  The stability problem of MHD Taylor-Couette flows with toroidal magnetic
fields is considered in dependence on the magnetic Prandtl number. Only the
most uniform (but not current-free) field with B\_in = B\_out has been
considered. For high enough Hartmann numbers the toroidal field is always
unstable. Rigid rotation, however, stabilizes the magnetic (kink-)instability.
  The axial current which drives the instability is reduced by the
electromotive force induced by the instability itself. Numerical simulations
are presented to probe this effect as a possibility to measure the turbulent
conductivity in a laboratory. It is shown numerically that in a sodium
experiment (without rotation) an eddy diffusivity 4 times the molecular
diffusivity appears resulting in a potential difference of ~34 mV/m. If the
cylinders are rotating then also the eddy viscosity can be measured. Nonlinear
simulations of the instability lead to a turbulent magnetic Prandtl number of
2.1 for a molecular magnetic Prandtl number of 0.01. The trend goes to higher
values for smaller Pm.
