Subcritical excitation of the current-driven Tayler instability by super-rotation

TL;DR

This paper investigates how super-rotation and other rotation laws influence the subcritical excitation of the Tayler instability in conducting fluids, revealing conditions under which the instability can be triggered at lower currents.

Contribution

It demonstrates that super-rotation can support the Tayler instability at subcritical currents, especially in narrow gaps and for various magnetic Prandtl numbers, expanding understanding of magnetic instabilities in rotating fluids.

Findings

Super-rotation can lower the critical current for instability.

The azimuthal drift direction depends on magnetic Prandtl number.

Minimal currents of 3.6 kAmp can trigger instability in sodium experiments.

Abstract

It is known that in a hydrodynamic Taylor-Couette system uniform rotation or a rotation law with positive shear ('super-rotation') are linearly stable. It is also known that a conducting fluid under the presence of a sufficiently strong axial electric-current becomes unstable against nonaxisymmetric disturbances. It is thus suggestive that a cylindric pinch formed by a homogeneous axial electric-current is stabilized by rotation laws with $d\Omega/dR \geq 0$. However, for magnetic Prandtl numbers Pm$\neq 1$ and for slow rotation also rigid rotation and super-rotation support the instability by lowering their critical Hartmann numbers. For super-rotation in narrow gaps and for modest rotation rates this double-diffusive instability even exists for toroidal magnetic fields with rather arbitrary radial profiles, the current-free profile $B_\phi\propto 1/R$ included. For rigid rotation and for super-rotation the sign of the azimuthal drift of the nonaxisymmetric hydromagnetic instability pattern strongly depends on the magnetic Prandtl number. The pattern counterrotates with the flow for Pm$\ll 1$ and it corotates for Pm$\gg 1$ while for rotation laws with negative shear the instability pattern migrates in the direction of the basic rotation for all Pm. An axial electric-current of minimal 3.6 kAmp flowing inside or outside the inner cylinder suffices to realize the double-diffusive instability for super-rotation in experiments using liquid sodium as the conducting fluid between the rotating cylinders. The limit is 11 kAmp if a gallium alloy is used.