In this chapter we look at two theories for time-dependent reconnection that are not as well known as the tearing mode. The first of these is X-type collapse, which was first considered by Dungey (1953) and has been briefly described in Section 2.1. The second is the time-dependent, Petschek-type theory developed by Semenov et al. (1983a). Both theories provide new perspectives on reconnection because they describe behaviour which is not encompassed within the scope of either the steady-state or tearing-mode theories.

X-Type Collapse

Dungey's (1953) work on X-type collapse is the earliest analysis ever done on magnetic reconnection and predates both the tearing-mode (Furth et al., 1963) and the Sweet–Parker (1958) theories. Dungey considered what happens when a small, but uniform, current perturbation is imposed at a current-free X-line (i.e., an X-point in any intersecting plane). Before the current is imposed, the separatrices are at right angles to one another, but after the current is added the separatrices scissor, as shown in Figure 7.1. Assuming that the plasma pressure in a strongly magnetized plasma can be ignored, Dungey argued that the initial perturbation would grow with time and rapidly lead to the formation of a current sheet at the X-line. Cowling (1953) objected that the growth of the current density would violate Lenz's Law, but this was eventually resolved by Dungey (1958), who pointed out the role of the v × B term in the evolution of the plasma.