Recent developments in collisionless reconnection theory: Applications to laboratory and astrophysical plasmas

Recent developments in the theory and simulation of nonlinear collisionless reconnection hold the promise for providing solutions to some outstanding problems in laboratory and astrophysical plasma physics. Examples of such problems are sawtooth oscillations in tokamaks, magnetotail substorms, and impulsive solar and stellar flares. In each of these problems, a key issue is the identification of fast reconnection rates that are insensitive to the mechanism that breaks field lines (resistivity and/or electron inertia). The classical models of Sweet-Parker and Petschek sought to resolve this issue in the realm of resistive magnetohydrodynamics (MHD). However, the plasmas mentioned above are weakly collisional, and hence obey a generalized Ohm's law in which the Hall current and electron pressure gradient terms play a crucial role. Recent theoretical models and simulations on impulsive (or triggered) as well as quasi-steady reconnection governed by a generalized Ohm's law are reviewed. In the impulsive reconnection problem, not only is the growth rate fast but the time-derivative of the growth rate changes rapidly. In the steady-state reconnection problem, explicit analytical expressions are obtained for the geometric characteristics (that is, length and width) of the reconnection layer and the reconnection rate. Analytical results are tested by Hall MHD simulations. While some of the geometric features of the reconnection layer and the weak dependence of the reconnection rate on resistivity are reminiscent of Petschek's classical model, the underlying wave and particle dynamics mediating the reconnection dynamics in the presence of the Hall current and electron pressure gradient are qualitatively different. Quantitative comparisons are made between theory and observations. Open and unresolved issues are identified.