Space charge effects and induced signals in resistive plate chambers

Using special integral representations of the solution for the static electric field of a point charge in a three layer geometry with different permittivities, we calculate the effect of the space charge on the avalanche in the gas gap of an RPC. A detailed Monte Carlo simulation was developed which allows calculation of the actual charge spectrum. Results of this simulation are presented, using the example of a trigger-RPC with 2 mm gas gap, similar to the ones used by ATLAS (ATLAS TDR 10, CERN-LHCC-97-22), and a timing RPC with 300 mum gas gap (Nucl. Instr. and Meth. A 449 (2000) 295). Finally, we also present analytic solutions for the weighting field of an RPC readout strip, which allow to calculate the directly induced crosstalk and induced signals.