Improved Numerical Cherenkov Instability Suppression in the Generalized PSTD PIC Algorithm

TL;DR

This paper presents a new method to completely eliminate the fundamental numerical Cherenkov instability in generalized PSTD PIC algorithms, significantly improving simulation stability for relativistic beams and plasmas.

Contribution

The authors introduce a novel approach that fully suppresses the fundamental mode of the numerical Cherenkov instability with minimal transverse field modifications.

Findings

Complete elimination of the fundamental instability mode.

Residual growth rates are minimized and computed.

Some cases show no numerical instabilities in the linear regime.

Abstract

The family of generalized Pseudo-Spectral Time Domain (including the Pseudo-Spectral Analytical Time Domain) Particle-in-Cell algorithms offers substantial versatility for simulating particle beams and plasmas, and well written codes using these algorithms run reasonably fast. When simulating relativistic beams and streaming plasmas in multiple dimensions, they are, however, subject to the numerical Cherenkov instability. Previous studies have shown that instability growth rates can be reduced substantially by modifying slightly the transverse fields as seen by the streaming particles . Here, we offer an approach which completely eliminates the fundamental mode of the numerical Cherenkov instability while minimizing the transverse field corrections. The procedure, numerically computed residual growth rates (from weaker, higher order instability aliases), and comparisons with WARP simulations are presented. In some instances, there are no numerical instabilities whatsoever, at least in the linear regime.