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Stable and Unstable Solutions of the Nonlinear Dynamo Problem

Published online by Cambridge University Press:  12 April 2016

Reinhard Meinel
Reinhard Meinel*
Affiliation:
Astrophysikalisches Observatorium Potsdam, O-1560 Potsdam, Fed. Rep. of Germany

Abstract

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A local potential approach to nonlinear dynamo models which allows the use of variational techniques to investigate the problem of stability is introduced. The method applies at least to quasi-kinematic dynamo models, i.e. to models which include the back-reaction of the magnetic field on the fluid motion in a simplified way. A special application leads to a previously investigated one-dimensional dynamo model which shows a coexistence of a periodic solution (limit cycle) with two stable steady solutions of opposite polarities. The inclusion of some small-amplitude noise leads to interesting transition phenomena which may be of relevance to explain the behaviour of astrophysical dynamos. A simple dynamical system with a two-dimensional phase-space is used for illustration.

Type
Part II Current stellar dynamo theory
Information
International Astronomical Union Colloquium , Volume 130: The Sun and Cool Stars: activity, magnetism, dynamos , 1991 , pp. 103 - 111
Copyright
Copyright © Springer-Verlag 1991

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