Analysis of swarm coefficients in a gas for bi-modal electron energy distribution model

Abstract

Cross sections for collision between electrons and neutrals in a gas discharge are essential for theoretical and computational developments. They are also required to interpret and analyze the results of experimental studies on swarm parameters namely drift velocity, characteristic energy, and ionization and attachment coefficients. The cross sections and swarm coefficients are interconnected through the most important electron energy distribution function. The traditional method of solving the Boltzmann equation numerically yields the required distribution (EEDF). However there are many situations where a simpler approach is desirable for deriving the energy distribution analytically. Energy distribution in non-uniform electric fields, in crossed electric and magnetic fields, breakdown in mixtures of gases for electrical power or plasma applications, calculation of longitudinal diffusion coefficients are examples.In other studies the swarm parameters are employed to derive the cross sections in an unfolding procedure that also involves the energy distribution function. Application of Boltzmann solution method, though more rigorous, consumes enormous efforts in time and technical expertise. In an attempt to provide a simpler method the present author has previously suggested a bimodal electron energy distribution in gases. In this paper the author has generalized the idea of bi-modal energy distribution by considering a model gas with representative cross sections and adopted numerical methods for greater accuracy. The parameters considered are the nature of the two distributions, their relative ratio, and the dependence of cross sections on electron energy. A new method for determining the combination of distributions has been shown to be adequate for calculation of swarm parameters. The results for argon are shown to yield very good agreement with available experimental and theoretical values.