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

2025-02-23

AI Summary

This work addresses the challenge of high-fidelity electron kinetics modeling in low-pressure radio-frequency glow discharge plasmas. We present Boltzsim—the first efficient, Eulerian-frame, one-dimensional spatial solver for the electron Boltzmann transport equation (BTE). Boltzsim innovatively combines Chebyshev spectral collocation in physical space with a hybrid Galerkin–discrete-ordinate method in velocity space, and incorporates self-consistent convergence verification alongside cross-validation against particle-in-cell/direct simulation Monte Carlo (PIC-DSMC) results. Over a pressure range of 0.1–2 Torr, Boltzsim reduces the cycle-averaged electron number density profile error by up to 80× compared to conventional BTE approximations, with improvements as low as 0.98× in certain regimes; discrepancies are most pronounced below 1 Torr, enabling— for the first time—the systematic quantification of pressure-dependent errors inherent in classical approximations. These results establish the necessity of high-fidelity BTE solvers for low-pressure plasma modeling and provide a new benchmark tool for RF-glow discharge plasma applications.

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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.

Problem

• Solve 1D electron Boltzmann equation
• Model low-temperature plasma applications
• Compare RF-GDP simulation methodologies

Innovation

• Eulerian formulation for BTE solver
• Chebyshev collocation in physical space
• Galerkin and discrete ordinates in velocity