Electron kinetics in proportional counters

A Boltzmann equation description of the electron behavior under the non-uniform field geometry is presented for modeling the gas amplification process of the proportional counters. Specifically, we apply the arrival-time spectra (ATS) method to deduce the equation leading to the counter gas gain. In addition, the behavior of the electron multiplication process in spatially distorted field conditions is demonstrated using a Monte Carlo simulation to investigate the physical aspects of the ionization coefficient.