Final Results of Drift Cell Simulation and Parametrization 1 Final Results of Drift Cell Simulation and Parametrization A. Gresele and T. Rovelli Bologna University & INFN Cell Simulation Procedure Method Used to Parametrize Final Results Conclusions 9/12/98 A. Gresele - CMS week

Simulated Tracks Granularity 2 Simulated Tracks Granularity 1 mm between x = 0 cm and 2 cm; 5 degree between d = 0o and 45o (between d = -45o and 45o when Bw not 0) 0.03 T between Bd = 0 and 0.3 T 0.1 T between Bn = 0 and 1 T 0.03 T between Bw = 0 and 0.3 T Bn Bw  Bd Only BnBw and BnBd pairs to reduce the num- ber of simulated tracks. x sense wire cathode track 9/12/98 A. Gresele - CMS week

Method Used to Produce the Drift Times 3 Method Used to Produce the Drift Times Full simulation on ALPHA machines ; Bologna Condor facility used ; Four tracks for each x, , B considered .  For each track we assumed the drift time is given by : 50% one electron 40% two electrons 10% three electrons 9/12/98 A. Gresele - CMS week

Method Used to Parametrize the Drift Times 4 Method Used to Parametrize the Drift Times The drift lines are more complicated when there is a magnetic field component along the sense wire , Bw . we used different methods for the parametrization with Bw and Bn. 9/12/98 A. Gresele - CMS week

5 Drift Lines when Bw = 0.3 T 9/12/98 A. Gresele - CMS week

Drift Time Variations with the track angle when B = 0 6 Drift Time Variations with the track angle when B = 0 To study the dependence of the drift time on the track, we calculated the difference between the drift time with   0 o and  = 0 o . This variation is given in function of the track angle for 3 points , x = 0.6cm, x= 1.1cm and x = 1.6cm. xpos = 0.6 cm xpos = 1.1 cm xpos = 1.6 cm 9/12/98 A. Gresele - CMS week

Parametrization of Drift Times vs Bw 7 Parametrization of Drift Times vs Bw We performs the regressions on the data for each  , x and Bw with HPARAM (in PAW). This in order to find the best polinomial parametrization of the drift time. 9/12/98 A. Gresele - CMS week

8 To study the quality of the fit we plot the difference between the parametrization and the points. These differences are   6ns. 9/12/98 A. Gresele - CMS week

Parametrization of Drift Times when Bn  0 9 Parametrization of Drift Times when Bn  0 xpos = 1.7 cm Bn = 1 T - Bn = 0 T The time variation (t) due to Bn is essentially independent of the track angle up to 45o and is fitted with a constant (at fixed position). 9/12/98 A. Gresele - CMS week

Final Parametrization of Bn 10 Final Parametrization of Bn For each value of Bn the results of the fit were plotted as a function of the distance from the wire. These points were then fitted with a straight line to obtain the final parametrization . Bn=1.0T-Bn=0T Bn=0.5T-Bn=0T Bn=0.1T-Bn=0T 9/12/98 A. Gresele - CMS week

Parametrization of Drift Times when Bd  0 11 Parametrization of Drift Times when Bd  0 The same procedure was used for Bd. The deviations are very small and no correction is required. Bd=0.30T-Bd=0T Bd=0.15T-Bd=0T Bd=0.03T-Bd=0T 9/12/98 A. Gresele - CMS week

Using this method we obtain... 12 Using this method we obtain... total of: 19 functions to parametrize Bw 10 functions to take into account Bn 9/12/98 A. Gresele - CMS week

Checks on parametrization 13 Checks on parametrization To check this procedure we generated 50 tracks at 3 points in the cell (x=0.2/0.4/0.6cm) where the expected deviations are largest.The angles and the magnetic field components ( Bn-Bw and Bn-Bd) were chosen randomly. The differences between the generated drift times and those computed with the parametrization procedure are ,for Bn-Bw, within  8ns and ,for Bn-Bd ,within 6ns . 9/12/98 A. Gresele - CMS week

 and Bd , Bn components are chosen randomly. Bw = 0 T Bn-Bd  0 T 14  and Bd , Bn components are chosen randomly. Bw = 0 T Bn-Bd  0 T 9/12/98 A. Gresele - CMS week

 and Bd , Bw components are chosen randomly Bd = 0 T Bn-Bw  0 T 15  and Bd , Bw components are chosen randomly Bd = 0 T Bn-Bw  0 T 9/12/98 A. Gresele - CMS week

-30o <  < +30o  t   5ns Bw = 0 T Bn-Bd  0 T 9/12/98 16 -30o <  < +30o  t   5ns Bw = 0 T Bn-Bd  0 T 9/12/98 A. Gresele - CMS week

-30o <   +30o  t   5ns Bd = 0 T Bn-Bw  0 T 9/12/98 17 -30o <   +30o  t   5ns Bd = 0 T Bn-Bw  0 T 9/12/98 A. Gresele - CMS week

18 Conclusions The parametrization procedure looks reasonable. In fact the differences between simulated and parametrized times are less than 8ns ( less than 5 ns if 30o   30o ) ; This parametrization is going to be introduced into CMSIM. 9/12/98 A. Gresele - CMS week