When solving partial differential equations, either analytically or numerically, the form, value, and number of the boundary conditions is of crucial importance. Indeed, often much physics is incorporated in the boundary conditions and, in the setting up of a numerical experiment with nonstandard boundary conditions, it is often the implementation of the boundary conditions that causes the most trouble. Petschek's mechanism, in which the boundary conditions at large distances are implicit, has been generalised in two distinct ways by adopting different boundary conditions to give regimes of almost-uniform reconnection (§5.1) and non-uniform reconnection (§5.2). Whereas Petschek's mechanism may be described as being almost-uniform and potential (§4.3), the first of these new families is in general nonpotential and the second is nonuniform. Also, surprisingly late in the day, a theory of linear reconnection was developed, which occurs when the reconnection rate is extremely slow (§5.3).

Almost-Uniform Non-Potential Reconnection

Vasyliunas (1975) clarified the physics of Petschek's mechanism by pointing out that the inflow region has the character of a diffuse fast-mode expansion, in which the pressure and field strength continuously decrease and the flow converges as the magnetic field is carried in. (This characterization of the inflow does not mean that a standing fast-mode wave is present in the inflow, since such a standing wave is not possible in a sub-fast flow.) A fast-mode disturbance has the plasma and magnetic pressure increasing or decreasing together, while a slow-mode disturbance has the plasma pressure changing in the opposite sense to the magnetic pressure.