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

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.