A desire to understand the dynamics of astrophysical and geophysical magnetic fields has led scientists to question the manner in which they are maintained. It seems clear that the only reasonable explanation for the existence of many observed magnetic fields is that of a hydromagnetic dynamo. In this scenario, magnetic field growth occurs via a transfer of kinetic to magnetic energy given a suitable flow and a seed magnetic field. In astrophysical scenarios, the magnetic Reynolds number, Rem, a key parameter in the dynamo problem, is typically huge; for example, Rem ~ 108 in the solar convection zone. Of particular interest, therefore, is (kinematic) dynamo action at large Rem, the so-called fast dynamo because of the fast convective timescale upon which the field is generated. The lifetime of the fast dynamo may be characterized by three distinct phases: growth, saturation, and equilibration, the relationship between which remains unclear. In this paper, we examine velocity and magnetic field structures in the different stages of the dynamo using a family of parameterized flows. In this way, we shed some light on the fundamental workings of the fast dynamo.
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