Magnetohydrodynamic flows of non-equilibrium plasmas

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Abstract
The present paper studies the interaction between non-equilibrium ionization phenomena in a plasma and the non-uniform flow of that plasma. The characteristics of non-equilibrium conditions are reviewed for the uniform flow situation in which electric and magnetic fields may exist. In order to permit study of the non-uniform flow situation a single-fluid theory is proposed in which the electrical conductivity is assumed to be a function of the absolute magnitude of the current density. The resulting highly simplified system of equations are then used to formulate the Hartmann-flow problem. For this case the formerly linear problem becomes non-linear. Despite this, solutions to within a quadrature are obtained when the Hall effect is neglected. The more complex problem including the Hall effect is solved numerically. Solutions showing velocity and current profiles are given. For certain values of the parameters governing the problem it is shown that no solutions exist.

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