Diagnosing numerical Cherenkov instabilities in relativistic plasma simulations based on general meshes

TL;DR

This paper extends the analysis of numerical Cherenkov radiation in electromagnetic particle-in-cell simulations from structured to unstructured meshes, examining how mesh shape and layout influence instabilities.

Contribution

It introduces a generalized analysis of NCR for finite-element EM-PIC algorithms on unstructured meshes, expanding understanding beyond traditional structured mesh studies.

Findings

Mesh shape and layout significantly affect NCR behavior.

Analytic predictions align with simulation results across different mesh types.

Unstructured meshes can mitigate or exacerbate NCR depending on their configuration.

Abstract

Numerical Cherenkov radiation (NCR) or instability is a detrimental effect frequently found in electromagnetic particle-in-cell (EM-PIC) simulations involving relativistic plasma beams. NCR is caused by spurious coupling between electromagnetic-field modes and multiple beam resonances. This coupling may result from the slow down of poorly-resolved waves due to numerical (grid) dispersion and from aliasing mechanisms. NCR has been studied in the past for finite-difference-based EM-PIC algorithms on regular (structured) meshes with rectangular elements. In this work, we extend the analysis of NCR to finite-element-based EM-PIC algorithms implemented on unstructured meshes. The influence of different mesh element shapes and mesh layouts on NCR is studied. Analytic predictions are compared against results from finite-element-based EM-PIC simulations of relativistic plasma beams on various mesh types.