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Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics

Part of: PLA Tribute to V D Shafranov: 1929-2014

Published online by Cambridge University Press:  27 November 2015

R. L. Dewar Open the ORCID record for R. L. Dewar [Opens in a new window] ,
Z. Yoshida ,
A. Bhattacharjee  and
S. R. Hudson
R. L. Dewar*
Affiliation:
Centre for Plasmas and Fluids, Research School of Physics and Engineering, The Australian National University, Canberra, ACT 2601, Australia
Z. Yoshida
Affiliation:
Graduate School of Frontier Sciences, University of Tokyo, Kashiwa, Chiba 277-8561, Japan
A. Bhattacharjee
Affiliation:
Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, NJ 08543, USA
S. R. Hudson
Affiliation:
Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, NJ 08543, USA
*
†Email address for correspondence: [email protected]
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Abstract

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.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 6 , December 2015 , 515810604
Copyright
© Cambridge University Press 2015 

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