An Explosive Scaling Law for Nonlinear Magnetic Reconnection and Its Insensitivity to Microscopic Scales’⁰

The nonlinear phase of magnetic reconnection is investigated by numerically solving a gyrofluid model. The scaling law for the explosive reconnection rate, which has been recently derived for an ideal two-fluid model [Hi-rota et al., Phys. Plasmas 22, 052114 (2015)], is found to consistently hold when either the ion-sound gyroradius ρ_S or the ion gyroradius ρ_i is comparable to the electron skin depth d_e, even in the presence of finite resistivity η. In this explosive phase, a local X-shaped current layer is spontaneously generated, in which the reconnection speed is closely related to the macroscopic shape of the layer and is almost independent of the layer width. The reconnection speed is therefore insensitive to the size of the microscopic scales, ρ_S, ρ_i, d_e and n. On the other hand, in the cold plasma limit, where ρ_S = ρ_i = 0, the intermittent acceleration of the reconnection speed is caused by the plasmoid instability. This also seems to be explosive on average, but the rate always falls below the explosive scaling law. The reconnection time extrapolated from this scaling law is shown to be fast enough to explain the time scale ofsolar flares.