  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 time. This technique is extended here so as to
analyze the evolution of magnetic structure. Such a generalization is made with
the help of new dimensionless quantities called "slip-squashing factors". Their
large values define the surfaces that border the reconnected or
to-be-reconnected magnetic flux tubes for a given period of time during the
magnetic evolution. The proposed method is universal, since it assumes only
that the time sequence of evolving magnetic field and the tangential boundary
flows are known. The application of the method is illustrated for simple
examples, one of which was considered previously by Hesse and coworkers in the
framework of the general magnetic reconnection theory. The examples help us to
compare these two approaches; they reveal also that, just as for magnetic null
points, hyperbolic and cusp minimum points of a magnetic field may serve as
favorable sites for magnetic reconnection. The new method admits a
straightforward numerical implementation and provides a powerful tool for the
diagnostics of magnetic reconnection in numerical models of solar-flare-like
phenomena in space and laboratory plasmas.
