Accelerated and fast magnetic reconnection through enhanced resistive dissipation for MHD equations
Gennaro Ciampa, Renato Lucà
TL;DR
The paper investigates accelerated magnetic reconnection in three-dimensional MHD with resistivity $\eta>0$ on the torus by leveraging advection-driven enhanced diffusion. It constructs a dissipation-enhancing reference flow based on a 2D Euler solution and uses a perturbative energy framework plus high-norm diffusion estimates to prove reconnection occurs on a time scale faster than the resistive one, with rate $\lambda_{rec}(\eta)=c_2\frac{\eta^{1/2}}{|\ ln\eta|}$. A key novelty is the demonstration that the advection term actively accelerates reconnection via enhanced diffusion of high Sobolev norms (Theorem B'), and the approach is shown to be structurally stable to small perturbations. The framework is extended to a viscous MHD system with stochastic forcing, yielding a probabilistic fast reconnection rate $\lambda_{rec}(\eta)=\frac{c_2}{|\ln\eta|}$, highlighting robustness of the mechanism under random perturbations. Overall, the work provides the first analytic construction where advection actively speeds up reconnection, with potential implications for Hall-MHD and plasma physics in regimes beyond purely resistive diffusion.
Abstract
We consider the phenomenon of magnetic reconnection, namely a change in the topology of magnetic lines, for sufficiently regular solutions of the three-dimensional periodic magnetohydrodynamic (MHD) equations. We provide examples where magnetic reconnection occurs on time scales shorter than the resistive one, due to enhanced dissipation emerging from advective effects. This is the first analytical result where the advection term plays an active role in the reconnection process. A key aspect of our approach is a new estimate for enhanced diffusion of high Sobolev norms, which is of independent interest beyond its application to the MHD equations.