Simulation study of magnetic reconnection in high magnetic Reynolds number plasmas

Magnetic reconnection is an important process for dynamics in space and laboratory plasmas. Magnetic reconnection is basically dominated by magnetic diffusion at thin current sheet as proposed by Sweet (1958) and Parker (1963). According to their theory, the reconnection rate must be inversely proportional to the square root of the magnetic Reynolds number (S). In magnetosphere and the solar corona, however, in spite of high magnetic Reynolds number (>10^12), reconnection rate is measured to be about 10^-2 that is much higher than the Sweet and Parker's prediction. Although Petschek proposed that the slow mode shock may accelerate reconnection, numerical simulations suggested that the Petschek's type reconnection cannot be sustained with uniform resistivity. On the other hand, it is pointed out that in high magnetic Reynolds number, the thin current sheet becomes unstable to the so-called secondary tearing instability, which generates many plasmoids and drives a sort of fast reconnection. Although Baty (2012) recently investigated the possibility of Petschek-like structure in relatively high-S (~10^4) regime, it is still unclear whether and how the magnetic reconnection is able to be accelerated in higher-S regime (S>10^5). In this paper, we developed the high-resolution magnetohydrodynamics (MHD) simulation of magnetic reconnection for very high-S (S~10^4-10^6) aiming at revealing the acceleration mechanism of magnetic reconnection. We applied the HLLD Riemann solver, which was developed by Miyoshi and Kusano (2005), to the high resolution two-dimensional MHD simulation of current sheet dynamics. In our model, the initial state is given by the Harris sheet equilibrium plus perturbation. As a result, in the case for S=10^5, multiple X-line reconnection appears as a result of the secondary tearing instability and magnetic reconnection is accelerated through the formation of multiple magnetic islands as pointed out by the previous studies. Furthermore, we found that the electric current sheets between some particular magnetic islands bifurcate to V-shape current layers and that the reconnection at the apex of bifurcated current layers is preferentially accelerated. In the case for S = 10^6, it is shown that the bifurcated current layers create slow mode shocks which more accelerate the reconnection rate up to about 0.05. The slow mode shocks are not stationary. They are repeatedly created and dissolved corresponding to the formation and transportation of magnetic islands. These results indicate that, even though resistivity is uniform, when the magnetic Reynolds number increases higher than 10^6, the multiple X-line reconnection of Sweet-Parker current sheets is switched to a new regime called 'dynamical Petschek's type reconnection', in which the slow mode shocks are repeatedly created and accelerate reconnection.