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Non-axisymmetric magnetostatic equilibrium

I. A perturbation theory

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Abstract

This paper considers the structural properties of a sunspot-like magnetic flux tube which lacks perfect axisymmetry. The flux tube is taken to be in static equilibrium with an atmosphere in a uniform gravity. Assuming the departure from axisymmetry to be slight, the equations for the first order non-axisymmetric part of the equilibrium are derived in cylindrical coordinates. These first order equations reduce to a linear second order hyperbolic partial differential equation in the r-z plane. Whereas Cauchy type boundary conditions are appropriate for hyperbolic equations, physical considerations dictate the specification of boundary conditions on a closed surve for our problem of interest. The construction of solutions to this boundary value problem is illustrated with three analytically soluble cases, where the zero-order axisymmetric equilibria are chosen to have magnetic field geometry of different complexity. A physical discussion of the results is given.

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Authors and Affiliations

  1. High Altitude Observatory, National Center for Atmospheric Research, U.S.A.

    W. R. Hu, Y. Q. Hu & B. C. Low

Authors
  1. W. R. Hu
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  2. Y. Q. Hu
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  3. B. C. Low
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Additional information

On leave from the Institute of Mechanics, Academia Sinica, Beijing, China.

On leave from the University of Science and Technology, China.

The National Center for Atmospheric Research is supported by the National Science Foundation.

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Hu, W.R., Hu, Y.Q. & Low, B.C. Non-axisymmetric magnetostatic equilibrium. Sol Phys 83, 195–205 (1983). https://doi.org/10.1007/BF00148274

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  • DOI: https://doi.org/10.1007/BF00148274

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