Abstract
Necessary and sufficient conditions are derived for the hydromagnetic stability of a tubular pinch with a very thin current layer. The derivation is based on the energy principle, according to which a system is stable if and only if the energy integral is positive for every virtual displacement. The virtual displacements are divided into two types, depending on whether their radial components are continuous or discontinuous in the limit of an infinitely thin layer. Separate stability criteria are given for each type, and stability diagrams are constructed on the basis of numerical calculations. The tubular-pinch results are supplemented with a brief discussion of the columnar pinch, and it is concluded that the tubular pinch is easier to stabilize.
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