Three-fluid Ohm's law

We develop a three-fluid theory, including electrons, ions, and neutral par ticles and their collisions, to describe the interaction between the magnet osphere, ionosphere, and thermosphere, We derive Ohm's law including the co llisions between ions, electrons, and neutrals. In particular, our analysis includes the effects of electron-ion collisions. The electron and ion equa tions are solved in a completely coupled manner. The complete form of three -fluid Ohm's law in the plasma frame is obtained for a steady-state, unifor m, three-fluid flow. This form of Ohm's law can be simplified to obtain the ideal MHD frozen-in condition when all collisions are neglected and the ge neralized Ohm's law when the collisions with neutrals are neglected. In our form the neutral velocity in the conventional collisional Ohm's law is rep laced by the plasma velocity. More physical insights can be obtained from t his form of Ohm's law in the context of magnetosphere-ionosphere coupling. This form describes the magnetosphere-ionosphere coupling without involveme nt of the neutral wind. The ionospheric velocity continuously deviates from the electric drift velocity from high altitudes to low altitudes. In addit ion, the plasma momentum equation for steady-state uniform three-fluid flow is derived. It describes ionosphere-thermosphere coupling. The Ohm's law i n the neutral wind frame, or the conventional form of Ohm's law, can be der ived by combining the Ohm's law in the plasma frame with the momentum equat ion. The conductivities become the same as the conventional ones under a fe w approximations. Combination of the two forms of Ohm's law provides the re lationship between the electric field and the ionospheric velocity. When th e neutral wind stays still? this relationship can be used to describe magne tosphere-ionosphere coupling.