ИСТИНА

Topology of magnetic field lines is directly involved in magnetohydrodynamic (MHD) theorems and equations. Being an invariant of motion in ideal MHD conditions, the magnetic field-line topology is a natural obstacle to the relaxation of magnetic field into a current-free (potential) eld and contrariwise limits a dynamo generation. Usage of these conservational laws and writing of numerical relations require a quantication of topology. One of the simplest existing measures of magnetic topology is the mutual magnetic helicity, that expresses the combined action of interaction and linkage between different magnetic field lines. For practical purposes there exists the revised concept of relative magnetic helicity, that allows to estimate the complexity of field-line topology in case of open volume, i.e. when magnetic lines cross the boundaries of given 3D region. At the same time this concept remains a simple interpretation of linkage number in terms of individual lines. Our point however is that magnetic helicity is far from being unique or comprehensive quantication of magnetic field-line topology. To improve the situation we introduce a set of higher invariants which extends the idea of relative helicity and provides a new means to describe the magnetic field-line topology. To practically study the possibility of implementation of higher topological invariants we reconstruct several moments of mutual helicity from observed solar vector magnetograms with extrapolated magnetic field above the photosphere and discuss to what extent such knowledge could be instructive for understanding of the solar magnetic field evolution.