Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models

TLDR

Fluid models of gas discharges require transport and rate coefficients that depend on the electron energy distribution, which are typically obtained by solving the electron Boltzmann equation from collision cross‑section data. This work introduces BOLSIG+, a user‑friendly Boltzmann equation solver that is more general and easier to use than most existing solvers. BOLSIG+ computes steady‑state solutions using a two‑term expansion, handles various field types and collision processes, employs an exponential scheme for the resulting convection‑diffusion equation, and defines coefficients to maximize consistency with fluid equations. The solver demonstrates that the Boltzmann equation reduces to a convection‑diffusion continuity equation with a non‑local energy source, and it shows how the derived coefficients should be applied in fluid models while highlighting the impact of key parameters and approximations.

Abstract

Fluid models of gas discharges require the input of transport coefficients and rate coefficients that depend on the electron energy distribution function. Such coefficients are usually calculated from collision cross-section data by solving the electron Boltzmann equation (BE). In this paper we present a new user-friendly BE solver developed especially for this purpose, freely available under the name BOLSIG+, which is more general and easier to use than most other BE solvers available. The solver provides steady-state solutions of the BE for electrons in a uniform electric field, using the classical two-term expansion, and is able to account for different growth models, quasi-stationary and oscillating fields, electron–neutral collisions and electron–electron collisions. We show that for the approximations we use, the BE takes the form of a convection-diffusion continuity-equation with a non-local source term in energy space. To solve this equation we use an exponential scheme commonly used for convection-diffusion problems. The calculated electron transport coefficients and rate coefficients are defined so as to ensure maximum consistency with the fluid equations. We discuss how these coefficients are best used in fluid models and illustrate the influence of some essential parameters and approximations.