Macroscopic description for a quantum plasma micro-instability: the quantum Weibel solution

TL;DR

This paper develops a macroscopic fluid-like model to analyze the quantum Weibel instability in plasmas, incorporating quantum effects that modify the classical dispersion relations and introduce a cutoff wave-number.

Contribution

It introduces a novel macroscopic description of quantum plasma micro-instabilities, highlighting quantum effects of first and second kind on the Weibel instability.

Findings

Quantum effects alter the dispersion relations of the Weibel instability.

A cutoff wave-number exists even under strong temperature anisotropy.

Quantum modifications lead to higher-order dispersion relations.

Abstract

The Weibel instability in the quantum plasma case is treated by means of a fluid-like (moments) approach. Quantum modifications to the macroscopic equations are then identified as effects of first or second kind. Quantum effects of the first kind correspond to a dispersive term, similar to the Bohm potential in the quantum hydrodynamic equations for plasmas. Effects of the second kind are due to the Fermi statistics of the charge carriers and can become the dominant influence for strong degeneracy. The macroscopic dispersion relations are of higher order than those for the classical Weibel instability. This corresponds to the presence of a cutoff wave-number even for the strong temperature anisotropy case.