Dispersion Relations and Polarizations of Low-frequency Waves in Two-fluid Plasmas

TL;DR

This paper derives analytical dispersion relations and polarization properties of low-frequency waves in two-fluid magnetized plasmas, revealing how wave modes change with propagation angle and plasma beta, and identifying polarization transitions.

Contribution

It provides new analytical expressions for wave dispersion and polarization in two-fluid plasmas across different beta regimes and propagation angles, enhancing understanding of plasma wave behavior.

Findings

Fast and Alfvén modes become circularly polarized near-parallel propagation.

Polarization characteristics depend on plasma beta and temperature ratios.

Approximate dispersion relations accurately describe wave modes in specific limits.

Abstract

Analytical expressions for the dispersion relations and polarizations of low-frequency waves in magnetized plasmas based on two-fluid model are obtained. The properties of waves propagating at different angles (to the ambient magnetic field $\mathbf{B}_{0}$) and \beta (the ratio of the plasma to magnetic pressures) values are investigated. It is shown that two linearly polarized waves, namely the fast and Alfv\'{e}n modes in the low-\beta $\left( \beta \ll 1\right)$ plasmas, the fast and slow modes in the \beta \sim 1 plasmas, and the Alfv\'{e}n and slow modes in the high-\beta $\left( \beta \gg 1\right)$ plasmas, become circularly polarized at the near-parallel (to $\mathbf{B}_{0}$) propagation. The negative magnetic-helicity of the Alfv\'{e}n mode occurs only at small or moderate angles in the low-\beta plasmas, and the ion cross-helicity of the slow mode is nearly the same as that of the Alfv\'{e}n mode in the high-\beta plasmas. It also shown the electric polarization $\delta E_{z}/\delta E_{y}$ decreases with the temperature ratio $T_{e}/T_{i}$ for the long-wavelength waves, and the transition between left- and right-hand polarizations of the Alfv\'{e}n mode in $T_{e}/T_{i}\neq 0$ plasmas can disappear when $T_{e}/T_{i}=0$. The approximate dispersion relations in the near-perpendicular propagation, low-\beta, and high-\beta limits can quite accurately describe the three modes.