Scaling theory of magnetic reconnection spreading

Observations of magnetic reconnection at the dayside magnetopause, magnetotail and in two-ribbon solar flares suggest that the magnetic reconnection process often begins in a localized region and spreads in the out-of-plane direction as it proceeds. Much has been learned from 3D numerical simulations of quasi-2D current sheets about how reconnection spreads, including an empirical understanding of the direction and the out-of-plane spreading speed as a function of system parameters for idealized systems. For anti-parallel reconnection the spreading occurs at the speed and direction of the current carriers, while for reconnection with a large out-of-plane (guide) magnetic field it spreads bi-directionally at the Alfven speed. However, the understanding of the physics of reconnection spreading from first principles remains primitive. We develop a scaling theory of 3D magnetic reconnection spreading from first principles. We identify the key micro- and meso-scale physics causing the spreading of reconnection with and without a guide field, and predict the spreading speed in current sheets with uniform and non-uniform thicknesses. For current sheets with uniform equilibrium thickness, the predictions reproduce previous empirical results. For spreading with no guide field in current sheets with a non-uniform equilibrium thickness, a key prediction is that in the thicker regions, the spreading is slower than the local current carriers. We confirm these predictions via a parametric study using 3D two-fluid numerical simulations. The results are potentially important for understanding systems in which reconnection spreads, including why the observed spreading speed is often at sub-Alfvenic speeds in two-ribbon solar flares and the dayside magnetopause. The results also have applications to laboratory reconnection experiments and in the solar wind.