  A conducting Taylor-Couette flow with quasi-Keplerian rotation law containing
a toroidal magnetic field serves as a mean-field dynamo model of the
Tayler-Spruit-type. The flows are unstable against nonaxisymmetric
perturbations which form electromotive forces defining $\alpha$ effect and eddy
diffusivity. If both degenerated modes with $m=\pm 1$ are excited with the same
power then the global $\alpha$ effect vanishes and a dynamo cannot work. It is
shown, however, that the Tayler instability produces finite $\alpha$ effects if
only an isolated mode is considered but this intrinsic helicity of the
single-mode is too low for an $\alpha^2$ dynamo. Moreover, an $\alpha\Om$
dynamo model with quasi-Keplerian rotation requires a minimum magnetic Reynolds
number of rotation of ${\rm Rm}\simeq 2.000$ to work. Whether it really works
depends on assumptions about the turbulence energy. For a
steeper-than-quadratic dependence of the turbulence intensity on the magnetic
field, however, dynamos are only excited if the resulting magnetic eddy
diffusivity approximates its microscopic value, $\eta_{\rm T}\simeq \eta$. By
basically lower or larger eddy diffusivities the dynamo instability is
suppressed.
