Properties of low and medium frequency modes in two-fluid plasma

Based on a two-fluid plasma model where the electron mass and the displacement current are neglected, the eigenmode properties such as the frequency and the compressibility are studied. It is found that these properties strongly depend on the two-fluid parameter k ℓi, where k is the wave number of a mode and ℓi is the ion skin depth. Especially it is found that as the two-fluid parameter k ℓi increases beyond unity, the Alfv́n wave, which is an incompressible mode in the magnetohydrodynamics (MHD) limit, becomes compressible and its phase velocity approaches to the acoustic speed. The slow magnetosonic wave, which is compressible in the MHD limit, becomes incompressible as k ℓi increases. Implications of these results are also discussed.