Instabilities of rotational flows in azimuthal magnetic fields of arbitrary radial dependence

TL;DR

This paper analyzes the stability of rotational flows in magnetic fields with arbitrary radial profiles, revealing conditions under which perturbations grow, especially for Keplerian flows with specific magnetic field profiles.

Contribution

It provides a linear stability analysis using WKB approximation for flows with arbitrary azimuthal magnetic field profiles, including a closed-form growth rate expression.

Findings

Growth rate can be positive for Keplerian velocity profiles with slightly shallower magnetic fields than R^{-1}

Stability depends on the radial profiles of the magnetic field and flow velocity

The analysis applies to viscous, electrically conducting fluids in azimuthal magnetic fields.

Abstract

Using the WKB approximation we perform a linear stability analysis for a rotational flow of a viscous and electrically conducting fluid in an external azimuthal magnetic field that has an arbitrary radial profile B_{phi}(R). In the inductionless approximation, we find the growth rate of the three-dimensional perturbation in a closed form and demonstrate in particular that it can be positive when the velocity profile is Keplerian and the magnetic field profile is slightly shallower than R^{-1}.