Three-Dimensional Magnetic Reconnection Spreading in Current Sheets of Non-Uniform Thickness

Abstract

Magnetic reconnection in naturally occurring and laboratory settings often begins locally and elongates, or spreads, in the direction perpendicular to the plane of reconnection. Previous work has largely focused on current sheets with a uniform thickness, for which the predicted spreading speed for anti-parallel reconnection is the local speed of the current carriers. We derive a scaling theory of three-dimensional (3D) spreading of collisionless anti-parallel reconnection in a current sheet with its thickness varying in the out-of-plane direction, both for spreading from a thinner to thicker region and a thicker to thinner region. We derive an expression for calculating the time it takes for spreading to occur for a current sheet with a given profile of its thickness. A key result is that when reconnection spreads from a thinner to a thicker region, the spreading speed in the thicker region is slower than both the Alfvén speed and the speed of the local current carriers by a factor of the ratio of thin to thick current sheet thicknesses. This is important because magnetospheric and solar observations have previously measured the spreading speed to be slower than previously predicted, so the present mechanism might explain this feature. We confirm the theory via a parametric study using 3D two-fluid numerical simulations. We use the prediction to calculate the time scale for reconnection spreading in Earth's magnetotail during geomagnetic activity. The results are also potentially important for understanding reconnection spreading in solar flares and the dayside magnetopause of Earth and other planets.

Key Points: - 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

Plain Language Summary: Magnetic reconnection is fundamental process in plasmas that converts magnetic energy into kinetic and thermal energy and is known to mediate eruptive solar flares and geomagnetic substorms that create the northern lights. The x-line where magnetic reconnection occurs can elongate or spread over time in the direction normal to the plane of reconnection, 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 study presents a scaling theory of the three-dimensional (3D) spreading of anti-parallel magnetic reconnection in current sheets with thickness varying in the out-of-plane direction. A key result is that when reconnection spreads from a thinner to a thicker region, the spreading speed in the thicker region is slower than expected. This is important because magnetospheric and solar observations have observed slower spreading speeds than previously predicted, so the present mechanism might explain this feature. We confirm the theory with 3D numerical simulations and use the prediction to calculate the time scale for reconnection spreading in Earth's magnetotail during geomagnetic activity.