Helicity and celestial magnetism

This informal article discusses the central role of magnetic and kinetic helicity in relation to the evolution of magnetic fields in geophysical and astrophysical contexts. It is argued that the very existence of magnetic fields of the intensity and scale observed is attributable in large part to the chirality of the background turbulence or random-wave field of flow, the simplest measure of this chirality being non-vanishing helicity. Such flows are responsible for the generation of large-scale magnetic fields which themselves exhibit magnetic helicity. In the geophysical context, the turbulence has a 'magnetostrophic' character in which the force balance is primarily that between buoyancy forces, Coriolis forces and Lorentz forces associated with the dynamo-generated magnetic field; the dominant nonlinearity here arises from the convective transport of buoyant elements erupting from the 'mushy zone' at the inner core boundary. At the opposite extreme, in a highly conducting low-density plasma, the near-invariance of magnetic field topology (and of associated helicity) presents the challenging problem of 'magnetic relaxation under topological constraints', of central importance both in astrophysical contexts and in controlled-fusion plasma dynamics. These problems are reviewed and open issues, particularly concerning saturation mechanisms, are reconsidered.