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Thermodynamics of MHD flows with axial symmetry

Nicolas Leprovost·Pierre-Henri Chavanis·Berengere Dubrulle
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Abstract

We present strategies based upon extremization principles, in the case of the axisymmetric equations of magnetohydrodynamics (MHD). We study the equilibrium shape by using a minimum energy principle under the constraints of the MHD axisymmetric equations. We also propose a numerical algorithm based on a maximum energy dissipation principle to compute in a consistent way the equilibrium states. Then, we develop the statistical mechanics of such flows and recover the same equilibrium states giving a justification of the minimum energy principle. We find that fluctuations obey a Gaussian shape and we make the link between the conservation of the Casimirs on the coarse-grained scale and the process of energy dissipation.

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Nicolas Leprovost, Pierre-Henri Chavanis, Berengere Dubrulle. 2004-07-05. Thermodynamics of MHD flows with axial symmetry. https://doi.org/10.1103/physreve.71.036311

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