Comparison of kinetic calculation techniques for the analysis of electron swarm transport at low to moderate E/N values

Abstract

We present a comparison between results for the electron velocity distribution function (evdf), and transport and rate coefficients of an electron swarm obtained under different assumptions for the space and angular dependence of the evdf. Several solution techniques for the Boltzmann equation as well as Monte Carlo simulations have been tested. The comparison is made in neon at a constant and homogeneous reduced electric field in the range 10 Td ≤ E/N ≤ 500 Td taking into account the production of electrons in ionizing collisions. The results show that to obtain an accurate description of the electron swarm we need to take into account the variation in space of the electron density in the representation of the evdf. In what regards the angular dependence on velocity we discuss criteria to estimate the importance of the anisotropy of the evdf for any gas. Depending on the solution technique and on the E/N value, we find good to excellent agreement between the Boltzmann results obtained with a half-range method, a multi-term Legendre expansion, an elliptic approximation and the Monte Carlo results. The accuracy of the transport and rate coefficients obtained with each approach is evaluated and it is found that although the two-term velocity expansion is not sufficiently accurate to be used for cross section fitting, the corresponding rate and transport coefficients can generally be used in discharge modelling.