Two-fluid theory of acoustic-gravity waves in a plasma

The dispersion relation for acoustic-gravity waves in a plasma atmosphere with different electron and ion temperatures is derived from a two-fluid description of the plasma. The electrons are assumed to satisfy an isothermal equation of state and the ions an adiabatic equation of state. This model together with the quasi-neutrality condition is shown to reproduce the one-fluid hydrodynamic dispersion relation for acoustic-gravity waves, provided that both the acoustic cut-off frequency and the Brunt–Väisälä frequency are properly expressed in terms of the ion-sound velocity, including the contribution from the ion temperature.