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

• Published in: Monthly notices of the Royal Astronomical Society 2011-07, Vol.414 (3), p.2696-2701
• Main Authors: Gellert, M., Rüdiger, G., Hollerbach, R.
• Format: Article
• Language: English
• Subjects: Astronomy; dynamo; Earth, ocean, space; Exact sciences and technology; instabilities; magnetic fields; stars: magnetic field
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1111/j.1365-2966.2011.18583.x

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 α zz 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.