Simulation benchmarks for low-pressure plasmas: Capacitive discharges

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. * Electronic address: miles.turner@dcu.ie 2

Controlling plasma properties under differing degrees of electronegativity using odd harmonic dual frequency excitation

“…In this context, it is important to consider if these additional assumptions influence the accuracy of the simulation results. Insight into such effects can be gained from the works of Becker et al [68], Turner et al [69] and Surendra [70] who have undertaken detailed comparisons between PIC simulations and fluid simulations similar to those used in this work. In the work of Becker et al, the authors found that the investigated parameters, for example, electron density and ion flux at the electrodes, agreed to between 10% and 50% between the different fluid approaches studied and PIC simulations for He and Ar CCPs.…”

Verification of particle-in-cell simulations with Monte Carlo collisions

“…more of the code is being tested. In combination, the mezzanine test cases discussed here cover the principal functions involved in solving the benchmark problems presented in an earlier paper [21]. Table 1 summarizes this coverage of the test problems.…”

“…The present author and a group of collaborators recently developed a benchmark [21] applicable to a class of codes implementing the particle-in-cell with Monte Carlo collisions procedure [11,2,3]. We constructed four benchmark cases related to capacitive discharges in helium.…”

A new hybrid scheme for simulations of highly collisional RF-driven plasmas

“…To this end in the next section we compare the simulation results of the hybrid code with the simulation results of the GPU PIC/MCC code. The latter has been verified in the benchmark study of [16], but this time it has been ran assuming the atmospheric pressure in a pure He discharge using a simple reduced chemistry set similar to the one used in [5] and listed in Table I. Such a chemistry set does not represent the actual physics taking place in such discharges because metastable atoms and excimer molecules are neglected, whereas they usually dominate the electron production through the pooling reactions.…”

“…For our hybrid code we used the 128 bit Xoorshift pseudorandom number generator suggested in [14], which has period of 2 128 − 1. To accelerate the computations, the kinetic PIC/MCC part of the present hybrid code was implemented on a graphics processing unit (GPU) analagous to the GPU PIC/MCC code used in the benchmarking study [16].…”