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.
Detailed measurements of the trapped magnetic fields and currents in plasma structures generated by conical theta-pinches are reported. Studies of these structures interacting with a magnetic barrier, and with each other in a collision at the centre of a magnetic mirror, are reported. The magnetic well formed by the collision has been studied by simultaneous use of several diagnostic techniques. The measurements are in agreement with a force-free, collinear magnetic field configuration (Wells 1972). Arguments relating superposability and collinearity of flow fields to these observations are given.
A simple current-sheet model of a hydromagnetic shock is employed in an attempt to explain the origin of the Bθ and vpoloidal observed previously in the hydromagnetic vortex rings produced in the conical θ pinch. Although this simple model has its limitations, it nevertheless shows clearly that the Bθ and the vortex structure are due to Hall currents which are driven by shear in acceleration, and that the existence of any right handedness and left handedness and of the plasma vortex structure itself depends upon the fact that negative electricity (electrons) are light and positive electricity (protons) are heavy. The model also gives a plausible explanation and description of the origin of θ rotation, i.e., vθ in the θ pinch.
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