Calculation
of the Linear Force-Free Magnetic Field above
a Solar Active Region
V. I. Abramenko
Crimean
Astrophysical Observatory, Ukrainian Academy of Sciences, p/o
Nauchnii, Crimea, 334413 Ukraine
Received September
2, 1996
Abstract—Modeling
of the linear force-free fields above solar active regions is
based on application of either Fourier transforms or Green
functions. The modeling results depend significantly on the a
priori conditions specified for the edges of the volume
studied. However, none of the methods that have been developed
allow direct specification of the values for the field at the
nonphotospheric boundaries of the volume. A method that allowed
for this would make it possible to study the influence of lateral
boundary conditions on the solution inside the volume of
interest, and to use a priori information about the field
in the corona. Here, an algorithm is presented for calculation of
the linear force-free field in a limited volume (in the shape of
a parallelepiped, 
) using the distribution of the Bz
component of the field at all boundaries of and the
distribution of Bx and By
in the frame made up by the intersection of a lateral surface of and a
single arbitrarilychosen plane z = const. The algorithm is
verified using a numerical model, permitting calculation of the
linear force-free field of a dipole in a half-space using exact
formulas. The rms deviation of the calculated and analytical
solutions at each layer along the z axis does not exceed
1%. Exchanging the force-free boundary conditions with the
potential boundary conditions at the nonphotospheric border of
the volume leads to a substantial change in the resulting
magnetic configuration.
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