Evolving force-free magnetic fields. IV - A variational formulation of the problem

Details Evolving force-free magnetic fields. IV - A variational formulation of the problem Evolving force-free magnetic fields. IV - A variational formulation of the problem

Sep 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978apj...224..668l&link_type=abstract

Astrophysical Journal, Part 1, vol. 224, Sept. 1, 1978, p. 668-670.

Astronomy and Astrophysics

Astrophysics

10

Force-Free Magnetic Fields, Photosphere, Solar Magnetic Field, Stellar Models, Variational Principles, Astronomical Models, Boundary Value Problems, Magnetohydrodynamics

Scientific paper

A theoretical model of evolving force-free magnetic fields is reformulated by taking the distribution of photospheric footpoints as the starting point of the model. A previously considered case of two-dimensional geometry is treated, and the equations for the force-free fields above the photosphere are derived from a variational principle. It is shown that the approach adopted leads to a formidable nonlinear boundary-value problem and that the physical relationship between photospheric footpoint motions and magnetic-field evolution can be more fruitfully investigated by using the original formulation in which the starting point is to take as given the value of the longitudinal field and a transverse field at the photosphere. The questions of the existence and uniqueness of the solution to the nonlinear boundary-value problem are briefly considered.

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