Simulation benchmarks for low-pressure plasmas: capacitive discharges

TL;DR

This paper presents four carefully defined benchmark cases for capacitive discharges, validated across five independent particle-in-cell codes, providing a reliable basis for assessing simulation accuracy and physical model fidelity.

Contribution

The paper introduces a set of standardized benchmark cases for low-pressure capacitive discharges, validated across multiple codes to ensure reliability and facilitate comparison of simulation methods.

Findings

Simulation results are statistically indistinguishable within uncertainty bounds.

Benchmarks can evaluate both implementation accuracy and physical model fidelity.

Methodology can be extended to broader plasma phenomena.

Abstract

Benchmarking is generally accepted as an important element in demonstrating the correctness of computer simulations. In the modern sense, a benchmark is a computer simulation result that has evidence of correctness, is accompanied by estimates of relevant errors, and which can thus be used as a basis for judging the accuracy and efficiency of other codes. In this paper, we present four benchmark cases related to capacitively coupled discharges. These benchmarks prescribe all relevant physical and numerical parameters. We have simulated the benchmark conditions using five independently developed particle-in-cell codes. We show that the results of these simulations are statistically indistinguishable, within bounds of uncertainty that we define. We therefore claim that the results of these simulations represent strong benchmarks, that can be used as a basis for evaluating the accuracy of other codes. These other codes could include other approaches than particle-in-cell simulations, where benchmarking could examine not just implementation accuracy and efficiency, but also the fidelity of different physical models, such as moment or hybrid models. We discuss an example of this kind in an appendix. Of course, the methodology that we have developed can also be readily extended to a suite of benchmarks with coverage of a wider range of physical and chemical phenomena.