Aspects of three-dimensional magnetic reconnection (Invited review)

In this review paper we discuss several aspects of magnetic reconnection th eory, focusing on the field-line motions that are associated with reconnect ion. A new exact solution of the nonlinear MHD equations for reconnective a nnihilation is presented which represents a two-fold generalization of the previous solutions. Magnetic reconnection at null points by several mechani sms is summarized, including spine reconnection, fan reconnection and separ ator reconnection, where it is pointed out that two common features of sepa rator reconnection are the rapid flipping of magnetic field lines and the c ollapse of the separator to a current sheet. In addition, a formula for the rate of reconnection between two flux tubes is derived. The magnetic field of the corona is highly complex, since the magnetic carpet consists of a m ultitude of sources in the photosphere. Progress in understanding this comp lexity may, however, be made by constructing the skeleton of the field and developing a theory for the local and global bifurcations between the diffe rent topologies. The eruption of flux from the Sun may even sometimes be du e to a change of topology caused by emerging flux break-out. A CD-ROM attac hed to this paper presents the results of a toy model of vacuum reconnectio n, which suggests that rapid flipping of field lines in fan and separator r econnection is an essential ingredient also in real non-vacuum conditions. In addition, it gives an example of binary reconnection between a pair of u nbalanced sources as they move around, which may contribute significantly t o coronal heating. Finally, we present examples in TRACE movies of geometri cal changes of the coronal magnetic field that are a likely result of large -scale magnetic reconnection.