Do Plasmoids Induce Fast Magnetic Reconnection in Well-resolved Current Sheets in 2D Magnetohydrodynamic Simulations?

Abstract We investigate the development of tearing-mode instability using the highest-resolution 2D magnetohydrodynamic simulations of reconnecting current sheets performed on a uniform grid, for Lundquist numbers of 10 3 ≤ S ≤ 5 × 10 5 , reaching up to 65,536 2 grid cells. We demonstrate a Sweet–Parker scaling of the reconnection rate V rec ∼ S −1/2 up to Lundquist numbers S ∼ 10 4 . For larger values of Lundquist number, between 2 × 10 4 ≤ S ≤ 2 × 10 5 , plasmoid formation sets in, leading to a slight enhancement of the reconnection rate, V rec ∼ 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 × 10 5 , we observe the nonlinear development of the tearing-mode instability, with plasmoid coalescence and a saturation of the reconnection rate at V rec / V A ∼ 0.01. At such high S , however, the corresponding Reynolds number is large, reaching 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 3D effects in the reconnection process.