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 $alpha_{phiphi}$ 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 $alphaOmega$ 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.
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