Dispersion surfaces for low-frequency modes

This paper derives analytical expressions of the dispersion relations for the three basic ideal MHD waves, namely, fast, slow and Alfven waves, as well as their generalizations to include non-ideal MHD effects. It is shown that while the Hall-MHD physics accurately describes ion-cyclotron resonance, it fails to include lower-hybrid resonance. In contrast, the cold two-fluid formalism does account for the lower-hybrid resonance as part of the magnetosonic-whistler mode dispersion surface. However, the cold-plasma approximation rules out the ion-sound mode at the outset. Moreover, it cannot deal with the kinetic Alfven-ion cyclotron (AIC) mode. Therefore, the cold-plasma AIC mode is extended to kinetic AIC mode. Thermal ion-sound wave dispersion relation is also derived by retaining the kinetic thermal correction.