A New Distribution Function for Relativistic Counterstreaming Plasmas

TL;DR

This paper derives a new relativistic distribution function for counterstreaming plasmas based on the Maxwell-Boltzmann-Jüttner distribution, facilitating analytical and numerical studies of plasma instabilities.

Contribution

It introduces a velocity-space distribution function for relativistic counterstreaming plasmas derived from the classical Maxwell-Boltzmann-Jüttner distribution, enabling improved modeling.

Findings

Demonstrates differences in two-stream instability analysis using the new distribution

Provides a framework for velocity-space calculations in relativistic plasmas

Enhances analytical and simulation accuracy for plasma interactions

Abstract

The particle distribution function that describes two interpenetrating plasma streams is re-investigated. It is shown how, based on the Maxwell-Boltzmann-J\"uttner distribution function that has been derived almost a century ago, a counterstreaming distribution function can be derived that uses velocity space. Such is necessary for various analytical calculations and numerical simulations that are reliant on velocity coordinates rather than momentum space. The application to the electrostatic two-stream instability illustrates the differences caused by the use of the relativistic distribution function.