Multiterm solution of Boltzmann’s equation for electrons in a gas in an electric field

Abstract

The conventional two-term solution of Boltzmann’s equation for electrons in a gas in an electric field is extended to orders higher than the first. Numerical solutions are obtained under the assumption that the Legendre polynomial expansion of the velocity distribution function can be truncated after four terms. Monte Carlo simulations are used to assess the accuracy of the new theoretical approach and the limits of the four-term approximation itself in a simple model gas with a single inelastic process. Substantial improvements are observed when using the four-term approximation for the calculation of energy distributions and transport or rate coefficients in comparison with analogous calculations performed with the conventional approach. Conditions under which the four-term approximation becomes inadequate because of the high rate of inelastic collisions are also analysed.