Three‐dimensional magnetic reconnection without null points: 1. Basic theory of magnetic flipping

Abstract

In two or three dimensions, magnetic reconnection may occur at neutral points and is accompanied by the transport of magnetic field lines across separatrices, the field lines (or flux surfaces in three dimensions) at which the mapping of field lines is discontinuous. Here we show that reconnection may also occur in three dimensions in the absence of neutral points at so-called "quasiseparatrix layers," where there is a steep gradient in field line linkage. Reconnection is a global property, and so, in order to determine where it can occur, the first step is to enclose the volume being considered by a boundary (such as a spherical surface). Then the mapping of field lines from one part of the boundary to another is determined, and quasi-separatrix layers may be identified as regions where the gradient of the mapping or its inverse is very much larger than normal. The most effective measure of the presence of such layers is the norm of the displacement gradient tensor; their qualitative location is robust and insensitive to the particular surface that is chosen. Reconnection itself occurs when there is a breakdown of ideal MHD and a change of connectivity of plasma elements, where the field line velocity becomes larger than the plasma velocity, so that the field lines slip through the plasma. This breakdown can occur in the quasi-separatrix layers with an electric field component parallel to the magnetic field. In three dimensions the electric field E (and therefore the field line velocity vñ) depends partly on the imposed values of E (or v_c) at the boundary and partly on the gradients of the inverse mapping function. We show that the inverse mapping determines the location of the narrow layers where the breakdown of ideal MHD can occur, while the imposed boundary values of vñ determine mainly the detailed flow pattern inside the layers. Thus, in general, E (and therefore v_c) becomes much larger than its boundary values at locations where the gradients of the inverse mapping function are large. An example is given of a sheared X field, where a slow smooth continuous shear flow imposed on the boundary across one quasi-separatrix produces a flipping of magnetic field lines as they slip rapidly through the plasma in the other quasi-separatrix layer. It results in a strong plasma jetting localized in, and parallel to, the separatrix layers.

Three-dimensional magnetic reconnection and its application to solar flares

“…Slipping reconnection Reconnection without a null point but in the presence of a parallel electric field due to the stress of magnetic fields near regions of strong distortions of the magnetic connectivities, was generalised in a series of papers and applied to the understanding of solar flares (see § 2.2). In such a case, magnetic field lines are also seen to flip (Priest & Forbes 1992) or slip (Priest & Démoulin 1995), as they undergo a continuous change of connectivity in the reconnection layer.…”

“…When thin enough, QSLs behave physically as separatrices even though there are no true mathematical discontinuities of the field line mapping. This generalisation to QSLs was introduced by the seminal works of Priest & Démoulin (1995) and Démoulin, Priest & Lonie (1996b). QSLs are defined as regions of space where the connectivity of the magnetic field is drastically changing, while remaining continuous in general.…”

“…Then, reconnection does not need to be associated with magnetic nulls, closed field lines or other singular structures. For magnetic reconnection to occur, there is a need to create a dissipation layer where the electric current density is important: Priest & Démoulin (1995) and Démoulin et al (1996a) added that such regions are created if the magnetic field connectivity is strongly distorted but can still remain continuous.…”

GREGOR observations of a small flare above a sunspot

“…The flare energy originates in the stressed solar magnetic fields and is released by the process of magnetic reconnection (e.g., Priest & Forbes 2000). Newly reconnected magnetic field lines constitute various observed structures, such as flare loops and the erupting flux rope.…”

“…In these cases, the reconnection occurs in the quasi-separatrix layers (QSLs, Priest & Démoulin 1995), which are regions where the magnetic connectivity has strong gradients, but is still continuous. The QSLs thus still constitute "boundaries" between different flux systems.…”