INTRODUCTION

Many astrophysical bodies possess magnetic fields that arise from dynamo action. The case of the Earth is a unique one because the observational data available are much more detailed for the Earth than for any other astrophysical body, making possible a rather detailed comparison of geodynamo theory with observations. To meet this unique opportunity we therefore need a geodynamo theory that is very detailed. To develop the fully-fledged theory of such a complicated system as the geodynamo, even with the help of modern computers, it is however necessary to possess a qualitative understanding of its structure. This can be achieved by preliminary ‘scouting’ calculations of some artificially simplified models that are much simpler than the full geodynamo model but nevertheless help to understand it. A kinematic dynamo theory is the first step towards this goal. Kinematic models provide us with an understanding of its electrodynamics (the magnetic field generation process). The next necessary step is an understanding of its mechanics. The model-Z geodynamo emerges as a result of this step of scouting calculations. It may be considered as a specific case of a more general model that we call the nonlinear (pseudo-) axisymmetric dynamo model. This is a natural generalisation of the linear, nearly axisymmetric, kinematic dynamo model (Braginsky 1964a, b, c, d), and it is ‘intermediate’ between the kinematic and the complete theories of the geodynamo.

The nonlinear axisymmetric dynamo model aims at understanding the specific features of the main convective flow and the production of axisymmetric field in the core while the field generation due to the non-axisymmetric motion (a-effect) is considered as given. Another direction for an essential ‘intermediate’ investigation is to explore non-axisymmetric magnetoconvection.