Stability of a Circular Toroidal Plasma under Average Magnetic Well Conditions

The simplest closed-line-of-force plasma containment system whose average magnetic curvature is stabilizing against pressure-driven instabilities for zero β is the circular torus with small rotational transform. The energy principle is applied to the simplest case, where the rotational transform is produced by a plasma current and where r/R, Bθ/B, and (β)1/2 are taken as small quantities of the same order so that an expansion procedure can be adopted. Final minimization of the energy integral leads to three simultaneous second-order differential equations, which are the toroidal equivalent of the well-known Euler equation for the linear pinch discharge. In addition to the necessary stability criterion which follows from these Euler equations, a sufficient condition shows that a β at least as high as r2/4R02 will be stable against both pressure-driven and j∥-driven instabilities.