Pinch-type instability experiments in magnetic Taylor-Couette flows

The linear stability problem of MHD Taylor-Couette flows with toroidal magnetic fields and with resting outer cylinder is considered for very small magnetic Prandtl numbers. Except for radial profiles of B-phi(R) proportional to 1/R (the current-free solution) the magnetic field destabilizes the flow. In particular, the most uniform field with B-in = B-out has been considered. For weak fields the TC-flow is stabilized until for growing magnetic amplitude disturbances with m = 1 a dramatic destabilization of the flow starts. For high enough Hartmann numbers the toroidal field is always (pinch-) unstable independent of any details of the flow. The electrical currents which are necessary for experiments in the laboratory must have amplitudes of a few kA for liquid sodium. The wider the gap of the container the weaker currents are necessary so that for wide-gap flows even experiments with gallium (Pr similar or equal to 10(-6)) are possible. There are many fundamental applications of the Tayler (or pinch-type) instability in astrophysics.