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 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, Omega) using the distribution of the B-z component of the field at all boundaries of Omega and the distribution of B-x and B-y in the frame made up by the intersection of a lateral surface of Omega 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 Omega leads to a substantial change in the resulting magnetic configuration.