R(t) Relations from inclusive MDT tubes drift time distributions

1
R(t) Relationsfrom inclusive MDT tubes drift
time distributions

• M. Barone
• Software and Analysis Meeting
• ATLAS/Frascati

2
Outline

• Introduction
• Nomenclature
• The idea
• The recipe
• Garfield simulation
• Drift velocity
• r distribution
• r(t) determination
• Arrival time distribution
• R(t) relation
• Data time spectrum t0 determination
• Results
• Residual
• Conclusions

3
Nomenclature
muon track

• Assumption
• Uniform illumination of drift tube with tracks
• Definitions
• Rthr Distance traveled by the 25th ionization
  electron (under the assumption that the signal
  threshold is reached by the 25th e-)
• R Distance of minimum approach of the track to
  the sensing wire
• r generic distance of a point from the sensing
  wire
• Dy average distance of the 25th e- origin
  from the point of closest approach

Rthr
Dy
R
r

• Goal
• Associate the arrival time of the 25th e- to
  the tracks distance of minimum approach (R) ?
  determine the R(t) relation

4
R(t) relation determination the idea

• R(t) relation is expected to be non-linear, due
  to the Ar/CO2 gas mixture and to the radial
  electric field

• Drift velocity is not constant as a function of
  R v (E (R) )
• In principle the distribution of the tracks with
  respect to R is flat, but
• Cluster fluctuations
• Charge fluctuations
• ?-rays
• Inefficiency at the borders
• need to be included.
• Possible method to define the R(t) relation
• We know the time distribution (from data)
• We can use the simulation to determine the R
  distribution

correct R distribution
time spectrum from data


R(t) relation
5
R(t) relation determination Recipe

• Even though Garfield does not reproduce with
  adequate precision the drift velocity, it allows
  to determine thecorrect Rthr distribution on an
  event-by-event basis, independent on the gas
  mixture (hypothesis to be verified)
• Integrating over many tracks produced in an
  interval ?R, all possible effects (d-rays,
  position of production of the 25th e- -Rthr,
  charge fluctuations, etc.) are averaged.
• Recipe
• Get the r(t) distribution from MC this is the
  distance r at which an e- needs to be created in
  order to reach the sensing wire at time t.
• Obtain from MC the arrival time of the 25th e-
  for each simulated track.
• Use the r(t) function to obtain a distribution
  of Rthr in the MC corresponding to the previous
  simulated arrival times.

Garfield drift velocity for a given gas mixture
Garfield time spectrum


correct Rthr distribution
6
Garfield gas mixture

• Garfield-Magboltz used to calculate properties of
  three different gas-mixture
• Ar 93 , CO2 7 (standard mixture)
  ? GAS_MIX_1
• GAS_MIX_1 100ppm H20
  ? GAS_MIX_2
• Ar 93.25, CO2 6.75 100ppm H20
  ? GAS_MIX_3
• Use of 100 ppm content of water vapor suggested
  by previous studies
• (ATL-COM-MUON-2003-035)

7
Garfield Drift velocity determination v(E)

• Determination of the drift velocity starting from
  given values of the electric field E (V/cm)

E field
v_drift (E)
Magboltz
v_drift vs E
cm/ms
GAS_MIX_1

• Does not require tracking

V/cm
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Garfield Drift velocity determination v(r)
1) Each value of E(V/cm) corresponds to a value
of r (cm) ? Drift velocity as a function of r can
be automatically determined
E field
r
v_drift vs r
v_drift (r)
cm/ms
GAS_MIX_2
GAS_MIX_3
cm
9
Garfield r(t) determination
2) Using the v(r) function we can calculate the
drift time by integration
3) t (r) can be inverted to obtain r(t)
10
Garfield Arrival time distribution
MC GAS_MIX_2

• Signal simulation
• 146000 tracks
• t00 is the time given by the primary muon
• Signal simulation parameters

global volt 3080global gain 20000 global nelec
25global thr1 -50.E-06nelecglobal ENC
4200global peak 0.23 global noisigma
ENCpeak1.609e-7global tau0.025 ..............
.... convolute-signals transfer-function
(1-t/(2tau))(t/tau)exp(-t/tau)
The recorded time t is the arrival time of the
25th electron for each track
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Garfield Rthr distribution

• Rthr distribution can be determined from the time
  spectrum and the r(t) relation obtained for a
  given gas mixture

MC GAS_MIX_2


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Garfield Rthr distribution, check

• Hypothesis Rthr distributions should be the
  same for different gas mixture
• (verified simulating 14600 tracks for each gas
  mixture)

Yes!
MC GAS_MIX_1
MC GAS_MIX_2
MC GAS_MIX_3
Rthr (cm)
13
Test beam data time spectrum
data run 1559 BIL2, ml1

• Translate horizontally MC time spectrum to
  superimpose it with the data histo
• Register the value of the shift t0 585
  counts
• Register the value of tmax
• tmax 1520 counts

Garfield
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Test beam data time spectrum
tmin 0 tmax 925 counts
15
R(t) relation determination
MC
1) Divide the Rmax-Rmin interval in 100 bins,
each one containing an equal number of events
Nevents(MC)/nbins 1442.66
1) Divide the tmax-tmin interval in 100 bins,
each one containing an equal number of events
Nevents(data)/nbins 1962.24
Nevents (data) 196224 nbins 100 max_content
Nevents/nbins 1962.24
Nevents (MC) 144266 nbins 100 max_content
Nevents/nbins 1442.66
2) Use the extreme of all these intervals do
define Rthr values transform Rthr into R by
quadratically subtracting the average Dy (see
figure on slide 3)
2) Use the extreme of all these intervals do
define TDC values
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R(t) relation result
4) The relationship between the corresponding
values provide us with the R(t) relation we were
looking
Garfield data
Garfield
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Residuals for run 1559
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Check
1) divide the MC sample of 146000 drift times in
two independent sub-samples containing 73000
events each MC1, MC2
2) use MC1 sample to determine Rthr distribution
MC1


MC1
3) use MC2 sample and Rthr distribution from MC1
sample to determine r(t) relation
MC2


MC1
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Check
4) compare the r(t) relation with the relation
obtained by Garfield using sample MC1
50 micron
Garfield (MC1) MC2
Garfield (MC1)

• Mean -0.7E-02
• RMS 0.2E-01

n 100 bins
Delta r (mm)
20
Conclusions

• A method for the determination of R(t)
  relations has been proposed.
• Benefits
• a lot of available statistics
• R(t) relation can be determined for each tube
• no dependence on the tracking method
• very fast method

• Work in progress
• use of clean TDC spectra
• analysis of more runs
• MC more statistics
• comparison with other R(t) relations (Calib, )
• Understand and quantify the limit of this method
  (by tracking, )
• ..