Saturated logistic avalanche model

The search for an adequate avalanche RPC working model evidenced that the simple exponential growth can describe the electron multiplication phenomena in the gas with acceptable accuracy until the external electric field is not perturbed by the growing avalanche. We present here a model in which the saturated growth induced by the space charge effects is explained in a natural way by a constant coefficient non-linear differential equation, the Logistic equation, which was originally introduced to describe the evolution of a biological population in a limited resources environment. The RPCs, due to the uniform and intense field, proved to be an ideal device to test experimentally the presented model.