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The study of magnetic connectivity in the solar corona reveals a need to generalize the field line mapping technique to arbitrary geometry of the boundaries and systems of coordinates. Indeed, the global description of the connectivity in the corona requires the use of the photospheric and solar wind boundaries. Both are closed surfaces and therefore do not admit a global regular system of coordinates. At least two overlapping regular systems of coordinates for each of the boundaries are necessary in this case to avoid spherical-pole-like singularities in the coordinates of the footpoints. This implies that the basic characteristic of magnetic connectivity - the squashing degree or factor $Q$ of elemental flux tubes (Titov et al., 2002) - must be rewritten in covariant form. Such a covariant expression of $Q$ is derived in this work. The derived expression is very flexible and highly efficient for describing the global magnetic connectivity in the solar corona. In addition, a general expression for a new characteristic $Q_perp$ which defines a squashing of the flux tubes in the directions perpendicular to the field lines is determined. This new quantity makes it possible to filter out the quasi-separatrix layers whose large values of $Q$ are caused by a projection effect at the field lines nearly touching the photosphere. Thus, the value $Q_perp$ provides a much more precise description of the volumetric properties of the magnetic field structure. The difference between $Q$ and $Q_perp$ is illustrated by comparing their distributions for two configurations, one of which is the Titov-Demoulin (1999) model of a twisted magnetic field.
A general method for describing magnetic reconnection in arbitrary three-dimensional magnetic configurations is proposed. The method is based on the field-line mapping technique previously used only for the analysis of magnetic structure at a given t
In the present work we study evolution of magnetic helicity in the solar corona. We compare the rate of change of a quantity related to the magnetic helicity in the corona to the flux of magnetic helicity through the photosphere and find that the two
By defining an appropriate field line helicity, we apply the powerful concept of magnetic helicity to the problem of global magnetic field evolution in the Suns corona. As an ideal-magnetohydrodynamic invariant, the field line helicity is a meaningfu
Two of the most widely observed and yet most puzzling features of the Suns magnetic field are coronal loops that are smooth and laminar and prominences/filaments that are strongly sheared. These two features would seem to be quite unrelated in that t
Understanding many physical processes in the solar atmosphere requires determination of the magnetic field in each atmospheric layer. However, direct measurements of the magnetic field in the Suns corona are difficult to obtain. Using observations wi