Topological classification of global magnetic fields in the solar corona
Numerous magnetic fragments in the interior of the Sun give rise to many interesting energy processes in the solar corona, for example solar flares and prominences. Magnetic charge topology explains these phenomena by appearance and disappearance of heteroclinic trajectories (separators) --- magnetic lines that belong to an intersection of stable and unstable invariant two-dimensional manifolds (fans) of different saddle singularities (nulls). Separators are the locations in the magnetic field configuration where the magnetic energy is transferred from one region (a connected component into which the fans divide the solar corona) to another. Many recent papers has gone into investigation of the configurations that arise in different concrete models. In the present paper we solve the problem of interrelation between existence of separators of any given magnetic field in the Solar corona and the type and the number of saddle singularities and charges. Following the classical definition we introduce the concept of equivalence of two magnetic fields and get a classification of such fields up to topological equivalence.