Three-dimensional magnetic reconnection without null points 2. Application to twisted flux tubes

Magnetic reconnection has traditionally been associated exclusively with the presence of magnetic null points or field lines tangential to a boundary. However, in many cases introducing a three-dimensional perturbation in a two-and-half-dimensional magnetic configuration implies the disappearance of separatrices. Faced with this structural instability of separatrices when going from two-and-half to three-dimensional configurations, several approaches have been investigated to replace the topological ideas familiar in two-dimensional, but no unanimity has yet emerged on the way reconnection should be defined. While it is true that the field line linkage is continuous in three-dimensional, we show here that extremely thin layers (called quasi-separatrix layers (QSLs)) are present. In these layers the gradient of the mapping of field lines from one part of a boundary to another is very much larger than normal (by many orders of magnitude). Even for highly conductive media these extremely thin layers behave physically like separatrices. Thus reconnection without null points can occur in QSLs with a breakdown of ideal MHD and a change in connectivity of plasma elements. We have analyzed several twisted flux tube configurations, going progressively from two-and-half to three-dimensional, showing that QSLs are structurally stable features (in contrast to separatrices). The relative thickness w of QSLs depends mainly on the maximum twist; typically, with two turns, w~10^-6, while with four turns, w~10^-12. In these twisted configurations the shape of the QSLs, at the intersection with the lower planar boundary, is typical of the two ribbons observed in two-ribbon solar flares, confirming that the accompanying prominence eruption involves the reconnection of twisted magnetic structures. We conclude that reconnection occurs in three-dimensional in thin layers or QSLs, which generalise the traditional separatrices (related only to magnetic null points or field lines tangential to the boundary).