Scaling laws for magnetic reconnection, set by regulation of the electron pressure anisotropy to the firehose threshold

Abstract

Magnetic reconnection in a weakly collisional plasma, such as in the Earth's magnetosphere, is known to be accompanied by electron pressure anisotropy. For reconnection scenarios including moderate guide magnetic field, electrons are magnetized throughout the reconnection region, and the anisotropy drives extended electron current layers. Along these layers, the anisotropy nears the firehose threshold. We describe how the anisotropy stagnates at this threshold by a mechanism that does not involve pitch-angle mixing. Using previously established anisotropic equations of state and by imposing the marginal firehose condition, scaling laws are obtained for quantities along the current layers as functions of plasma parameters upstream of the reconnection region. The predicted reconnection region quantities include the magnetic field strength, plasma density, and the parallel and perpendicular electron pressures, allowing for a characterization of electron energization solely as a function of the upstream plasma conditions. This characterization is in agreement with simulations and spacecraft observations.