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Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics

Published online by Cambridge University Press:  27 November 2015

R. L. Dewar*
Centre for Plasmas and Fluids, Research School of Physics and Engineering, The Australian National University, Canberra, ACT 2601, Australia
Z. Yoshida
Graduate School of Frontier Sciences, University of Tokyo, Kashiwa, Chiba 277-8561, Japan
A. Bhattacharjee
Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, NJ 08543, USA
S. R. Hudson
Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, NJ 08543, USA
Email address for correspondence:


Ideal magnetohydrodynamics (IMHD) is strongly constrained by an infinite number of microscopic constraints expressing mass, entropy and magnetic flux conservation in each infinitesimal fluid element, the latter preventing magnetic reconnection. By contrast, in the Taylor relaxation model for formation of macroscopically self-organized plasma equilibrium states, all these constraints are relaxed save for the global magnetic fluxes and helicity. A Lagrangian variational principle is presented that leads to a new, fully dynamical, relaxed magnetohydrodynamics (RxMHD), such that all static solutions are Taylor states but also allows state with flow. By postulating that some long-lived macroscopic current sheets can act as barriers to relaxation, separating the plasma into multiple relaxation regions, a further generalization, multi-region relaxed magnetohydrodynamics (MRxMHD) is developed.

Research Article
© Cambridge University Press 2015 

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