Scaling Theory of 3D Magnetic Reconnection X-Line Spreading

Abstract

Magnetic reconnection is fundamental process in plasmas that converts magnetic energy into kinetic and thermal energy via a change in magnetic topology. Magnetic reconnection is known to mediate eruptive solar flares, geomagnetic substorms that create the Northern lights, heating and particle acceleration in controlled fusion devices, and is thought to be an important process in numerous settings in high-energy astrophysics. Classical models of reconnection are two-dimensional (2D), but naturally occurring reconnection is three-dimensional (3D), and a manifestation of the 3D nature is that the x-line where the magnetic field topology changes has a finite extent in the direction normal to the plane of reconnection. The x-line can also elongate or spread over time, and this trait has been observed in the laboratory, Earth's magnetosphere, and is thought to be related to the elongation of chromospheric ribbons during solar flares. This dissertation presents a first‐principles scaling theory of the three-dimensional spreading of quasi-2D magnetic reconnection of finite extent in the out of plane direction. This theory addresses systems with or without an out of plane (guide) magnetic field, with or without Hall physics, in current sheets with thicknesses that are both uniform and non‐uniform in the out of plane direction. The theory reproduces known spreading speeds and directions with and without guide fields, unifying previous knowledge in a single theory, along with new results: (1) Reconnection spreads in a particular direction if an x‐line is induced at the interface between reconnecting and non‐reconnecting regions, which is controlled by the out of plane gradient of the electric field in the outflow direction. (2) The theory explains why anti‐parallel reconnection in resistive‐magnetohydrodynamics does not spread. (3) Numerical simulations of anti-parallel reconnection initiated with a pressure pulse instead of a magnetic perturbation suggest magnetosonic waves do not play a role in the propagation of quasi-2D anti-parallel reconnection, as had previously been speculated. (4) In current sheets of non‐uniform thickness, when anti-parallel reconnection spreads from a thinner to a thicker region of a current sheet, the spreading speed is both sub‐Alfv\'enic and slower than the speed of the local current carriers predicted for a uniform current sheet of equivalent local thickness; this is due to the initial reconnecting magnetic field being effectively reduced. We confirm these results using 3D two‐fluid and resistive‐magnetohydrodynamics simulations. The result can be used to predict the time scale of reconnection spreading in Earth's magnetotail, where the near Earth cross‐tail current