Resonance instability of axially-symmetric magnetostatic equilibria

TL;DR

This paper reviews the stability of axisymmetric magnetostatic fields, revealing that resonant MHD waves can cause instability regardless of the poloidal to toroidal field ratio, challenging previous simulation-based conclusions.

Contribution

It identifies a class of resonant MHD waves that induce instability in axisymmetric fields, highlighting limitations of current 3D simulations in capturing this effect.

Findings

Resonant MHD waves cause instability at all poloidal-toroidal ratios.

Large azimuthal wave numbers are involved in the instability.

Previous simulations may have overlooked this instability.

Abstract

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 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 3-d numerical simulations, can miss this instability because of the very large azimuthal wave numbers involved and its resonant character.