Self-generated turbulence in magnetic reconnection

Classical Sweet-Parker models of reconnection predict that reconnection rates depend inversely on the resistivity, usually parameterized using the dimensionless Lundquist number ($\text{Lund}$). We describe magnetohydrodynamic (MHD) simulations using a static, nested grid that show the development of a three-dimensional instability in the plane of a current sheet between reversing field lines without a guide field. The instability leads to rapid reconnection of magnetic field lines at a rate independent of $\text{Lund}$ over at least the range $3.2\times {10}^3\lesssim \text{Lund}\lesssim 3.2\times {10}^5$ resolved by the simulations. We find that this instability occurs even for cases with $\Lund \lesssim 10^4$ that in our models appear stable to the recently described, two-dimensional, plasmoid instability. Our results suggest that three-dimensional, MHD processes alone produce fast (resistivity independent) reconnection without recourse to kinetic effects or external turbulence. The unstable reconnection layers provide a self-consistent environment in which the extensively studied turbulent reconnection process can occur.