Quantum kinetic theory of the filamentation instability

TL;DR

This paper develops a quantum kinetic theory for the filamentation instability in plasmas, deriving analytical expressions and comparing quantum and classical models to understand instability characteristics.

Contribution

It re-derives the quantum electromagnetic dielectric tensor from the gauge invariant Wigner-Maxwell system and applies it to analyze the filamentation instability.

Findings

Derived analytical expressions for cutoff wave vector and growth rate.

Compared quantum kinetic results with quantum fluid and classical models.

Identified differences in instability behavior between models.

Abstract

The quantum electromagnetic dielectric tensor for a multi species plasma is re-derived from the gauge invariant Wigner-Maxwell system and presented under a form very similar to the classical one. The resulting expression is then applied to a quantum kinetic theory of the electromagnetic filamentation instability. Comparison is made with the quantum fluid theory including a Bohm pressure term, and with the cold classical plasma result. A number of analytical expressions are derived for the cutoff wave vector, the largest growth rate and the most unstable wave vector.