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Nested toroidal flux surfaces in magnetohydrostatics. Generation via soliton theory

Published online by Cambridge University Press:  25 November 2003

W. K. SCHIEF
Affiliation:
Department of Applied Mathematics, School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia ([email protected])

Abstract

It is shown that the classical magnetohydrostatic equations of an infinitely conducting fluid reduce to the integrable potential Heisenberg spin equation subject to a Jacobian condition if the magnitude of the magnetic field is constant along individual magnetic field lines. Any solution of the constrained potential Heisenberg spin equation gives rise to a multiplicity of magnetohydrostatic equilibria which share the magnetic field line geometry. The multiplicity of equilibria is reflected by the local arbitrariness of the total pressure profile. A connection with the classical Da Rios equations is exploited to establish the existence of associated helically and rotationally symmetric equilibria. As an illustration, Palumbo's ‘unique’ toroidal isodynamic equilibrium is retrieved.

Type
Papers
Copyright
2003 Cambridge University Press

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