A constructing method for a self-consistent three-dimensional solution of the magnetohydrostatic equations using full-disk magnetogram data

A technique is proposed for constructing self-consistent 3-D solutions satisfying the magnetohydrostatic (MHS) equations, and fitting observations along the line of sight of the magnetic field at the photosphere. The technique is a generalization of a potential-field extrapolation method (Rudenko, 2001) using full-disk magnetogram data. The solution of the problem under consideration is based on representing the magnetic field in terms of a scalar function, with its subsequent harmonic expansion in terms of the functional basic set of spherical functions that satisfies the specified boundary conditions. It is expected that a numerical realization of the proposed method will make possible a real-time modeling of the three-dimensional magnetic field, temperature, pressure and density distributions.