ABSTRACT
This chapter reviews the topic of fast dynamos, mainly from a numerical point of view. It introduces the history and motivation of the search for fast dynamos and explains the necessity for the flow to be chaotic before a fast dynamo is possible. The chapter also reviews the various numerical experiments which have been mounted to provide evidence that fast dynamos actually exist, and describes the physical processes whereby the field is generated. It provides some of the fast dynamos for which analytic solutions have been found: the flows cheat the chaos by localising it in artificial features outside which piecewise integration is possible, often using asymptotic methods. The chapter addresses what happens when fast dynamos enter the nonlinear regime and the Lorentz force is allowed to limit the growth of the field strength by reacting back on the motion. It summarises the achievements of fast dynamo theory and describes likely areas where further progress.
