On the deterministic and stochastic solutions of Space Charge models and their impact on high resolution timing

RPCs offer unique opportunities to investigate basic processes in gaseous electronics. The growth of a single avalanche can be studied in a regime where it reacts to its own field. This induces a saturation in its development, often described in a deterministic scenario by a nonlinear model. Once reinterpreted in a fully stochastic framework, the same feature corresponds to a negative feedback mechanism, which regulates the avalanche development and preserves its timing properties. Fluctuations are hence mostly produced in the initial phase of the growth. A clear evidence of the action of this stabilizing scheme is observed in data collected for single avalanches of fixed length.