Numerical studies on streamer probability in resistive plate chambers for eco-friendly gases

F-gas regulations foresee restrictions and bans of highly potent greenhouse gases such as R134a (C2H2F4) and SF6 used in RPCs. Current research is dedicated to finding an environmentally friendly gas mixture replacement for RPCs. Simulations of RPCs are crucial in supporting and extending the mostly experimental-based research of identifying suitable eco-friendly alternatives. To date, there is no comprehensive quantitative description of the avalanche-to-streamer transition in uniform electric fields. Particularly in the context of RPCs, this is essential for estimating the streamer probability of a particular mixture to predict the avalanche-streamer separation accurately. An improved form of the classical streamer inception criterion is introduced, predicting the transition phase to overcome this problem. The criterion is entirely based on the space-charge field of the many superimposed avalanches due to primary ionization. A rigorous simulation of the single-gap highpressure laminated RPC (HPL-RPC) is developed to integrate and test the improved streamer criterion along with the capability to estimate other performance parameters, such as the detector's efficiency. The simulation is based on Garfield++ and is extended for this study to include the axis-symmetric space-charge model originally developed by Christian Lippmann. A dedicated electrical signal transmission system is also modeled to replicate the experimental setup accurately. Validation of the simulation is achieved through comparison with acquired performance data of the experimental HPL-RPC setup at the GIF++ muon beam experiment for several eco-friendly gas mixtures. This contribution presents the detailed modeling of the RPC simulation and shows that for CO2-based standard mixtures (CO2/R134/i-C4H10/SF6), the experimentally measured separation between the efficiency and streamer probability curves is accurately modeled by the improved streamer criteria.