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

TL;DR

This study tests whether plasmoid formation triggers fast, resistivity-independent reconnection in well-resolved 2D MHD current sheets across $S=10^3$ to $2\times10^5$. Using high-resolution simulations with controlled perturbations and a rigorous energy-balance-based error estimator, the authors observe the Sweet-Parker scaling $V_{rec} \sim V_A S^{-1/2}$ up to $S \approx 2\times10^4$, followed by a slight enhancement to $V_{rec} \sim V_A S^{-1/3}$ once plasmoids form, consistent with tearing-mode theory. Crucially, plasmoids do not undergo a merger cascade in 2D; even at high $S$, the reconnection rate remains dependent on resistivity, disputing the notion of a universal fast reconnection in 2D plasmoid-dominated regimes. The work emphasizes that 2D results may not generalize to 3D astrophysical contexts where outflow turbulence and Reynolds-number effects dominate, underscoring the need for convergence-tested, high-resolution 3D studies to reliably characterize fast reconnection in nature.

Abstract

We investigate the development of tearing-mode instability using the highest resolution two-dimensional magnetohydrodynamic simulations of reconnecting current sheets on a uniform grid, for Lundquist numbers $10^3 \le S \le 2 \times 10^5$. Although the tearing-mode instability is commonly thought to trigger a plasmoid cascade that enables fast reconnection - i.e., independent of $S$ - our results, in broad agreement with the recent findings of Morillo \& Alexakis (2025), challenge this belief. 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, 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 our simulations, the plasmoids do not form a cascade of mergers, as they are rapidly advected out of the reconnection layer. Our findings call for the revision of the role of plasmoid formation in 2D high Lundquist number magnetic reconnection. Even if future studies demonstrate that 2D plasmoid-reconnection becomes resistivity-independent at sufficiently large $S$, directly extending those results to 3D astrophysical environments is not justified, as in realistic circumstances, the increase of $S$ also raises the Reynolds number of the outflows, making it essential to account for the dominant role of turbulence.

Figures (12)

• Figure 1: Initial configuration of magnetic field and density. Black arrows represent the in-plane component of the magnetic field, and the colormap is the density profile. The out-of-plane component of the magnetic field $(B_z)$ is set to be constant.
• Figure 2: Time evolution of the magnetic flux $\Phi_B$ for 2D MHD simulations with initial random noise perturbation, $S=5\times 10^4$, $\delta v = 10^{-2} \, V_A$ and different resolutions.
• Figure 3: Colormaps of the current density magnitude ($|\mathbf{J}| = |\nabla \times \mathbf{B}|$) at different time-steps for the simulation with $S=5 \times 10^4$ and $h^{-1}=8192$.
• Figure 4: Time evolution of the magnetic flux $\Phi_B$ for simulations with initial random noise perturbation, $S=5\times 10^4$, $h^{-1} = 4096$, and different amplitudes of initial random noise $\delta v$.
• Figure 5: Time evolution of the magnetic flux $\Phi_B$ for simulations with initial random noise perturbation and different Lundquist numbers at their respective best resolutions.