A multi-term Boltzmann equation analysis of electron swarms in gases

An accurate and efficient method for solving the Boltzmann equation for electron swarms in gases is proposed. The method utilises the conventional two-term expansion and a Galerkin technique for solution of the Boltzmann equations in an amalgamated form; the first two terms of the Legendre polynomial expansion of the electron energy distribution are obtained by the two-term method while the third and higher-order terms are deduced by the Galerkin method. Although a relaxation procedure has to be used for connecting the solutions and making them self-consistent by the two methods, the present amalgamated method can reduce the size of the matrix for the Galerkin technique, which may serve to make the computational time shorter. The present technique is applied to deduce the electron energy distribution and swarm parameters in methane gas, and good agreement with those calculated by Monte Carlo simulation is obtained. This shows the validity of the proposed method. The computational time of the present method is estimated to be roughly of the order of the geometric mean of those by the two-term expansion and Monte Carlo methods.