Comment on "Impact of particle number and cell-size in fully implicit charge- and energy-conserving particle-in-cell schemes" by N. Savard et al., Phys. Plasmas 32, 073903 (2025)

TL;DR

This paper critically examines a recent study on implicit particle-in-cell methods, revealing that its conclusions about particle number requirements are flawed due to procedural issues, and provides corrected insights.

Contribution

The authors identify and correct procedural issues in the previous study, challenging its conclusions and providing a more accurate understanding of particle number effects in implicit PIC schemes.

Findings

Procedural issues affected previous conclusions.

Corrected analysis shows different particle number requirements.

Highlights importance of diagnostics procedures in PIC simulations.

Abstract

We take issue with the conclusions in the recent publication by Savard et al. In the study, the authors implement a fully nonlinear charge- and energy-conserving implicit particle-in-cell method (ECC-IPIC), and use it to study the impact of particle number in the quality of the ECC-IPIC solutions for several problems, including an ion acoustic shockwave (IASW) problem and several sheath problems in bounded plasmas. From the study, the authors concluded that ``to reproduce highly resolved convergent solutions, a higher amount of particles per cell need to be used in the implicit scheme for both periodic and bounded simulations when the cell size exceeds the Debye length.'' We demonstrate that, according to our analysis for the IASW test, this conclusion does not survive independent scrutiny. We have identified several diagnostics procedural issues that are at the root of their conclusion, which when fixed dramatically change the outcome of the study.