Eulerian simulations of collisional effects on electrostatic plasma waves

TL;DR

This paper introduces a Eulerian time-splitting algorithm for simulating electrostatic plasma waves with collisions, using Fokker-Planck operators, and validates it against analytical predictions, focusing on nonlinear effects and numerical stability.

Contribution

It presents a novel Eulerian simulation method for collisional plasmas incorporating nonlinear Fokker-Planck operators, improving accuracy and stability in modeling wave phenomena.

Findings

Numerical results agree with analytical predictions in limit cases.

The method effectively models collisional damping of plasma waves.

A technique to prevent filamentation in Eulerian algorithms is demonstrated.

Abstract

The problem of collisions in a plasma is a wide subject with a huge historical literature. In fact, the description of realistic plasmas is a tough problem to attach, both from the theoretical and the numerical point of view, and which requires in general to approximate the original collisional Landau integral by simplified differential operators in reduced dimensionality. In this paper, a Eulerian time-splitting algorithm for the study of the propagation of electrostatic waves in collisional plasmas is presented. Collisions are modeled through one-dimensional operators of the Fokker-Planck type, both in linear and nonlinear form. The accuracy of the numerical code is discussed by comparing the numerical results to the analytical predictions obtained in some limit cases when trying to evaluate the effects of collisions in the phenomenon of wave plasma echo and collisional dissipation of Bernstein-Greene-Kruskal waves. Particular attention is devoted to the study of the nonlinear Dougherty collisional operator, recently used to describe the collisional dissipation of electron plasma waves in a pure electron plasma column. A receipt to prevent the filamentation problem in Eulerian algorithms is provided by exploiting the property of velocity diffusion operators to smooth out small velocity scales.