Finite grid instability and spectral fidelity of the electrostatic Particle-In-Cell algorithm

TL;DR

This paper investigates the Finite Grid Instability in electrostatic Particle-In-Cell simulations by analyzing spectral fidelity and aliasing effects at the single particle and collective levels, revealing the primary cause of FGI.

Contribution

It provides a spectral domain analysis of FGI in PIC models, quantifying errors from charge deposition and interpolation, and links spectral aliasing to the instability.

Findings

Spectral phase and amplitude errors are quantified.

Aliased spatial modes cause spectral fidelity loss.

Spectral fidelity issues are identified as the main FGI cause.

Abstract

The origin of the Finite Grid Instability (FGI) is studied by resolving the dynamics in the 1D electrostatic Particle-In-Cell (PIC) model in spectral domain at the single particle level and at the collective motion level. The spectral fidelity of the PIC model is contrasted with the underlying physical system or the gridless model. The systematic spectral phase and amplitude errors from the charge deposition and field interpolation are quantified for common particle shapes used in the PIC models. It is shown through such analysis and in simulations that the lack of spectral fidelity relative to the physical system due to the existence of aliased spatial modes is the major cause of the FGI in the PIC model.