Rate effects in resistive plate chambers

Abstract

The resistive plates in RPCs cause a drop of the electric field in the gas gap at high particle rates or large gas gain, which affects efficiency and time resolution. This effect is typically estimated by assuming the particle flux to be a DC current that causes a voltage drop when it passes through the resistive plate. In an improved model by Abbrescia (Nucl. Instr. Meth. A 533 (2004) 7), the fluctuation of the field in the gas gap is modelled by assuming that the avalanche partially discharges a small capacitor which gets recharged with a time constant characteristic for the given RPC. In our approach, the effect is calculated by using the exact analytic solution for the time dependent electric field of a point charge sitting on the surface of a resistive plate in an RPC. This is, by definition, the best possible approximation to reality. The solution is obtained using the quasi-static approximation of Maxwell's equations. The formulas are presented as integral representations with 'cured' integrands, which allow easy numerical evaluation for Monte Carlo simulations. The solutions show that the charges in RPCs are 'destroyed' with a continuous distribution of time constants which are related in a very intuitive way to some limiting cases. Using these formulas we present a Monte Carlo simulation of rate effects, proving the applicability of this approach. Finally, we compare the Monte Carlo results to analytical calculations, similar to the ones proposed by Gonzalez-Diaz et al. (see proceedings of this conference).