Non-axisymmetric instability of axisymmetric magnetic fields

TL;DR

This paper analyzes the stability of axisymmetric magnetic fields with both toroidal and axial components, revealing that non-axisymmetric perturbations can lead to instabilities with high growth rates, especially at short wavelengths.

Contribution

It provides a linear ideal MHD stability analysis of combined toroidal and axial magnetic fields, highlighting the dominance of short-wavelength non-axisymmetric instabilities.

Findings

Instability occurs for a wide range of azimuthal wavenumbers m.

Growth rate increases with increasing m.

Maximum growth occurs when the axial wave-vector makes the Alfvén frequency nearly zero.

Abstract

The MHD instabilities can generate complex field topologies even if the initial field configuration is a very simple one. We consider the stability properties of magnetic configurations containing a toroidal and an axial field. In this paper, we concentrate mainly on the behavior of non-axisymmetric perturbations in axisymmetric magnetic configurations. The stability is treated by a linear analysis of ideal MHD equations.In the presence of an axial field, it is shown that the instability can occur for a wide range of the azimuthal wavenumber $m$, and its growth rate increases with increasing $m$. At given $m$, the growth rate is at its maximum for perturbations with the axial wave-vector that makes the Alfv\'en frequency approximately vanishing. We argue that the instability of magnetic configurations in the ideal MHD can typically be dominated by perturbations with very short azimuthal and axial wavelengths.