Inertia-Controlled Ambipolar Diffusion

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Abstract
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.

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