Numerical Stability Improvements for the Pseudo-Spectral EM PIC Algorithm

TL;DR

This paper enhances the numerical stability of the PSATD particle-in-cell algorithm, effectively reducing instabilities like the numerical Cherenkov instability in relativistic beam simulations through combined approaches and filtering.

Contribution

It introduces new methods and filtering techniques that significantly mitigate numerical instabilities in the PSATD PIC algorithm, especially for relativistic and low-energy beams.

Findings

Numerical Cherenkov instability is substantially reduced.

The combined approaches improve stability at relativistic energies.

Filtering techniques are effective in stabilizing low-energy beam simulations.

Abstract

The pseudo-spectral analytical time-domain (PSATD) particle-in-cell (PIC) algorithm solves the vacuum Maxwell's equations exactly, has no Courant time-step limit (as conventionally defined), and offers substantial flexibility in plasma and particle beam simulations. It is, however, not free of the usual numerical instabilities, including the numerical Cherenkov instability, when applied to relativistic beam simulations. This paper presents several approaches that, when combined with digital filtering, almost completely eliminate the numerical Cherenkov instability. The paper also investigates the numerical stability of the PSATD algorithm at low beam energies.