Oscillating alpha-square dynamos

A simple way to interpretate the reversal mechanism of the Earth's magnetic field has been achieved in theoretical models based on the interplay between very few magnetic modes.

Motivated by the temporal behavior of elementary multipolar components of the Earth's magnetic field during the last reversal 780ka ago, (Leonhardt & Fabian 2007) the possibility of interacting magnetic modes is examined in a simple mean field model.

Field modes that are suitable canditates to be involved in the reversal process are oscillating eigenfunctions of the linear eigenvalue problem for geodynamo models of alpha² type.

Regarding the spectrum of the dynamo operator time-dependent solutions arise at so called exceptional points where two stationary modes merge and continue at a single oscillating eigenfunction. In the present model this behavior essentially involves dipolar and octupolar modes. The spectrum exhibits further time-dependent modes of higher order that appear at coupling points of different radial field modes.

In order to couple odd ("dipolar-like") and even ("quadrupolar-like") modes equatorial symmetry breaking is required. However, instead of oscillating eigenfunctions an equatorial asymmetry results in stationary hemispherical dynamos. This behavior can be explained by the approximate dipole-quadrupole degeneration for the unperturbed problem.

More complicated scenarios occur in case of (more realistic) anisotropies of alpha- and beta-effect or through non-linearities caused by the backreaction of the magnetic field (magnetic quenching).