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

It is known that in a hydrodynamic Taylor-Couette system, uniform rotation or a rotation law with positive shear (“super-rotation”) is 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 cylindrical pinch formed by a homogeneous axial electric-current is stabilized by rotation laws with dΩ/dR ≥ 0. For magnetic Prandtl number Pm ≠ 1 and for slow rotation, however, rigid rotation and super-rotation support the instability by lowering the critical Hartmann numbers. This double-diffusive instability of super-rotation even exists for toroidal magnetic fields with rather arbitrary radial profiles, the current-free profile B_ϕ ∝ 1/R included. 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 ≪ 1 and it corotates for Pm ≫ 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 kA 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 kA if a gallium alloy is used.