Burnett function expansion with a bi-Maxwellian weight function for electron swarm physics

Abstract

In the solution of Boltzmann's equation by polynomial expansion techniques it is important to choose the weight function as close as possible to the actual distribution function in order to ensure rapid convergence. In the case of electron motion through neutral gases in the presence of external electric and magnetic fields, the so-called moment method has had considerable success. The method is essentially a polynomial expansion of the electron velocity distribution function about a Maxwellian weight function at some arbitrary temperature. By choosing the temperature carefully in order to approximate the actual distribution adequate convergence can usually be obtained. However when the interactions between the electrons and the molecules is `soft' and/or reactive processes cause a significant increase in the population of the high energy tail of the distribution function, convergence of the expansion rapidly deteriorates and may not be achieved. In this article we investigate the use of a bi-Maxwellian weight function to improve convergence by the use of a model interaction between the electrons and molecules. The idea being that a Maxwellian at the lower temperature should be sufficient to characterise the electrons in the bulk of the distribution, while a second Maxwellian of smaller amplitude but at a some what higher temperature is used to characterised the electrons in the high energy tail of the distribution.