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Large-scale dynamo action of magnetized Taylor-Couette flows

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 $α$ effect and eddy diffusivity. If both degenerated modes with $m=\pm 1$ are excited with the same power then the global $α$ effect vanishes and a dynamo cannot work. It is shown, however, that the Tayler instability produces finite $α$ effects if only an isolated mode is considered but this intrinsic helicity of the single-mode is too low for an $α^2$ dynamo. Moreover, an $α\Om$ 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, $η_{\rm T}\simeq η$. By basically lower or larger eddy diffusivities the dynamo instability is suppressed.