An elementary model of Earth's magnetic field reversals

The Earth's magnetic field undergoes polarity reversals with a mean reversal rate that varies from zero during superchrons to 4 per Myr in the present. Typically, these reversals have a strongly asymmetric shape with a decay time of around 50 kyr and a recreation time of around 5 kyr. Despite the recent successes of three-dimensional fully coupled dynamo models, there is no agreement yet on the basic principle of reversal. We investigate a simple mean-field dynamo model and compare the resulting time series and the phase space trajectories with those of paleomagnetic measurements. In the case of highly supercritical dynamos a very good agreement with recent paleomagnetic data is achieved. We show that the typical reversal dynamics traces back to the spectral properties of non-selfadjoint dynamo operators which exhibit so-called exceptional points where two real eigenvalues coalesce and continue as a complex conjugated pair of eigenvalues. Within this picture we can also explain the observed general tendency of highly supercritical dynamos to self-tune into reversal prone states. We conclude with a speculation on the possible role of the inner core growth for the long term changes
of the reversal rate and for the occurrence of superchrons.