A semi-analytical approach to modeling performance deterioration in irradiated resistive plate chambers

Resistive plate chambers (RPCs) are widely used for detecting ionizing radiation in high-energy physics experiments. Abundant background radiation, however, decreases the detection performance due to the resistive layers, preventing immediate electric charge removal. The resulting localized voltage drop across the layer containing the gas mixture (gas gap) determines the intensity of the deterioration of the detection efficiency, time resolution, and charge spectrum. This is a key part of assessing novel eco-friendly gas mixtures, which must exhibit certain robustness against irradiation. This work introduces a novel mathematical framework based on the stochastic distribution of voltage across the gas gap to quantify the performance deterioration of irradiated RPCs. A fast and precise semi-analytical method for calculating the voltage distribution is presented and validated against Monte Carlo simulations. Its validity is demonstrated up to a certain rate, which depends on the charge magnitudes released by the background radiation. The method and formalism are demonstrated on the single-cell model developed by M. Abbrescia and compared with previous work. Further, the single-cell model is compared to its two-dimensional extension, which models the spatial variations of the voltage drop from first principles. Results show that the single-cell and two-dimensional models are similar at high irradiation rates, but differ at small irradiation rates. However, the novel definitions of the deterioration of the performance parameters generally predict a lower level of performance in comparison with the state-of-the-art methods. These new definitions also indicate that the experimentally observed reduction of the maximal detection efficiency can be explained.