Various expressions are derived for the Green's functions for a point charge in an infinite plane condensor comprising one or three homogeneous isolating parallel dielectric layers. In view of numerical evaluations needed for calculating space charge effects in detectors (e.g. RPC's) the merits of these (series and integral) representations are discussed. It turns out that in most cases the integral representations are more favourable after their convergence has been improved. This is done by subtracting simple terms having the same asymptotic behaviour as certain too slowly converging terms and adding closed expressions resulting from the integration of the simple terms. The method is demonstrated in some detail. In addition analytic expressions for the weighting field of a strip electrode are derived which allow calculation of induced signals and crosstalk.

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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 [1], and a timing RPC with 300 µm gas gap [2]. 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.