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Astron. Astrophys. 325, 847-856 (1997)

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Nonlinear self-consistent three-dimensional arcade-like solutions of the magnetohydrostatic equations

T. Neukirch

School of Mathematical and Computational Sciences, University of St. Andrews, St. Andrews, KY16 9SS, UK (thomas@dcs.st-and.ac.uk)

Received 18 November 1996 / Accepted 15 January 1997

Abstract

Exact self-consistent solutions of the magnetohydrostatic equations in three dimensions with a nonlinear relationship between the magnetic field and the current density are presented. The derivation is carried out in Cartesian coordinates including a constant gravitational force pointing into the negative z-direction. Out of several solution classes only one has an arcade-like magnetic field topology. This solution class is investigated further and two examples are shown for specific choices of the free functions and parameters which the solution class has.

Key words: magnetohydrodynamics – magnetic fields – plasmas – Sun: magnetic fields – Sun: corona – stars: magnetic fields

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© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998

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