We develop a first-principles scaling theory of the spreading of three-dimensional (3D) 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, and with or without Hall physics. The theory reproduces known spreading speeds and directions with and without guide fields, unifying previous knowledge in a single theory. New results include the following: (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 spreading mechanism for anti-parallel collisionless reconnection is convection, as is known, but for guide field reconnection it is magnetic field bending. We confirm the theory using 3D two-fluid and resistive-magnetohydrodynamics simulations. (3) The theory explains why anti-parallel reconnection in resistive-magnetohydrodynamics does not spread. (4) The simulation domain aspect ratio, associated with the free magnetic energy, influences whether reconnection spreads or convects with a fixed x-line length. (5) We perform a simulation initiating anti-parallel collisionless reconnection with a pressure pulse instead of a magnetic perturbation, finding spreading is unchanged rather than spreading at the magnetosonic speed as previously suggested. The results provide a theoretical framework for understanding spreading beyond systems studied here and are important for applications including two-ribbon solar flares and reconnection in Earth's magnetosphere.
The abrupt release of magnetic energy in substorms in Earth's magnetosphere and flares in the solar corona are key features of the dynamics of these systems and have an important impact on Earth's technological infrastructure. In both processes, magnetic reconnection is the driver of the rapid energy conversion (McPherron et al., 1973;Priest & Forbes, 2000) via a change in magnetic field connectivity (Dungey, 1953;Vasyliunas, 1975). Observations have revealed that reconnecting x-lines (the collection of points where the magnetic field connectivity changes) often start in a localized region of space, and then elongate or spread in time, orthogonal to the reconnection plane in two-ribbon solar flares (
We derive a theory of three-dimensional spreading of collisionless anti-parallel reconnection in current sheets with non-uniform thickness.• Spreading from a thinner to a thicker current sheet occurs slower than local electron and Alfvén speeds, a key prediction of the theory.• We apply the theory to reconnection spreading in Earth's magnetotail and discuss potential implications for solar flare ribbons.
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