Modelling of the Electron and Ion Kinetics in Cylindrical Proportional Counters

Abstract

Abstract This paper gives an overview of the state of the art in the modelling of electron and ion kinetics in proportional counters. Three specific points are emphasised. First, we determine, by using an accurate solution of the Boltzmann equation, the electron transport parameters (ionisation coefficient, drift velocity, diffusion coefficient) in methane over a very large range of values of the ratio electric field upon pressure. We then calculate the gas gain of the counter by using our calculated data. The calculation of this gas gain is generally based on the assumption that the ionisation coefficient and other transport paraments, at a given location in space, depend only on the value of the local electric field (equilibrium assumption). In a proportional counter, the electric field can present large spatial variations over distances of the order of one or a few electron mean free paths (especially for low gas pressure) and the equilibrium assumption can become questionable. The second objective of this work is to investigate the importance of these non-equibibrium effects. The existence of space charge fields in the counter can greatly affect its gain. In order to estimate the magnitude of these effects, self-consistent calculations based on a macroscopic description (continuity and momentum transfer equations) of the electron and ion kinetics coupled with Poisson equation are carried out. We show how such calculations make possible the determination of the onset and the importance of space charge effects in the counter.