Chaotic flows and kinematic magnetic dynamos: A tutorial review

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Abstract
This paper reviews results on fast kinematic dynamo theory, emphasizing the recent realization that Lagrangian chaos of the underlying flow is the key element for understanding of the problem. Simple models for singular behavior of the magnetic field in the large magnetic Reynolds number limit are described and used to illustrate the tendency for fractal magnetic field distributions with extreme cancellation properties. The relation of ergodic properties of the chaotic flow to properties of the dynamo (e.g., growth rate, fractal dimension) are also discussed.