A survey of the numerical methods currently in use to describe the motion of an electron swarm in a weakly ionized gas

Abstract

We first detail the formalism, based on a Boltzmann equation approach, which allows a simplified description of the motion of an electron swarm. We show that, in spite of its simplicity, this formalism is sufficient to obtain the macroscopic parameters measured in actual swarm experiments. This constitutes the so-called hydrodynamic approach and we see that it can be carried out by taking the moments relative to the position space of the continuity equation and of the Boltzmann equation. This technique allows a rigourous definition of the various swarm parameters. Some of the most accurate methods for the solution of these equations are then given. The connection between these methods and those currently in use in transport theory is stressed. With the formalism introduced above, we are not able to take into account the influence of the boundaries on the motion of electrons. When these boundaries need to be considered, new methods of solutions have to be developed. These methods, based either on a Monte-Carlo or on a Boltzmann equation treatment are similar with those involved in neutron transport or radiative transfert theory. The main drawback, in our case, is the presence of an electric field. For this reason, some important modifications must be made to treat correctly this problem. We present the two methods, based on the Boltzmann equation approach, which have been developed to this moment. This first one is based on the probability collision theory, the second one is a modified form of the SN method. Finally, we give some of typical results obtained with the various methods introduced above.