Harris Dispersion Relation and Bernstein Modes in Dense Magnetized Quantum Plasmas

TL;DR

This paper extends the classical Bernstein wave theory to dense magnetized quantum plasmas using quantum kinetic theory, deriving a quantum Harris dispersion relation and analyzing quantum effects on wave behavior.

Contribution

It introduces a quantum version of the Harris dispersion relation for Bernstein modes, incorporating quantum effects like Landau quantization and finite temperature in a self-consistent framework.

Findings

Quantum Bernstein waves differ significantly from classical ones when ar is comparable to Fermi energy.

Quantum effects alter wave dispersion and stability properties.

Numerical solutions reveal new behaviors in dense quantum plasma regimes.

Abstract

The Bernstein wave is a well-known electrostatic eigen-mode in magnetized plasmas, and it is of broad connection to multiple disciplines, such as controlled nuclear fusions and astrophysics. In this work, we extend the Bernstein mode from classical to quantum plasmas by means of the quantum kinetic theory in a self-consistent manner, and especially the quantum version of the Harris dispersion relation is derived. The studied quantum effects appear in the form of pseudo-differential operators (\textgreek{Y}DO) in the formula, which are exactly solved using numerical methods. Furthermore, by utilizing the magnetized equilibrium Wigner function, Landau quantization and finite temperature effects are rigorously contained. It is found that behaviours of the quantum Bernstein wave departure significantly from its classical counterpart, especially when $\hbar\omega_{\mathrm{c}}$ is of the same order of the Fermi energy.