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arXiv · 0911.4465

Dynamo Onset as a First-Order Transition: Lessons from a Shell Model for Magnetohydrodynamics

Ganapati Sahoo·Dhrubaditya Mitra·Rahul Pandit
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Abstract

We carry out systematic and high-resolution studies of dynamo action in a shell model for magnetohydrodynamic (MHD) turbulence over wide ranges of the magnetic Prandtl number $Pr_{\rm M}$ and the magnetic Reynolds number $Re_{\rm M}$. Our study suggests that it is natural to think of dynamo onset as a nonequilibrium, first-order phase transition between two different turbulent, but statistically steady, states. The ratio of the magnetic and kinetic energies is a convenient order parameter for this transition. By using this order parameter, we obtain the stability diagram (or nonequilibrium phase diagram) for dynamo formation in our MHD shell model in the $(Pr^{-1}_{\rm M}, Re_{\rm M})$ plane. The dynamo boundary, which separates dynamo and no-dynamo regions, appears to have a fractal character. We obtain hysteretic behavior of the order parameter across this boundary and suggestions of nucleation-type phenomena.

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Ganapati Sahoo, Dhrubaditya Mitra, Rahul Pandit. 2009-11-23. Dynamo Onset as a First-Order Transition: Lessons from a Shell Model for Magnetohydrodynamics. https://doi.org/10.1103/physreve.81.036317

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