Helicity and alpha-effect by current-driven instabilities of helical magnetic fields

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 $α$-effect scale with the current helicity of the background field. The $α$-tensor is highly anisotropic as the components $α_{ϕϕ}$ and $α_{zz}$ have opposite signs. The amplitudes of the azimuthal $α$-effect computed with the cylindrical 3D MHD code are so small that the operation of an $αΩ$ 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 $α$-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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