Stability of magnetic configurations containing the toroidal and axial fields

TL;DR

This paper analyzes the stability of magnetic configurations with toroidal and axial fields using linear analysis, revealing different instability conditions and regimes based on field strength and profile.

Contribution

It introduces new stability criteria for magnetic configurations with combined toroidal and axial fields, differing from traditional conditions.

Findings

Instability conditions differ from the classical $d (s B_{\phi})/ds > 0$ criterion.

Growth rates of instability are calculated across various parameters.

Two distinct instability regimes depend on axial field strength and toroidal profile.

Abstract

Stability properties of magnetic-field configurations containing the toroidal and axial field are considered. The stability is treated by making use of linear analysis. It is shown that the conditions required for the onset of instability are essentially different from those given by the necessary condition $d (s B_{\phi})/ds > 0$, where $s$ is the cylindrical radius. The growth rate of instability is calculated for a wide range of the parameters. We argue that the instability can operate in two different regimes depending on the strength of the axial field and the profile of the toroidal field.