A fast solver for the spatially homogeneous electron Boltzmann equation

TL;DR

This paper introduces a fast, Eulerian numerical solver for the spatially homogeneous electron Boltzmann equation, enabling efficient modeling of electron transport in low-temperature plasmas with various collision processes.

Contribution

It presents a novel Eulerian solver using spherical harmonics and B-splines, supporting complex collision models and higher-order anisotropic terms, with demonstrated convergence and open-source availability.

Findings

Solver shows good convergence properties.

Comparison with Monte-Carlo and Bolsig+ validates accuracy.

Analyzes relaxation times of anisotropic correction terms.

Abstract

We present a numerical method for the velocity-space, spatially homogeneous, collisional Boltzmann equation for electron transport in low-temperature plasma (LTP) conditions. Modeling LTP plasmas is useful in many applications, including advanced manufacturing, material processing, semiconductor processing, and hypersonics, to name a few. Most state-of-the-art methods for electron kinetics are based on Monte-Carlo sampling for collisions combined with Lagrangian particle-in-cell methods. We discuss an Eulerian solver that approximates the electron velocity distribution function using spherical harmonics (angular components) and B-splines (energy component). Our solver supports electron-heavy elastic and inelastic binary collisions, electron-electron Coulomb interactions, steady-state and transient dynamics, and an arbitrary nmber of angular terms in the electron distribution function. We report convergence results and compare our solver to two other codes: an in-house particle Monte-Carlo ethod; and Bolsig+, a state-of-the-art Eulerian solver for electron transport in LTPs. Furthermore, we use our solver to study the relaxation time scales of the higher-order anisotropic correction terms. Our code is open-source and provides an interface that allows coupling to multiphysics simulations of low-temperature plasmas.