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.
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