1. LNF, 20 febbraio 2004 1 R(t) Relations from inclusive MDT tubes drift time distributions M. Barone Software and Analysis Meeting ATLAS/Frascati

2. LNF, 20 febbraio 2004M. Barone 2 Outline Introduction Garfield simulation  Drift velocity  R distribution  Arrival time distribution R(t) relation  t0 determination  Results  Residual Conclusions

3. LNF, 20 febbraio 2004M. Barone 3 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 These effects have to be included in the “autocalibration” procedure Is there an alternative 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/CO 2 gas mixture and to the radial electric field

4. LNF, 20 febbraio 2004M. Barone 4 R(t) relation determination: the idea Garfield simulation includes all these effects. Even though Garfield does not reproduce with adequate precision the drift velocity, it allows to determine a “correct” R distribution, independent on the gas mixture (hypothesis to be verified): Recipe: “correct” R distribution Garfield time spectrum + time spectrum from data + = R(t) relation Garfield drift velocity for a given gas mixture = “correct” R distribution

5. LNF, 20 febbraio 2004M. Barone 5 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-x)%, CO2 (6.75-x)% + x=100ppm H20  GAS_MIX_3 Use of 100 ppm content of water vapor suggested by previous studies (ATL-COM-MUON-2003-035)

6. LNF, 20 febbraio 2004M. Barone 6 Garfield: Drift velocity determination v(E) Determination of the drift velocity starting from given values of the electric field E (V/cm) E fieldv_drift v_drift vs E GAS_MIX_1 Does not require tracking Magboltz

7. LNF, 20 febbraio 2004M. Barone 7 Drift velocity as a function of R can be automatically determined Using the v(R) function we can calculate the maximum drift time by integration Garfield: Drift velocity determination v(R) Each value of E(V/cm) corresponds to a value of R (cm): E field v_drift R v_drift vs r GAS_MIX_2 GAS_MIX_3

8. LNF, 20 febbraio 2004M. Barone 8 Garfield: Arrival time distribution MC: GAS_MIX_2 14600 tracks t0=0 is the time given by the primary muon threshold: 25 e t is the drift time of the 25 th electron transfer-function (1-t/(2*0.0213))*(t/0.0213)*exp(-t/0.0213)

9. LNF, 20 febbraio 2004M. Barone 9 Garfield: R distribution R distribution can be determined from the time spectrum and the drift velocity, for each different gas mixture Hypothesis: R distributions should be the same for different gas mixture MC: GAS_MIX_2 Yes! MC: GAS_MIX_1 MC: GAS_MIX_2

10. LNF, 20 febbraio 2004M. Barone 10 T0 determination MC: GAS_MIX_2 Translate horizontally MC spectra to superimpose it with the data histo Register the value of the shift: t0 =585 counts (BIL2, ml1&ml2) RUN 1559 tmin = 0 tmax = 925 counts tmin = 0 tmax = 925 counts multilayer 1 multilayer 2

11. LNF, 20 febbraio 2004M. Barone 11 R(t) determination 1) We start with 2 histogram: DATA from t0 to tmax MC from Rmin to Rmax 2) We divide the tmax-tmin interval in n bins, each one containing an equal number of events Ntot/n 3) Similarly, we divide the Rmax-Rmin interval in n bins 4) We use the extreme of all these intervals do define TDC values and R values. 5) The relationship between the corresponding values provide us with the R(t) relation we were looking DATAMC

12. LNF, 20 febbraio 2004M. Barone 12 R(t) relation: results Garfield+data Calib preliminary

13. LNF, 20 febbraio 2004M. Barone 13 Residuals for run 1559 cm

14. LNF, 20 febbraio 2004M. Barone 14 Conclusions An alternative method for the determination of R(t) relations has been proposed. Benefits: a lot of statistics R(t) relation can be determined for each tube no dependence on the tracking method Technical details have to be better investigated and the mechanism has to be tuned “clean” TDC spectra Analysis of more runs MC: more statistics Understand and quantify the limit of this method …..