doctoral thesis

x LIST OF FIGURES
2.17 The weighting field mechanism to calculate induced currents . . . . . 55
2.18 RPC geometry with strips . . . . . . . . . . . . . . . . . . . . . . . . 56
2.19 z- and x-component of the weighting field . . . . . . . . . . . . . . . 57
2.20 Precursor and streamer signal . . . . . . . . . . . . . . . . . . . . . . 59
3.1 Avalanches started by one electron at the same position . . . . . . . . 65
3.2 Examples for avalanches with longitudinal diffusion . . . . . . . . . . 68
3.3 Geometry for the 1.5-D simulation . . . . . . . . . . . . . . . . . . . 70
3.4 Comparison of the potentials of a point charge and transverse charge
distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.5 The influence of the step size on the simulation . . . . . . . . . . . . 71
3.6 Comparison of the fields of two transverse Gaussian charge distributions
with different standard deviations . . . . . . . . . . . . . . . . . 72
3.7 Avalanches with space charge effect . . . . . . . . . . . . . . . . . . 73
3.8 Snapshots of a simulated avalanches with space charge effect . . . . . 75
3.9 Example avalanches with longitudinal repulsive/attractive forces . . . 76
3.10 Geometry for calculating the electric field of a charge ring . . . . . . 78
3.11 Plots of the elliptic integrals of the first kind and of the second kind . 80
3.12 The coordinate system and the electric field vector in the two dimensional
system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.13 Electron density in the 3-D simulation . . . . . . . . . . . . . . . . . 85
4.1 Schematic images of Timing RPCs . . . . . . . . . . . . . . . . . . . 88
4.2 Calculated Timing RPC spectra . . . . . . . . . . . . . . . . . . . . . 92
5.1 Simulated efficiencies and time resolution of Timing RPCs . . . . . . 94
5.2 Simulated efficiencies and time resolution of Trigger RPCs . . . . . . 95
5.3 Measured charge-to-time correlation . . . . . . . . . . . . . . . . . . 96
5.4 Correlation of the charge threshold crossing time to the induced charge
with read out electronics, simulation . . . . . . . . . . . . . . . . . . 96
6.1 Influence of the space charge effect on the Timing RPC time resolution 100
6.2 Influence of the space charge effect on the Trigger RPC time resolution 100
6.3 Some simulated avalanches in Timing RPCs . . . . . . . . . . . . . . 101
6.4 Simulated and measured value of (α − η)vD . . . . . . . . . . . . . . 102
6.5 Simulated Timing RPC charge spectrum without space charge effect . 103
6.6 Simulated avalanche in a Timing RPC . . . . . . . . . . . . . . . . . 105
6.7 Simulated signal charge spectra for Timing RPCs, 0.3 mm gap . . . . 106
6.8 Comparison of simulated and measured spectra of the signal charge
for Timing RPCs, 0.3 mm gap . . . . . . . . . . . . . . . . . . . . . 106
6.9 Comparison of simulated and measured spectra of the signal charge
for Timing RPCs, 0.1 mm gap . . . . . . . . . . . . . . . . . . . . . 108
6.10 Simulated spectra of the total signal charge for Timing RPCs, 0.2 mm
gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108