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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 α-effect scale with the current helicity of the background field. The α-tensor is highly anisotropic as the components αϕϕ and αzz have opposite signs. The amplitudes of the azimuthal α-effect computed with the cylindrical 3D magnetohydrodynamics 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 megayears.