Azimuthal magnetorotational instability with super-rotation

TL;DR

This paper demonstrates that azimuthal magnetorotational instability (AMRI) can occur with radially increasing rotation rates, expanding understanding of flow stability under magnetic fields in Taylor-Couette systems.

Contribution

It shows that AMRI is possible with positive shear flows and explores stability conditions across different magnetic Prandtl numbers and boundary conditions.

Findings

AMRI occurs with positive shear flows.

Minimum Hartmann number occurs at radius ratio 0.9.

Critical Reynolds numbers are below 10,000.

Abstract

It is demonstrated that the azimuthal magnetorotational instability (AMRI) also works with radially increasing rotation rates contrary to the standard magnetorotational instability for axial fields which requires negative shear. The stability against nonaxisymmetric perturbations of a conducting Taylor-Couette flow with positive shear under the influence of a toroidal magnetic field is considered if the background field between the cylinders is current-free. For small magnetic Prandtl number Pm-->0 the curves of neutral stability converge in the Hartmann number/Reynolds number plane approximating the stability curve obtained in the inductionless limit Pm=0. The numerical solutions for Pm=0 indicate the existence of a lower limit of the shear rate. For large Pm the curves scale with the magnetic Reynolds number of the outer cylinder but the flow is always stable for magnetic Prandtl number unity as is typical for double-diffusive instabilities. We are particularly interested to know the minimum Hartmann number for neutral stability. For models with resting or almost resting inner cylinder and with perfect-conducting cylinder material the minimum Hartmann number occurs for a radius ratio of 0.9. The corresponding critical Reynolds numbers are smaller than 10.000.