  Helical magnetic background fields with adjustable pitch angle are imposed on
a conducting fluid in a differentially rotating cylindrical container. The
small-scale kinetic and current helicities are calculated for various field
geometries, and shown to have the opposite sign as the helicity of the
large-scale field. These helicities and also the corresponding $\alpha$-effect
scale with the current helicity of the background field. The $\alpha$-tensor is
highly anisotropic as the components $\alpha_{\phi\phi}$ and $\alpha_{zz}$ have
opposite signs. The amplitudes of the azimuthal $\alpha$-effect computed with
the cylindrical 3D MHD code are so small that the operation of an
$\alpha\Omega$ dynamo on the basis of the current-driven, kink-type
instabilities of toroidal fields is highly questionable. In any case the low
value of the $\alpha$-effect would lead to very long growth times of a dynamo
in the radiation zone of the Sun and early-type stars of the order of
mega-years.
