1. Study of non-uniformity of magnetic field
Simulation
Real data analysis (CR)
Summary and outlook

2. Simulation of electron drift in E and non-uniformed B field
Drift velocity of electron in E, B field (Langevin equation)
First order Runge-Kutta integration was applied

3. Strategy of simulation
Determine T0 in the case of B=0 (vd=5cm/usec).
T0 = L0/ vd(B=0), where L0 is a drift length in z-direction
between the pad plane and the source point.
Execute Runge-Kutta intergration in non-uniform B
Calculate the drift length Lsim (Lsim = zf-zi)
Calculate the residual in z-direction (ResZ)
ResZ = Lsim-L0 <- corresponding to the resZ in the real data?

4. Result of simulation tracks of electrons Source point:
center of each pad,
zi = 40cm
Pad plane:
z = -35.6cm
Deviation is larger at outer pads.
Z direction (cm)
Radius (cm)
Phi-direction (cm)

5. Electron tracks (Zi =0 cm)

6. ResZ vs. radius ResZ is decreasing as the radius is increased.
In the worst case, the gap is 1.6mm
(zi = 40 cm)

7. Source files saho:/home/uchida/sim/eDrift/
Please check the bugs in the program!

8. Real data (CR) analysis
Run #: 28895, before correction
Cut condition: chi2Pad > 0.02, chi2Z > 0.02,
-0.4 < lambda (dip angle) <0.4

9. Correction offset values are added in deriving the z-position.
zcorr [ilay] = z0[ilay]+offset[ilay]
= vd t + offset[ilay]
offset valued are determined to adjust the mean of the residual-Z into zero in each layer at -1400<z<-1300.
See the source code
(saho:/home/uchida/ana/TPC/TPCana0.41/src/anaCluster.c
Function: setHit() )

10. Run # after correction
Mean values are improved (not perfect), the RMS not!

11. Summary and outlook
Simulation and CR data have the same tendency due to non-uniformity of the magnetic field.
Offset correction would be effective for improvement of the mean value of the resZ, but not for the RMS of the resZ.
We need the detailed investigation for the optimizations of the offset values. Sawada-kun is now under construction of the frame-work.
Z-dependence of resZ will be also studied in his frame-work.