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A general metriplectic framework with application to dissipative extended magnetohydrodynamics

Part of: Hamiltonian Methods in Plasma Physics

Published online by Cambridge University Press:  19 May 2020

Baptiste Coquinot Open the ORCID record for Baptiste Coquinot [Opens in a new window]  and
Philip J. Morrison Open the ORCID record for Philip J. Morrison [Opens in a new window]
Baptiste Coquinot*
Affiliation:
Département de Physique, École Normale Supérieure, 24 rue Lhomond, 75005, Paris, France
Philip J. Morrison*
Affiliation:
Department of Physics and Institute for Fusion Studies, University of Texas at Austin, 2515 Speedway, Austin, TX 78712, USA
*
†Email addresses for correspondence: baptiste.coquinot@ens.fr, morrison@physics.utexas.edu
†Email addresses for correspondence: baptiste.coquinot@ens.fr, morrison@physics.utexas.edu
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Abstract

General equations for conservative yet dissipative (entropy producing) extended magnetohydrodynamics are derived from two-fluid theory. Keeping all terms generates unusual cross-effects, such as thermophoresis and a current viscosity that mixes with the usual velocity viscosity. While the Poisson bracket of the ideal version of this model has already been discovered, we determine its metriplectic counterpart that describes the dissipation. This is done using a new and general thermodynamic point of view to derive dissipative brackets, a means of derivation that is natural for understanding and creating dissipative dynamics without appealing to underlying kinetic theory orderings. Finally, the formalism is used to study dissipation in the Lagrangian variable picture where, in the context of extended magnetohydrodynamics, non-local dissipative brackets naturally emerge.

Keywords

plasma dynamics
Type
Research Article
Information
Journal of Plasma Physics , Volume 86 , Issue 3 , June 2020 , 835860302
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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