A simple theory for signals induced by a point charge moving in a resistive plate chamber

A simple model for computing the current through the pick-up strips of a resistive plate chamber (RPC) is developed; a simple approximate but quite accurate formula for this current is found. The model is an infinite plane condensor filled with two layers; one is vacuum and represents the gas gap. The other one represents the anode and is a dielectric with a relative dielectric constant between 2 and 4; its weak conductivity is neglected as it was shown by Schöpf and Schnizer (Nucl. Instr. and Meth. A 323 (1992) 338) [1]that for the high values of the specific resistance of melamine–phenolic laminate or glass it has no influence on the signals so that the quasi-static approximation can be applied. It turns out that the influence of the dielectric on the signal is also small and may be neglected; so a formula derived for an empty condensor and giving the strip current as a function of the distance between the anode and the cathode, of the width of the strip and of the distance between the strip and the trajectory of the charge is a good approximation to the real case. The deviations due to a gap between the strips are discussed.