Sufficient criterion for magneto-hydrodynamic stability and the low-shear limit

Abstract

For arbitrary toroidal magnetohydrostatic equilibria, a sufficient stability criterion is derived whose evaluation requires no more than solving a one-dimensional problem at every closed magnetic field line. This criterion is less restrictive than previously known similar sufficient criteria if all field lines are closed, low-order rational values of the rotation number being most favorable, and it shows that a closed-line equilibrium may be stable even if neighbouring low-shear equilibria are unstable.