Analytical solutions of the nonlinear force-free magnetic field equations

Details Analytical solutions of the nonlinear force-free magnetic field equations Analytical solutions of the nonlinear force-free magnetic field equations

Jan 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991a%26a...241..646c&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 241, no. 2, Jan. 1991, p. 646-655.

Astronomy and Astrophysics

Astrophysics

9

Force-Free Magnetic Fields, Magnetic Field Configurations, Solar Magnetic Field, Cylindrical Coordinates, Nonlinear Equations, Solar Corona, Stellar Models

Scientific paper

The paper develops an analytical method for solving nonlinear force-free magnetic field equations in the nonaxisymmetric case. This is done by performing the necessary calculations in an orthogonal system of coordinates in which one of the coordinates (e.g., u1) is taken along the local gradient of the scalar function alpha(r). Thus, alpha = alpha(u1) and B1 = 0, and equations for only the field components B2 and B3 have to be solved. Nonaxisymmetric solutions are obtained and examined. The analytical solutions obtainable by the proposed method can provide test cases for numerical methods designed to extrapolate magnetic fields above solar active regions.

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