Instabilities of Toroidal Magnetic Fields

  1. D. E. Smylie and
  2. Raymond Hide
  1. David R. Fearn

Published Online: 29 MAR 2013

DOI: 10.1029/GM046p0129

Structure and Dynamics of Earth's Deep Interior

Structure and Dynamics of Earth's Deep Interior

How to Cite

Fearn, D. R. (2013) Instabilities of Toroidal Magnetic Fields, in Structure and Dynamics of Earth's Deep Interior (eds D. E. Smylie and R. Hide), American Geophysical Union, Washington, D. C.. doi: 10.1029/GM046p0129

Author Information

  1. Department of Mathematics, University Of Glasgow, University Gardens, Glasgow, G12 8QW, UK

Publication History

  1. Published Online: 29 MAR 2013
  2. Published Print: 1 JAN 1988

ISBN Information

Print ISBN: 9780875904504

Online ISBN: 9781118666562



  • Earth—Core—Congresses;
  • Geodynamics—Congresses


Why are we interested in the stability of toroidal magnetic fields in rapidly rotating systems? To answer this question we begin by reviewing the geophysical background to the problem and discuss the constraints that magnetic instabilities may impose on the strength and configuration of planetary magnetic fields. Instabilities may also play a role in the geomagnetic secular variation and in reversals. We introduce a simple mathematical model and show that the various instabilities that have been found can be understood simply. The most important fall into one of two classes: ideal or resistive. We discuss the conditions required for instability, the instability timescale, and various characteristic features of each class. In the literature, several other instabilities have been identified. We propose that they may all be understood in the following manner. The effect of rotation on the ideal instability is stabilising. If some effect can be found to counteract the rotational constraint, then instability may arise. Destabilising ingredients are found to include stratification, fluid inertia, viscosity, and an axial magnetic field.