Abstract
Exact analytic solutions for the plasma/magnetic-field free-boundary problem are derived for three planar, surface magnetic field configurations: the picket fence, the simple magnetic slab, and the staggered magnetic slab. In the ideal magnetohydrodynamic limit, conformal mapping techniques yield explicit closed-form solutions for the free boundaries, the magnetic field lines, and the magnetohydrodynamic stability criteria. For configurations with plasma confined to one side of a continuous, sharp free boundary, it is found that with a given choice of the physical parameters (i.e., dimensions, current, and plasma pressure), there may be only one stable solution; only one unstable solution; two solutions, one stable and one unstable; or no solution at all. For the staggered slab, parameters can be chosen so that the conductors nearest the plasma are force free, an arrangement which could minimize the size of physical supports and the associated plasma loss in confinement applications.
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