Stability of the Sharp Pinch and Unpinch with Finite Conductivity

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Abstract
The stability of the sharp linear pinch and unpinch is analyzed using a model in which the magnetic fields are separated by a thin current layer of large, but finite electrical conductivity. Elsewhere the contained fluid is assumed to have zero conductivity, a model which may, for example, approximate a plasma pinch heated by the intermixing of skew magnetic fields. The perturbed radial displacement of the layer is assumed to be constant across the layer and small wavelength perturbations comparable to the layer thickness are not considered. Viscosity is also neglected. The infinitely conducting, ``stabilized'' pinch and the unpinch are now shown to be overstable to perturbations whose helices are approximately orthogonal to the helix of the mean magnetic field across the layer. The overstable growth rate is typically one tenth of the geometric mean of a fundamental, oscillatory frequency and the Ohmic diffusion rate of the layer.

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