Inertia-Controlled Ambipolar Diffusion

The general nonlinear ambipolar-flow equations are derived and discussed. The important non-linearities are caused by the inertia of the ions and by the heat-conduction mechanism. It is shown that all essential effects associated with these nonlinearities can be demonstrated in the plane-parallel case. The influence of the nonlinearity caused by the inertia is discussed in detail for the plane-parallel case and it is shown that this flow is analogous to the flow of a fluid with friction through a contracting nozzle. The limiting velocity—the isothermal or the adiabatic sound velocity—which is found in the exit of a nozzle is also found at the boundary in the case of inertia-controlled diffusion, provided this boundary acts like a perfect sink. Bohm's criterion—the ion drift velocity less than or equal to the sound velocity of the electron-ion gas in front of the boundary or the wall sheath—appears as an integral part of the inertia-controlled-diffusion theory. In the inertia-controlled-diffusion theory are incorporated, as integral parts, all the assumptions that necessarily must be added to the linear-diffusion theory in order to make it realistic. The isothermal and inertia-controlled diffusion leads always to wall-stabilized plasma configurations which directly correspond to the fundamental mode solution in the linear-diffusion theory.