Abstract
Motivated by the problem of the origin of astrophysical magnetic fields, we introduce two concepts. The first is that of a dynamo, i.e., a dynamo that can organize magnetic fields on the scale of the astrophysical object. The second is that of an essentially nonlinear dynamo. This is a dynamo which relies on a velocity driven by magnetic forces and/or magnetic instabilities. We construct a simple framework that can be used to study such dynamos and give examples in which the evolution is such to generate a system-scale field. We argue that this framework provides a valuable complementary approach to the more conventional studies based on kinematic mean-field dynamo theory.
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