Three-Dimensional Instability of Magnetic Islands

The three-dimensional stability of magnetic equilibria with islands is investigated with use of reduced magnetohydrodynamics. It is found numerically that tokamak equilibria with large $\frac{m}{n}=2\mathrm{}$ islands can be ideally unstable. The instability is explained by the strongly modified $q$ profile in the helical equilibrium, where the $q=\frac{3}{2},\frac{5}{3},\dots$ resonant surfaces are all close to the inner separatrix of the islands. An analytic treatment of the three-dimensional coalescence instability is given to illustrate this effect.