A dynamic method for charging-up calculations: the case of GEM

The simulation of Micro Pattern Gaseous Detectors (MPGDs) signal response is an important and powerful tool for the design and optimization of such detectors. However, several attempts to exactly simulate the effective gas gain have not been completely successful. Namely, the gain stability over time has not been fully understood. Charging-up of the insulator surfaces have been pointed as one of the responsible for the difference between experimental and Monte Carlo results. This work describes two iterative methods to simulate the charging-up in one MPGD device, the Gas Electron Multiplier (GEM). The first method, which uses a constant step size for avalanches time evolution, is very detailed but slow to compute. The second method instead uses a dynamic step-size that improves the computing time. Good agreement between both methods was achieved. Comparison with experimental results shows that charging-up plays an important role in detectors operation, explaining the time evolution of the gain. However it doesn't seem to be the only responsible for the difference between measurements and Monte Carlo simulations.