Elimination of Numerical Cherenkov Instability in flowing-plasma Particle-In-Cell simulations by using Galilean coordinates

TL;DR

This paper presents a method to eliminate the numerical Cherenkov instability in relativistic plasma PIC simulations by using Galilean coordinates, verified through empirical and theoretical analysis.

Contribution

The authors introduce a simple approach of using Galilean coordinates in spectral PIC simulations to remove NCI for flowing plasmas, applicable to Cartesian and cylindrical geometries.

Findings

NCI is eliminated in simulations with Galilean coordinates.

Method verified empirically and through theoretical analysis.

Applicable to both Cartesian and cylindrical geometries.

Abstract

Particle-In-Cell (PIC) simulations of relativistic flowing plasmas are of key interest to several fields of physics (including e.g. laser-wakefield acceleration, when viewed in a Lorentz-boosted frame), but remain sometimes infeasible due to the well-known numerical Cherenkov instability (NCI). In this article, we show that, for a plasma drifting at a uniform relativistic velocity, the NCI can be eliminated by simply integrating the PIC equations in Galilean coordinates that follow the plasma (also sometimes known as comoving coordinates) within a spectral analytical framework. The elimination of the NCI is verified empirically and confirmed by a theoretical analysis of the instability. Moreover, it is shown that this method is applicable both to Cartesian geometry and to cylindrical geometry with azimuthal Fourier decomposition.