Magnetohydrodynamic Stability of Toroidal Plasmas

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Abstract
The sufficient stability condition which follows directly from the energy principle is divided into the parts which depend, respectively, on j∥ and j⊥, which are the components of the equilibrium current parallel to, and perpendicular to, the magnetic field. The sufficient condition for j⊥ not to cause instability is found to depend on the average normal curvature of the magnetic surfaces in the direction of B. The corresponding condition for j∥ depends on the average geodesic torsion of the magnetic surfaces in the direction of B. For currents below approximately the Kruskal limit in a circular torus, the average normal curvature becomes negative and the j⊥‐modes are stable for negative pressure gradients. This confirms Mercier's earlier results for localized perturbations. On the other hand, to zero and first order in the aspect ratio of the torus (r/R0) the average geodesic torsion is the same as for a straight cylinder so that there is no toroidal stabilizing effect for j∥‐driven modes. Completely stable toroidal equilibria are possible which do not rely on magnetic shear. The relationship of these stability conditions with the ∫ (dl/B) criterion is discussed.

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