Non-axisymmetric magnetostatic equilibrium

Details Non-axisymmetric magnetostatic equilibrium Non-axisymmetric magnetostatic equilibrium

Mar 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983soph...83..195h&link_type=abstract

Solar Physics (ISSN 0038-0938), vol. 83, March 1983, p. 195-205.

Physics

17

Equilibrium Equations, Magnetic Flux, Magnetostatic Fields, Perturbation Theory, Solar Magnetic Field, Sunspots, Boundary Conditions, Boundary Value Problems, Cauchy Problem, Hyperbolic Differential Equations

Scientific paper

The structural properties of a sunspot-like magnetic flux tube which lacks perfect axisymmetry is examined. The flux tube is assumed to be in static equilibrium with an atmosphere in a uniform gravity. The equations for the first order non-axisymmetric part of the equilibrium are obtained in spherical coordinates and these first order equations are reduced to a linear second order hyperbolic partial differential equation in the r-z plane. It is shown that whereas Cauchy type boundary conditions are appropriate for hyperbolic equations, physical considerations dictate the specification of boundary conditions on a closed curve for this problem. Three analytically soluble cases are presented to illustrate the construction of solutions to this boundary value problem in which the zero-order axisymmetric equilibria are chosen to have magnetic field geometry of different complexities.

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