Low-shear magnetohydrodynamic stability

For arbitrary toroidal magnetohydrostatic equilibria, a sufficient stability criterion is derived whose evaluation requires no more than solving a one-dimensional problem at every magnetic field line. This criterion reduces to a previously known one in the presence of shear, but is less restrictive if all field lines are closed. Comparison with a necessary criterion shows that the stability threshold is discountinuous in the limit of zero shear, low-order rational values of the rotation number being more favorable than neighboring irrational ones. (orig.)