r(t) relations from inclusive mdt tubes drift time distributions

LNF, 19 March 2004 1

R(t) Relations

from inclusive MDT tubes drift time distributions

M. Barone

Software and Analysis Meeting

ATLAS/Frascati

LNF, 19 March 2004 M. Barone 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


Nomenclature 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 y = average distance of the “25th e-” origin from the

point of closest approach

Rthr

R

y

r

Goal Associate the arrival time of the “25th e-” to the track’s distance of minimum approach (R) determine the R(t) relation

Goal Associate the arrival time of the “25th e-” to the track’s distance of minimum approach (R) determine the R(t) relation

muon track


R(t) relation determination: the idea

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

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

“correct”

R distribution+

time spectrum from data = R(t) relation


R(t) relation determination: Recipe

Even though Garfield does not reproduce with adequate precision the drift velocity, it allows to determine the“correct” 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 (-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

time spectrum+

Garfield drift velocity for a given gas mixture

= “correct” Rthr distribution


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)


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)

v_drift vs Ev_drift vs E

GAS_MIX_1GAS_MIX_1

Does not require tracking

Magboltz

cm/

s

V/cm


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

v_drift (r)

r

v_drift vs rv_drift vs r

GAS_MIX_2

GAS_MIX_3

cm

cm/

s


Garfield: r(t) determination

2) Using the v(r) function we can calculate the drift time by integration

)(rv

drt

3) t (r) can be inverted to obtain r(t)


Garfield: Arrival time distribution

MC: GAS_MIX_2MC: GAS_MIX_2

Signal simulation: 146000 tracks t0=0 is the time given by the primary muon Signal simulation parameters:

The recorded time t is the arrival time of the 25th electron for each trackThe recorded time t is the arrival time of the 25th electron for each track

global volt= 3080global gain= 20000global nelec = 25global thr1 = -50.E-06*nelecglobal ENC = 4200global peak = 0.23global noisigma = ENC*peak*1.609e-7global tau=0.025

..................

convolute-signals transfer-function …(1-t/(2*tau))*(t/tau)*exp(-t/tau)


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_2MC: GAS_MIX_2

+ =


Garfield: Rthr distribution, check




Rthr (cm)

Hypothesis: Rthr distributions should be the same for different gas mixture

(verified simulating 14600 tracks for each gas mixture)

Yes!


Test beam data: time spectrum

Garfield

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


Test beam data: time spectrum

tmin = 0

tmax = 925 counts

tmin = 0

tmax = 925 counts


DATA MC

Nevents (data) = 196224nbins = 100max_content = Nevents/nbins = 1962.24

Nevents (MC) = 144266nbins = 100max_content = Nevents/nbins = 1442.66

2) Use the extreme of all these intervals do define TDC values

R(t) relation determination

1) Divide the tmax-tmin interval in 100 bins, each one containing an equal number of events Nevents(data)/nbins = 1962.24

1) Divide the Rmax-Rmin interval in 100 bins, each one containing an equal number of events Nevents(MC)/nbins= 1442.66

2) Use the extreme of all these intervals do define Rthr values; transform Rthr into R by quadratically subtracting the averagey (see figure on slide 3)

MC


R(t) relation: result

Garfield + data

Garfield

4) The relationship between the corresponding values provide us with the R(t) relation we were looking 4) The relationship between the corresponding values provide us with the R(t) relation we were looking


Residuals for run 1559


Check1) 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

+ =MC1

MC2


Check

Mean: -0.7E-02RMS: 0.2E-01

Delta r (mm)

Garfield (MC1) + MC2

Garfield (MC1)

4) compare the r(t) relation with the relation obtained by Garfield using sample MC1

50 micron

n = 100 bins


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, …)

…..

r(t) relations from inclusive mdt tubes drift time distributions

Documents

distance r

function of r

r distribution rt relation

rt distribution

drift ev

drift rrv

value of r

interval r