Helical magnetorotational instability of Taylor-Couette flows in the Rayleigh limit and for quasi-Kepler rotation

TL;DR

This paper investigates the helical magnetorotational instability (MRI) in Taylor-Couette flows, revealing conditions under which traveling wave solutions dominate and how these findings can inform laboratory experiments, especially for quasi-Kepler rotation.

Contribution

It provides a detailed analysis of the MRI in Taylor-Couette flows with helical magnetic fields, highlighting differences between local and global solutions and the dominance of axisymmetric or nonaxisymmetric modes.

Findings

Traveling wave solutions are preferred for flat rotation laws with helical magnetic fields.

Nonaxisymmetric modes dominate when B_phi >> B_z and Pm is not too small.

Critical Reynolds numbers for nonaxisymmetric modes are much higher in standard MRI configurations.

Abstract

The magnetorotational instability (MRI) of differential rotation under the simultaneous presence of axial and azimuthal components of the (current-free) magnetic field is considered. For rotation with uniform specific angular momentum the MHD equations for axisymmetric perturbations are solved in a local short-wave approximation. All the solutions are overstable for B_z \cdot B_\phi \neq 0 with eigenfrequencies approaching the viscous frequency. For more flat rotation laws the results of the local approximation do not comply with the results of a global calculation of the MHD instability of Taylor-Couette flows between rotating cylinders. -- With B_phi and B_z of the same order the traveling-mode solutions are also prefered for flat rotation laws such as the quasi-Kepler rotation. For magnetic Prandtl number Pm\to 0 they scale with the Reynolds number of rotation rather than with the magnetic Reynolds number (as for standard MRI) so that they can easily be realized in MHD laboratory experiments. -- Regarding the nonaxisymmetric modes one finds a remarkable influence of the ratio B_\phi /B_z only for the extrema. For B_\phi >> B_z and for not too small Pm the nonaxisymmetric modes dominate the traveling axisymmetric modes. For standard MRI with B_z >> B_\phi, however, the critical Reynolds numbers of the nonaxisymmetric modes exceed the values for the axisymmetric modes by many orders so that they are never prefered.