Three-dimensional Spontaneous Magnetic Reconnection

Abstract: Magnetic reconnection is best known from observations of the Sun where it causes solar flares. Observations estimate the reconnection rate a small, but non-negligible fraction of the Alfv\'en speed, so-called fast reconnection. Until recently, the prevailing pictures of reconnection were referring to either resistivity or plasma microscopic effects, which was contradictory to the observed rates. The alternative picture was either reconnection due to the stochasticity of magnetic field lines in turbulence or the tearing instability of the thin current sheet. In this paper I simulated long-term three-dimensional nonlinear evolution of a thin, planar current sheet subject to fast oblique tearing instability using direct numerical simulations of resistive-viscous MHD. The late-time evolution resembles generic turbulence with -5/3 power spectrum and scale-dependent anisotropy, so I conclude that the tearing-driven reconnection becomes turbulent reconnection. The turbulence is local in scale, so microscopic diffusivity should not affect large-scale quantities. This is confirmed by convergence of the reconnection rate towards $\sim 0.015 v_A$ with increasing Lundquist number. In this spontaneous reconnection with mean field and without driving the dissipation rate per unit area also converge to $\sim 0.006 \rho v_A^3$, the dimensionless constants $0.015$ and $0.006$ are governed only by self-driven nonlinear dynamics of the sheared magnetic field. Remarkably, this also means that thin current sheet has a universal fluid resistance depending only on its length to width ratio and to $v_A/c$.