Saturation properties of the Archontis dynamo

Astronomy and Astrophysics – Astronomy

Scientific paper

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Magnetic Fields, Mhd

Scientific paper

This paper discusses the generation and subsequent non-linear limiting of magnetic fields by motions in a periodic flow driven by a force whose components are proportional to (sinz, sinx, siny). This problem was originally studied by Archontis; the purpose of the present work is to remove certain complications present in the original model in order to understand better the underlying physical mechanism which limits the total magnetic energy growth. At high Reynolds numbers the resulting dynamos end up with almost equal total magnetic and kinetic energies, and thus yield fields strong enough to be astrophysically relevant. Until now, the existence of such dynamos has been doubted, so this demonstration of an example appears very important. At least up to Reynolds numbers of 800, these solutions are laminar and attracting.
We then present an argument showing that any stationary, incompressible dynamo can be used to create a family of solutions with an arbitrary ratio of magnetic to kinetic energies in the limit of large Reynolds numbers. The stability of such solutions is also discussed.

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