Effectiveness of Cyclonic Convection for Producing the Geomagnetic Field

The dynamo equations for the production of astrophysical magnetic fields are solved for a spherical shell of shear and two axisymmetric rings of cyclonic convective cells. The infinite series arising in the stationary eigenvalue problem is converted to a definite integral which is evaluated numerically so that the convergence of the eigenvalue is explicit. The results of the calculations show that, for the fluid dynamics expected in the Earth's core, dipolelike fields can be maintained with any locations of the rings of cyclones, although convective cells at midlatitudes are most efficient. Quadrupole-like fields are maintained only by high-latitude cyclones and generally require more vigorous fluid motions.