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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)

Luis Chacon, Guangye Chen, Lee Ricketson

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.

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)

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.
Paper Structure (5 sections, 4 equations, 2 figures)

This paper contains 5 sections, 4 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Particle initialization
  3. Diagnostics
  4. Results
  5. Conclusions

Figures (2)

  • Figure 1: Comparison of well-resolved IASW final solutions on both uniform and adaptive meshes from our ECC-IPIC implementation (DPIC) as well as Savard's (from Ref. savard2025impact).
  • Figure 2: Error analysis of the ECC-IPIC algorithm with respect to the number of particles, $N_{ppc}$. Top: quiet-start (QS) initialization with density matching. Middle: random initialization (RNG) with density matching. Bottom: RNG initialization without density matching. See text for description of various curves. Except for the spatial error level line, the reference solution is taken as the adaptive-mesh simulation with 20k PPC.