Steady-State Theory of an Intermediate-Pressure Discharge Column in a Magnetic Field

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Abstract
A steady‐state theory of a discharge column in a magnetic field is presented which covers the intermediate pressure range where the ion mean free path is neither much greater than, nor much less than, the discharge radius. With increasing pressure and magnetic field, its predictions tend to those obtainable from ambipolar diffusion theory. With decreasing pressure they approximate those of low‐pressure discharge theory based on the use of the third‐moment equation for the ions. The analysis in this paper is based on continuity and momentum‐transfer equations for the electrons and ions, but in contrast to linear ambipolar diffusion theory, the nonlinear ion inertia term is retained. In the plasma approximation, retention of this term gives rise to a plasma‐sheath boundary, where the density is nonzero and the potential finite, located where the ambipolar drift velocity reaches the isothermal sound speed [k(Te+Ti)/mi]1/2. Numerical solutions are presented for the profiles of density, velocity, and potential, for planar and cylindrical discharges. These indicate that potential inversion can occur, and that under such conditions the potential rises to a maximum and then decreases towards the plasma‐sheath boundary.

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