Finite spatial-grid effects in energy-conserving particle-in-cell algorithms

TL;DR

This paper analyzes energy-conserving particle-in-cell algorithms, showing they are stable against aliasing instabilities in stationary plasmas and have a practical stability threshold for drifting plasmas, unlike momentum-conserving algorithms.

Contribution

It provides the first analysis confirming stability of EC-PIC algorithms against aliasing instabilities and identifies a practical stability threshold for their use in simulations.

Findings

EC-PIC is stable for stationary plasmas.

EC-PIC has a benign stability threshold for drifting plasmas.

Momentum-conserving PIC algorithms are unstable for both plasma types.

Abstract

Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space-time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to resolve Debye lengths spatially. We also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas.