given by:

is the true covariance matrix of the 2n is the true covariance matrix of the 2n muon-beam phase-space parameters and muon-beam phase-space parameters and is the mass of the muon.is the mass of the muon.

The covariance matrix elements are given by:The covariance matrix elements are given by:

nnmNn V2 true

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2

true2nV

m

jjiiijn wwwwV true2

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Measurement ErrorMeasurement Error

The measured value mThe measured value mii of a true value w of a true value wii has the has the relation:relation:

Where Where ii is a small increment. is a small increment. The expression for VThe expression for Vtrue true can then be written in terms of can then be written in terms of

the measured parameters:the measured parameters:

The covariance matrix of the errors on the measured The covariance matrix of the errors on the measured track parameters can be defined:track parameters can be defined:

And the correlation matrix between the measured And the correlation matrix between the measured coordinates and the errors in the measurements:coordinates and the errors in the measurements:

VVtruetrue can then be written: can then be written:

iii mw

jjiijjiijjiijjiiijn mmmmmmmmV true2

jjiiijC

jjiiij mmR

CRRVV Tnn meas

2true2

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Transverse (4D) EmittanceTransverse (4D) Emittance

The transverse emittance The transverse emittance is determined from the four is determined from the four track parameters (X,Ptrack parameters (X,PXX,Y,P,Y,PYY).).

The resolution of the tracker as a The resolution of the tracker as a ratio of the RMS of the beam at ratio of the RMS of the beam at equillibrium (2.5 equillibrium (2.5 mm rad) is mm rad) is presented, followed by the results presented, followed by the results from the emittance calculation.from the emittance calculation.

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14 V

mN

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X PositionX Position

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Y PositionY Position

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X MomentumX Momentum

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Y MomentumY Momentum

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Transverse ResolutionTransverse Resolution

The difference between the resolution The difference between the resolution in X and Y momentum is partially due in X and Y momentum is partially due to the addition of the dE/dx correction to the addition of the dE/dx correction necessary for accurate reconstruction necessary for accurate reconstruction of the total momentum. This of the total momentum. This correction needs further work (hence correction needs further work (hence my earlier comment about this being my earlier comment about this being a “worst case” presentation).a “worst case” presentation).

All measured parameters are better All measured parameters are better than 14% RMS/RMS and only one is than 14% RMS/RMS and only one is (just) outside the 10% criteria.(just) outside the 10% criteria.

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Uncorrected 4D EmittanceUncorrected 4D Emittance

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Corrected 4D EmittanceCorrected 4D Emittance

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Cooling MeasurementCooling Measurement

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Longitudinal (2D) EmittanceLongitudinal (2D) Emittance

The longitudinal emittance The longitudinal emittance

is determined by the Energy measured in the is determined by the Energy measured in the tracker and the time from the TOF stations.tracker and the time from the TOF stations.

In the absence of a mature simulation and In the absence of a mature simulation and reconstruction of the TOF and matching to reconstruction of the TOF and matching to the SciFi tracker, the resolution in time at the SciFi tracker, the resolution in time at the tracker reference surface was varied the tracker reference surface was varied from 30 ps to 110 ps by smearing the Monte from 30 ps to 110 ps by smearing the Monte Carlo truth times with a gaussian Carlo truth times with a gaussian distribution.distribution.

Reminder: the longitudinal characteristics of Reminder: the longitudinal characteristics of the beam are the beam are E = 25 MeV and E = 25 MeV and t = 510 ps.t = 510 ps.

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12 V

mN

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EE

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Uncorrected Emittance: Uncorrected Emittance: t = 50 pst = 50 ps

Downstream Tracker – 50k Events per bin Upstream Tracker – 50k Events per bin

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Bias vs ResolutionBias vs Resolution

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Corrected Emittance: Corrected Emittance: t = 50 pst = 50 ps

Downstream Tracker – 50k Events per bin Upstream Tracker – 50k Events per bin

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Emittance Resolution vs Emittance Resolution vs tt

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Tracker Performance TableTracker Performance TableSimulation at Simulation at equillibrium equillibrium

emittance with emittance with

510 ps RMS in 510 ps RMS in time and 25 MeV time and 25 MeV

RMS in EnergyRMS in Energy

RMS of the Monte RMS of the Monte Carlo truth Carlo truth distributiondistribution

RMS of the RMS of the (Reconstructed – (Reconstructed –

Monte Carlo truth) Monte Carlo truth) distributiondistribution

Ratio of the RMS of Ratio of the RMS of the (Reconstructed the (Reconstructed

– truth) – truth) distribution to the distribution to the RMS of the Monte RMS of the Monte

Carlo truth Carlo truth distributiondistribution

RMS of the RMS of the (Reconstructed – (Reconstructed –

Monte Carlo truth) Monte Carlo truth) distribution if the distribution if the tracker volume tracker volume contains He gascontains He gas

XX 21.021.0 0.5430.543 2.58 %2.58 % 0.5420.542

YY 21.021.0 0.4420.442 2.10 %2.10 % 0.4400.440

PXPX 17.917.9 2.052.05 11.5 %11.5 % 2.052.05

PYPY 17.917.9 1.521.52 8.52 %8.52 % 1.521.52

EE 25.225.2 3.493.49 13.8 %13.8 % 3.483.48

PTPT 11.711.7 1.811.81 15.5 %15.5 % 1.8141.814

PZPZ 28.828.8 4.584.58 15.9 %15.9 % 4.604.60

X’X’ 0.09540.0954 0.01020.0102 10.7 %10.7 % 0.01020.0102

Y’Y’ 0.09530.0953 0.007350.00735 7.72 %7.72 % 0.007310.00731

T’T’ 0.05270.0527 0.009670.00967 18.3 %18.3 % 0.009820.00982

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He gas vs VacuumHe gas vs Vacuum

Simulation of tracker changed to replace Simulation of tracker changed to replace vacuum with 1 atm He.vacuum with 1 atm He.

Tracker performance compared with baseline Tracker performance compared with baseline case, results included in summary table.case, results included in summary table.

Conclusion: Conclusion: no significant difference in tracker performance.no significant difference in tracker performance.

Next steps:Next steps: What are the safety/engineering implications for What are the safety/engineering implications for

the rest of MICE?the rest of MICE? Review the implications for the tracker (the Review the implications for the tracker (the

tracker group will review this at the end of March tracker group will review this at the end of March in KEK).in KEK).

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SummarySummary RMS/RMS for parameters used in emittance RMS/RMS for parameters used in emittance

calculation (X,Pcalculation (X,PXX,Y,P,Y,PYY,E) is greater than 10% ,E) is greater than 10% in some cases, but less than 14%.in some cases, but less than 14%.

A correction procedure has been developed A correction procedure has been developed and shown to:and shown to: remove biasremove bias give resolution better than 0.1% for 200k eventsgive resolution better than 0.1% for 200k events

Issues:Issues: Understand use/resolution of TOFUnderstand use/resolution of TOF Derive correction matrices from “data” in MICE IIIDerive correction matrices from “data” in MICE III He vs VacuumHe vs Vacuum Study station spacingStudy station spacing

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ConclusionsConclusions

The tracker group feels that the The tracker group feels that the spirit (if not the exact letter) of spirit (if not the exact letter) of the tracker validation the tracker validation requirements have now been requirements have now been met.met.

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Tracker Performance Plots for Tracker Performance Plots for parameters not directly used in the parameters not directly used in the

emittance calculationsemittance calculations

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PPTT

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PPZZ

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X’X’

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Y’Y’

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T’T’