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Mean‐field dynamos: The old concept and some recent developments
Author(s) -
Rädler K.H.
Publication year - 2014
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.201412055
Subject(s) - dynamo , electromotive force , mean field theory , physics , magnetohydrodynamics , magnetic field , dynamo theory , isotropy , magnetohydrodynamic drive , field (mathematics) , quantum electrodynamics , classical mechanics , condensed matter physics , mechanics , mathematics , optics , quantum mechanics , pure mathematics
This article elucidates the basic ideas of electrodynamics and magnetohydrodynamics of mean fields in turbulently moving conducting fluids. It is stressed that the connection of the mean electromotive force with the mean magnetic field and its first spatial derivatives is in general neither local nor instantaneous and that quite a few claims concerning pretended failures of the mean‐field concept result from ignoring this aspect. In addition to the mean‐field dynamo mechanisms of α 2 and αΩ type several others are considered. Much progress in mean‐field electrodynamics and magnetohydrodynamics results from the test‐field method for calculating the coefficients that determine the connection of the mean electromotive force with the mean magnetic field. As an important example the memory effect in homogeneous isotropic turbulence is explained. In magnetohydrodynamic turbulence there is the possibility of a mean electromotive force that is primarily independent of the mean magnetic field and labeled as Yoshizawa effect. Despite of many efforts there is so far no convincing comprehensive theory of α quenching, that is, the reduction of the α effect with growing mean magnetic field, and of the saturation of mean‐field dynamos. Steps toward such a theory are explained. Finally, some remarks on laboratory experiments with dynamos are made. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)