2D Numerical Simulation of the Resistive Reconnection Layer

Magnetic reconnection is of great interest in many space and laboratory plasmas [1,2], and has been studied extensively for more than four decades. The most important question is that of the reconnection rate. The process of magnetic reconnection, is so complex, however, that this question is still not completely resolved, even within the simplest possible canonical model: twodimensional (2D) incompressible resistive magnetohydrodynamics (MHD) with uniform resistivity η in the limit of S →∞ (where S = VAL/η is the global Lundquist number, L being the half-length of the reconnection layer). Historically, there were two drastically different estimates for the reconnection rate: the Sweet–Parker model [3,4] gave a rather slow reconnection rate (ESP ∼ S−1/2), while the Petschek [5] model gave any reconnection rate in the range from ESP up to the fast maximum Petschek rate EPetschek ∼ 1/ logS. Up until the present it was still unclear whether Petschek-like reconnection faster than Sweet–Parker reconnection is possible. Biskamp’s simulations [11] are very persuasive that, in resistive MHD, the rate is generally that of Sweet–Parker. Still, his simulations are for S in the range of a few thousand, and his boundary conditions are somewhat tailored to the reconnection rate he desires, the strength of the field and the length of layer adjusting to yield the Sweet–Parker rate. Thus, a more systematic boundary layer analysis is desirable to really settle the question.