Boltzsim: A fast solver for the 1D-space electron Boltzmann equation with applications to radio-frequency glow discharge plasmas

TL;DR

This paper introduces Boltzsim, a fast, open-source solver for the 1D electron Boltzmann transport equation in low-temperature plasmas, with applications to radio-frequency glow discharge plasmas, validated against particle-in-cell simulations.

Contribution

The paper presents Boltzsim, a novel Eulerian-based, efficient solver for the 1D electron Boltzmann equation, including validation and application to RF glow discharge plasma modeling.

Findings

Boltzsim achieves self-convergence and matches PIC-DSMC results.

Differences between Boltzsim and existing methods vary with pressure, up to 80 times at low pressure.

The solver is effective for simulating low-temperature plasma phenomena.

Abstract

We present an algorithm for solving the one-dimensional space collisional Boltzmann transport equation (BTE) for electrons in low-temperature plasmas (LTPs). Modeling LTPs is useful in many applications, including advanced manufacturing, material processing, and hypersonic flows, to name a few. The proposed BTE solver is based on an Eulerian formulation. It uses Chebyshev collocation method in physical space and a combination of Galerkin and discrete ordinates in velocity space. We present self-convergence results and cross-code verification studies compared to an in-house particle-in-cell (PIC) direct simulation Monte Carlo (DSMC) code. Boltzsim is our open source implementation of the solver. Furthermore, we use Boltzsim to simulate radio-frequency glow discharge plasmas (RF-GDPs) and compare with an existing methodology that approximates the electron BTE. We compare these two approaches and quantify their differences as a function of the discharge pressure. The two approaches show an 80x, 3x, 1.6x, and 0.98x difference between cycle-averaged time periodic electron number density profiles at 0.1 Torr, 0.5 Torr, 1 Torr, and 2 Torr discharge pressures, respectively. As expected, these differences are significant at low pressures, for example less than 1 Torr.