Taylor relaxation in a torus of arbitrary aspect ratio and cross section

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Abstract
Taylor’s analysis of plasma relaxation is generalized to a toroidal plasma of arbitrary aspect ratio and cross section. A contribution to the energy incorrectly neglected by Taylor is included in the analysis. The contribution is due to the induced wall current, which must be greater than the current through the external field coils in a self-reversed z pinch. Although this contribution to the energy is substantial, it is shown to never alter the minimum energy state. Some of the general properties of the minimum energy state in a torus of arbitrary aspect ratio and cross section are also determined.