Modeling solar force-free magnetic fields

A class of nonlinear force-free magnetic fields is presented, described in terms of the solutions to a second-order, nonlinear ordinary differential equation. These magnetic fields are three-dimensional, filling the infinite half-space above a plane where the lines of force are anchored. They model...

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Bibliographic Details
Published inThe Astrophysical journal Vol. 352; no. 1; pp. 343 - 352
Main Authors LOW, B. C, LOU, Y. Q
Format Journal Article
LanguageEnglish
Published Chicago, IL University of Chicago Press 20.03.1990
Subjects
640104 - Astrophysics & Cosmology- Solar Phenomena
ALGORITHMS
Astronomy
ATMOSPHERES
BOUNDARY-VALUE PROBLEMS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Diameter, figure, rotation, mass
DIFFERENTIAL EQUATIONS
Earth, ocean, space
EQUATIONS
Exact sciences and technology
FORCE-FREE MAGNETIC FIELDS
MAGNETIC FIELDS
MAIN SEQUENCE STARS
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
PARTIAL DIFFERENTIAL EQUATIONS
SOLAR ATMOSPHERE
Solar physics
Solar system
STARS
SUN
VIRIAL THEOREM
Total energy
Magnetohydrodynamics
Differential equation
Digital simulation
Active region
Force free field
Sun
Free energy
Solar flare
Non linear equation
Multipole field
Theoretical model
Solar magnetic field
Electric current
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Summary:A class of nonlinear force-free magnetic fields is presented, described in terms of the solutions to a second-order, nonlinear ordinary differential equation. These magnetic fields are three-dimensional, filling the infinite half-space above a plane where the lines of force are anchored. They model the magnetic fields of the sun over active regions with a striking geometric realism. The total energy and the free energy associated with the electric current are finite and can be calculated directly from the magnetic field at the plane boundary using the virial theorem. In the study of solar magnetic fields with data from vector magnetographs, there is a long-standing interest in devising algorithms to extrapolate for the force-free magnetic field in a given domain from prescribed field values at the boundary. The closed-form magnetic fields of this paper open up an opportunity for testing the reliability and accuracy of algorithms that claim the capability of performing this extrapolation. The extrapolation procedure as an ill-posed mathematical problem is discussed. 22 refs.
ISSN:0004-637X
1538-4357
DOI:10.1086/168541