Astronomy and Astrophysics – Astrophysics
Scientific paper
Jul 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981a%26a...100..197a&link_type=abstract
Astronomy and Astrophysics, vol. 100, no. 1, July 1981, p. 197-200.
Astronomy and Astrophysics
Astrophysics
200
Chromosphere, Force-Free Magnetic Fields, Solar Corona, Boundary Conditions, Boundary Value Problems, Fast Fourier Transformations, Green'S Functions, Half Spaces, Magnetic Field Configurations
Scientific paper
Consideration is given to the boundary value problem of the determination of the strength and configuration of the magnetic field in the half space above the solar photosphere on the basis of photospheric observations for the case of a force-free magnetic field with constant alpha, a scalar relating the cross product of the currents and the field vectors to the field vector. Solutions are derived in terms of Fourier transforms and extended to regions far from the center of the disk. It is found that the large-scale components of the solutions involve a quasi-periodic variation of the field and current with height, carry infinite energy, and can be completely specified only with observations of a transverse field component at the boundary. The solutions are thus unphysical, however solutions are required for the small-scale solution to satisfy the boundary condition. It is pointed out that although numerical computations based on the fast Fourier transform are about 100 times faster than those based on the Green's function formulation, the use of a rectangular grid may result in important aliasing effects unless the observed field is placed in an array somewhat larger than the observed region.
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