Dissipation of magnetic flux and magnetic energy in partially ionized gases

Macroscopic equations of motion are used to derive several forms of the generalized Ohm's law for partially ionized ternary gases in magnetic fields, and a conductivity σ is defined that is independent of the magnetic field. A flux theorem is derived using a velocityu _H that can be defined to be the velocity of magnetic field lines;u _H is only slightly different from the velocity of the electron component of the gas. It is shown that σ is the conductivity relevant to the decay of magnetic flux through any surface moving everywhere with velocityu _H . The rate of increase of the thermal energy density of the gas arising through collisions between particles of different species can be resolved into Joule heating at the ratej ²/σ, wherej is the current density, and heating associated with ambipolar drift. The latter, contrary to what has been claimed by some authors, is not necessarily fully compensated by a decrease in the energy of the electromagnetic field. In many applications such compensation does occur, but it may not in interstellar clouds where large amounts of gravitational energy can be made available by collapse, and then both heating and an increase in electromagnetic field energy may occur.