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

Helical magnetic background fields with an 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 to 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 magnetohydrodynamics 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 megayears.