Flute instability of a current-carrying curved plasma column

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Abstract
Suydam's criterion for an arbitrarily curved plasma column is generalized. Mercier's well-known results concerning the local stability of a plasma in the vicinity of the magnetic axis are a special case arising from this criterion. In a curved plasma column, in addition to the stabilizing effect of shear, the stabilizing role of the “magnetic well” assumes importance. The magnetic well is produced by a displacement of the magnetic axis into the region where the toroidal magnetic field is weaker. The contribution to the magnetic well made by that part of the displacement which is associated with ballooning of the plasma column as a whole exactly cancels the ballooning mode. The part of the displacement due to electrodynamic stretching of the current column creates a “vacuum” magnetic well that is independent of plasma pressure. In stability criterion, given in this paper the stabilizing role of the vacuum magnetic well manifests itself in the coefficient F, which is dependent both on the mean curvature of the plasma column and on its harmonics. The condition for stabilization by the magnetic well, F > 1, imposes a limitation on the “stability safety factor” q = 2πr Bζ (r)/LBθ. The author considers regions where there are variations in the values q ensuring stability for systems of the racetrack and spatial figure-eight types.