QUASI-SEPARATRIX LAYERS IN SOLAR-FLARES .1. METHOD

Magnetic reconnection is usually thought to be linked to the presence of magnetic null points and to be accompanied by the transport of magn etic field lines across separatrices, the set of field lines where the mapping of field lines is discontinuous. In view of the variety of ob served flaring configurations, we show that this view is too restricti ve. Instead, Priest and Demoulin (1995) have explored a way of general ising the concept of separatrices to magnetic configurations without f ield-line linkage discontinuities. They propose that magnetic reconnec tion may also occur in 3D in the absence of null points at ''quasi-sep aratrix layers'' (QSLs), which are regions where there is drastic chan ge in field-line linkage. In previous studies we have shown that solar flare kernels are linked to the topology of the active-region magneti c field. The observed photospheric field was extrapolated to the coron a using subphotospheric magnetic sources and the topology was defined by the magnetic linkage between these sources, the method being called SM (for Source Method). In this paper we define a new method, called QSLM (for Quasi-Separatrix Layers Method), which finds the location of QSLs above the photosphere. It is designed to be applied to any kind of magnetic field representation, while, in the present paper, we appl y it only to simple theoretical magnetic configurations in order to co mpare it with the SM. It generalises the concept of separatrices to ma gnetic configurations without field-line linkage discontinuities. The QSLM determines elongated regions that are in general located along sm all portions of the separatrices defined by the SM, and in the limit o f very concentrated photospheric fields both methods give the same res ult. In bipolar magnetic configurations two QSLs are found at both sid es of the inversion line, while in quadrupolar configurations four app ear. We find that there is a wide range for the thickness of the QSLs, which is determined by the character (bipolar or quadrupolar) of the magnetic region and by the sizes of the photospheric field concentrati ons. We then show that smooth photospheric motions induce concentrated currents at the locations defined by the QSLM. We prove this only for initially potential configurations but, due to the form of the equati ons, we conjecture that it is also valid for any kind of initial magne tic equilibrium. We conclude that, even in bipolar configurations, the re are localized places where current build-up can be induced by photo spheric motions, leading to ideal MHD breakdown with strong flows and magnetic energy release.