CALCULATION OF THE LINEAR FORCE-FREE MAGNETIC-FIELD ABOVE A SOLAR ACTIVE-REGION

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 me thods that have been developed allow direct specification of the value s for the field at the nonphotospheric boundaries of the volume. A met hod that allowed for this would make it possible to study the influenc e of lateral boundary conditions on the solution inside the volume of interest, and to use a priori information about the field in the coron a. Here, an algorithm is presented for calculation of the linear force -free field in a limited volume (in the shape of a parallelepiped, Ome ga) using the distribution of the B-z component of the field at all bo undaries of Omega and the distribution of B-x and B-y in the frame mad e up by the intersection of a lateral surface of Omega and a single ar bitrarilychosen plane z = const. The algorithm is verified using a num erical model, permitting calculation of the linear force-free field of a dipole in a half-space using exact formulas. The rms deviation of t he 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 th e volume Omega leads to a substantial change in the resulting magnetic configuration.