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 } { \it \Omega } / { d } R \geq 0 .
However , for magnetic Prandtl number \mathrm { 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 \mathrm { Pm } \ll 1 and it corotates for \mathrm { Pm } \gg 1 while for rotation laws with negative shear the instability pattern migrates in the direction of the basic rotation for all \mathrm { 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 .