Dissipative Taylor-Couette flows under the influence of helical magnetic fields

TL;DR

This paper analyzes the stability of magnetohydrodynamic Taylor-Couette flows with helical magnetic fields, mapping transitions between different MRI modes and identifying conditions for Tayler instability, revealing complex interactions between magnetic field configurations and flow stability.

Contribution

It provides a comprehensive stability map of MHD Taylor-Couette flows under various helical magnetic field configurations, including transitions between MRI types and conditions for Tayler instability.

Findings

Transition from standard MRI to AMRI mapped across field parameters.

Most unstable modes spiral opposite to the background field for nonaxisymmetric MRI.

Tayler instability occurs for certain azimuthal field configurations, independent of rotation.

Abstract

The linear stability of MHD Taylor-Couette flows in axially unbounded cylinders is considered, for magnetic Prandtl number unity. Magnetic fields varying from purely axial to purely azimuthal are imposed, with a general helical field parameterized by \beta=B_\phi/B_z. We map out the transition from the standard MRI for \beta=0 to the nonaxisymmetric Azimuthal MagnetoRotational Instability (AMRI) for \beta\to \infty. For finite \beta, positive and negative wave numbers m, corresponding to right and left spirals, are no longer identical. The transition from \beta=0 to \beta\to\infty includes all the possible forms of MRI with axisymmetric and nonaxisymmetric modes. For the nonaxisymmetric modes, the most unstable mode spirals in the opposite direction to the background field. The standard (\beta=0) MRI is axisymmetric for weak fields (including the instability with the lowest Reynolds number) but is nonaxisymmetric for stronger fields. If the azimuthal field is due in part to an axial current flowing through the fluid itself (and not just along the central axis), then it is also unstable to the nonaxisymmetric Tayler instability, which is most effective without rotation. For large \beta this instability has wavenumber m=1, whereas for \beta\simeq 1 m=2 is most unstable. The most unstable mode spirals in the same direction as the background field.