A method of self-consistent three-dimensional solution of the magnetohydrostatic equations using magnetogram data

Abstract

A technique is proposed for constructing three-dimensional solutions comlplying with the self-consistent magnetohydrostatic (MHS) equations and with observations along the line of sight of the magnetic field at the photosphere. The technique is a generalization of a paper Rudenko, {\tt arXiv:astro-ph/0004222} to a potential-field approximation. The solution of the problem under consideration leans a representation of the magnetic field in terms of a scalar function, with its subsequent harmonic expansion in terms of a spherical functional basis that satisfies specified boundary conditions. A numerical realization of the proposed method is expected to permit a real-time modelling of three-dimensional magnetic field, temperature, pressure and density distributions.