Quantum Weibel Instability

TL;DR

This paper investigates how quantum effects influence the Weibel instability in plasmas, deriving a generalized dispersion relation and showing that quantum effects tend to suppress the instability, with applications to astrophysics and plasma control.

Contribution

It introduces a quantum generalization of the classical Weibel instability analysis using the Wigner-Maxwell model, extending understanding of plasma behavior in quantum regimes.

Findings

Quantum effects weaken or suppress the Weibel instability.

Derived a generalized dispersion relation for quantum plasmas.

Analyzed extreme temperature anisotropy and water bag distributions.

Abstract

The Weibel instability is analyzed for quantum plasmas described by the Wigner-Maxwell model. For a suitable class of electromagnetic potentials, the Wigner-Maxwell system is linearized yielding a general dispersion relation for transverse electromagnetic waves. For a double Gaussian equilibrium with temperature anisotropy, the derived dispersion relation generalizes the classical Weibel instability equation. More detailed analytical results are obtained for the cases of extreme temperature anisotropy and for a three-dimensional water bag distribution. In all cases, quantum effects tends to weaken or suppress the instability. Applications are discussed for dense astrophysical objects like white dwarfs and neutron stars as well as for tunnel-ionized plasmas with controllable perpendicular plasma temperature.