An explanation for the "switch-on'' nature of magnetic energy release and its application to coronal heating

A large class of coronal heating theories postulate that the random mixing of magnetic footpoints by photospheric motions leads to the formation of current sheets in the corona and, consequently, to energy release there via magnetic reconnection. Parker pointed out that in order for this process to supply the observed energy flux into the corona, the stress in the coronal magnetic field must have a fairly specific value at the time that the energy is released. In particular, he argued that the misalignment between reconnecting flux tubes must be roughly 30 degrees in order to match the observed heating. No physical origin for this number was given, however. In this paper we propose that secondary instability is the mechanism that "switches on" the energy release when the misalignment angle in the corona reaches the correct value. We calculate both the three-dimensional linear and fully nonlinear development of the instability in current sheets corresponding to various misalignment angles. We find that no secondary instability occurs for angles less than about 45 degrees, but for larger angles the instability grows at a rapid rate, and there is an explosive release of energy. We compare our results with the observed properties of the corona and discuss the implications for future observations.