Framework for solutions of the Boltzmann equation for ions of arbitrary mass

TL;DR

This paper introduces a flexible framework for solving the Boltzmann equation for ions of any mass ratio, using various basis sets and quadratures, with applications to electron and ion transport.

Contribution

It develops a general solution framework for the Boltzmann equation applicable to arbitrary mass ratios, utilizing different basis functions and quadrature methods.

Findings

Good convergence in transport quantities.

Particle distribution convergence can be inconsistent.

A new basis proposed for better handling strong fields.

Abstract

We present a framework for the solution of Boltzmann's equation in the swarm limit for arbitrary mass ratio, allowing for solutions of electron or ion transport. An arbitrary basis set can be used in the framework, which is achieved by using appropriate quadratures to obtain the required matrix elements. We demonstrate an implementation using Burnett functions and benchmark the calculations using Monte-Carlo simulations. Even though the convergence in transport quantities is always good, the particle distributions did not always converge, highlighting that simple benchmarks can give misleading confidence in a choice of basis. We postulate a different basis, which avoids a spherical harmonic expansion, which is better suited to strong electric fields or sharp features such as low-energy attachment processes.