Energy principle for 2D electromagnetic, relativistic, interpenetrating, counter streaming plasma flows

TL;DR

This paper develops an energy principle framework to analytically describe the 2D Weibel instability in relativistic, counter-streaming plasma flows, providing insights into the stability and dynamics of such systems.

Contribution

It presents a detailed analytical conservation theorem and energy principle analysis specifically for the 2D Weibel instability in relativistic beam-plasma systems, extending prior electrostatic analogs.

Findings

Analytical conservation theorem for 2D Weibel instability

Energy principle formulation for relativistic counter-streaming plasmas

Enhanced understanding of instability growth mechanisms

Abstract

A relativistic electron beam propagating through plasma induces a return current in the system. Such a system of counterstreaming forward and return current is susceptible to host of instabilities out of which Weibel remains a dominant mode for destabilizing the system. Weibel instability has been widely investigated in simulations, experiments, as well as, analytically using fluid and kinetic treatments. A purely growing mode like Weibel instability can also be understood by using conservation theorems and energy principle analysis. An electrostatic analog to the Weibel instability, two stream instability in a beam plasma system has already been investigated using energy principle analysis [Lashmore-Davies 2007]. A detailed analytical description of conservation theorem for 2D Weibel instability in a beam plasma system has been carried out in this manuscript.