This paper derives analytical expressions of the dispersion relations for the three basic ideal MHD waves, namely, fast, slow and Alfvén 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 Alfvén-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.
Fast Alfven eigenmodes in a cylindrical inhomogeneous plasma