Is the classical two-term approximation of electron kinetic theory satisfactory for swarms and plasmas?

Abstract

The ‘two-term’ approximation (representation of the electron distribution by the first two terms of an expansion in spherical harmonics in velocity space) continues to occupy a central role in the low-temperature plasma physics literature, in spite of the mass of evidence illustrating its inadequacy in the swarm (free diffusion) limit for many molecular gases. Part of the problem lies in the failure of many authors to specify quantitatively what they mean when they say that the two-term approximation is ‘acceptable’. Thus for example, an error of 10% in transport coefficients may well be acceptable in many plasma applications, but for analysis of highly accurate swarm experiments to compare with ab initio and beam-derived cross-sections, 0.1% or less is required, making ‘multi-term’ analysis mandatory. While reconciliation of the swarm and plasma literature along the lines of two different accuracy regimes may thus be possible, we dispute claims that the two-term approximation is generally satisfactory for inversion of swarm experiment data to obtain electron impact cross-sections. The unsatisfactory nature of other assumptions implicit in much of the modern plasma kinetic theory literature is also discussed.

The determination of low energy electron-molecule cross sections via swarm analysis

“…The investigation is carried out for electron swarms under the influence of varying configurations of electric and magnetic fields. Similar studies have been published previously for both model and real gases (White et al (1999(White et al ( ,2003)) but we extend these studies by: (i) highlighting the explicit effects of non-conservative collisions on the electron transport properties and (ii) addressing the temporal relaxation of spatial inhomogeneities through a study of the diffusion tensor. It is important to note that the application of an orthogonal configuration of electric and magnetic fields gives rise to an additional number of transport coefficients and thus one is able to exploit this in the inversion procedure.…”

High-order fluid model for streamer discharges: II. Numerical solution and investigation of planar fronts

“…As pointed out recently by White and co-workers [34,50] one may never be sure about the accuracy of the two-term approximation as various transport properties show different sensitivities with respect to this approximation in different energy ranges. For example, the inadequacy of the two-term approximation has been recently demonstrated for CF 4 [49] and CH 4 [50]. In the preceding paper, it was shown that the velocity of a streamer in the first-order fluid model is significantly affected by choosing either the two-term or the multi-term solution.…”

“…β is a parameter introduced to approximate the high-order tensors in the energy flux equation in terms of lower moments (see equation (50) of the preceding paper).…”

METHES: A Monte Carlo collision code for the simulation of electron transport in low temperature plasmas

“…The freely available Boltzmann solver BOLSIG+ [7] provides a user-friendly and fast option to calculate transport parameters and reaction rates and is compatible with the cross section data from LXCat. However, BOLSIG+ is based on the two-term approximation, whose applicability has been discussed in the literature [18,19]. The precision of Monte Carlo methods depends, when no numerical integrations are used, mainly on the precision of the used cross sections.…”