A study of global magnetic helicity in self-consistent spherical dynamos

Magnetic helicity is a fundamental constraint in both ideal and resistive magnetohydrodynamics. Measurements of magnetic helicity density on the Sun and other stars are used to interpret the internal behaviour of the dynamo generating the global magnetic field. In this note, we study the behaviour of the global relative magnetic helicity in three self-consistent spherical dynamo solutions of increasing complexity. Magnetic helicity describes the global linkage of the poloidal and toroidal magnetic fields (weighted by magnetic flux), and our results indicate that there are preferred states of this linkage. This leads us to propose that global magnetic reversals are, perhaps, a means of preserving this linkage, since, when only one of the poloidal or toroidal fields reverses, the preferred state of linkage is lost. It is shown that magnetic helicity indicates the onset of reversals and that this signature may be observed at the outer surface