Resonance instability of axially symmetric magnetostatic equilibria.

We review the evidence for and against the possibility that a strong enough poloidal field stabilizes an axisymmetric magnetostatic field configuration. We show that there does exist a class of resonant magnetohydrodynamic (MHD) waves which produce instability for any value of the ratio of poloidal and toroidal field strength. We argue that recent investigations of the stability of mixed poloidal and toroidal field configurations based on three-dimensional numerical simulations can miss this instability because of the very large azimuthal wave numbers involved and its resonant character.