Accuracy of the Explicit Energy-Conserving Particle-in-Cell Method for Under-resolved Simulations of Capacitively Coupled Plasma Discharges

TL;DR

This paper demonstrates that an explicit energy-conserving Particle-in-Cell method can accurately simulate capacitively coupled plasmas with larger cell sizes, reducing computational costs while maintaining precision.

Contribution

The study introduces an energy-conserving PIC algorithm that retains accuracy with larger cell sizes and non-uniform grids, improving efficiency for plasma simulations.

Findings

Accurately models plasma discharges with cell sizes up to 8x Debye length.

Non-uniform grids enable simulations with 9.4x fewer cells.

Potential for reduced computational cost in industrial plasma modeling.

Abstract

The traditional explicit electrostatic momentum-conserving Particle-in-cell algorithm requires strict resolution of the electron Debye length to deliver numerical accuracy. The explicit electrostatic energy-conserving Particle-in-Cell algorithm alleviates this constraint with minimal modification to the traditional algorithm, retaining its simplicity and ease of parallelization and acceleration on modern supercomputing architectures. In this article we apply the algorithm to model a one-dimensional radio-frequency capacitively coupled plasma discharge relevant to industrial applications. The energy-conserving approach closely matches the results from the momentum-conserving algorithm and retains accuracy even for cell sizes up to 8x the electron Debye length. For even larger cells the algorithm loses accuracy due to poor resolution of steep gradients in the radio-frequency sheath. This can be amended by introducing a non-uniform grid, which allows for accurate simulations with 9.4x fewer cells than the fully resolved case, an improvement that will be compounded in higher-dimensional simulations. We therefore consider the explicit energy-conserving algorithm as a promising approach to significantly reduce the computational cost of full-scale device simulations and a pathway to delivering kinetic simulation capabilities of use to industry.