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Eigenvalue problems for Beltrami fields arising in a three-dimensional toroidal magnetohydrodynamic equilibrium problem

Phys. Plasmas 14, 052505 (2007); doi:10.1063/1.2722721

Published 11 May 2007

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S. R. Hudson
Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543

M. J. Hole and R. L. Dewar
Department of Theoretical Physics and Plasma Research Laboratory, Research School of Physical Sciences and Engineering, The Australian National University, ACT 0200 Australia
A generalized energy principle for finite-pressure, toroidal magnetohydrodynamic (MHD) equilibria in general three-dimensional configurations is proposed. The full set of ideal-MHD constraints is applied only on a discrete set of toroidal magnetic surfaces (invariant tori), which act as barriers against leakage of magnetic flux, helicity, and pressure through chaotic field-line transport. It is argued that a necessary condition for such invariant tori to exist is that they have fixed, irrational rotational transforms. In the toroidal domains bounded by these surfaces, full Taylor relaxation is assumed, thus leading to Beltrami fields [del]×B=lambdaB, where lambda is constant within each domain. Two distinct eigenvalue problems for lambda arise in this formulation, depending on whether fluxes and helicity are fixed, or boundary rotational transforms. These are studied in cylindrical geometry and in a three-dimensional toroidal region of annular cross section. In the latter case, an application of a residue criterion is used to determine the threshold for connected chaos. ©2007 American Institute of Physics
History: Received 20 September 2006; accepted 15 March 2007; published 11 May 2007
Permalink: http://link.aip.org/link/?PHPAEN/14/052505/1
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KEYWORDS and PACS

Keywords
PACS
  • 52.55.Tn
    Ideal and resistive plasma MHD modes; kinetic modes
  • 52.30.Cv
    Plasma magnetohydrodynamics including electron magnetohydrodynamics
  • 52.25.Gj
    Plasma fluctuation and chaos phenomena
  • 52.25.Fi
    Plasma transport properties
  • 52.40.Hf
    Plasma–material interactions; boundary layer effects
  • YEAR: 2007

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ISSN:
1070-664X (print)   1089-7674 (online)
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