A variational approach to the dynamic stability of high-density plasmas in magnetic containment devices

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Abstract
Variational methods are used to determine the structure of dynamically stable plasmoids. The total energy of the plasmoid is varied subject to a set of constraint integrals on the flow. It is demonstrated that the resulting flow structure results in a plasmoid of the type observed experimentally when the angular momentum of the plasmoid is not conserved. This is the collinear vortex structure. New experimental results are presented which demonstrate that the structures observed in mirror trapping experiments may be of the type predicted by the variational calculation. It is demonstrated that the collinear plasmoid structures can propagate in a surrounding conducting gas as members of a class of non-linear transverse waves that trap and transport fluid mass. They may also exist as standing waves in a surrounding medium which supports currents and acts as a force-bearing shell. The interaction of the non-linear transverse waves (plasmoids) with each other and with the magnetic mirror field produces a reversed-field closed configuration. Experimental results are presented which illustrate these effects and show details of the structures. It is also demonstrated that a modification of these solutions that assumes conservation of angular momentum of the plasmoid describes another type of plasma structure which is centred on the magnetic field lines and moves at right angles to the field. This is the field-aligned plasma structure.

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