Do plasmoids induce fast magnetic reconnection in well-resolved current sheets in 2D MHD simulations?

Abstract

We investigate the development of tearing-mode instability using the highest-resolution two-dimensional magnetohydrodynamic simulations of reconnecting current sheets performed on a uniform grid, for Lundquist numbers of $10^3 \le S \le 5 \times 10^5$ , reaching up to $65,536^2$ grid cells. We demonstrate a Sweet--Parker scaling of the reconnection rate $V_{\text{rec}} \sim S^{-1/2}$ up to Lundquist numbers $S \sim 10^4$. For larger values of Lundquist number, between $2\times 10^4\le S \le 2 \times 10^5$, plasmoid formation sets in, leading to a slight enhancement of the reconnection rate, $V_{\text{rec}} \sim S^{-1/3}$, consistent with the prediction from linear tearing mode induced reconnection, indicating that reconnection remains resistivity-dependent and therefore slow. In this range of $S$-values, the plasmoids do not undergo a merger cascade, as they are rapidly advected out of the reconnection layer. Only for $S > 2 \times 10^5$, we observe the nonlinear development of the tearing-mode instability, with plasmoid coalescence and a saturation of the reconnection rate at $V_\text{rec} / V_A \sim 0.01$. At such high $S$, however, the corresponding Reynolds number is large, reaching $\text{Re} > 2000$ even on scales comparable to the current-sheet thickness. We therefore conclude that, in astrophysical systems, it is essential to account for the dominant influence of turbulence and three-dimensional effects in the reconnection process.