First-Principles Theory of the Rate of Magnetic Reconnection in Magnetospheric and Solar Plasmas

TL;DR

This paper develops a first-principles theory explaining why magnetic reconnection occurs at a rate of about 0.1 in collisionless plasmas, linking pressure depletion at the reconnection site to the fast reconnection rate observed.

Contribution

It provides the first theoretical prediction of the magnetic reconnection rate based on pressure dynamics and Hall fields, explaining the universal fast rate.

Findings

Hall fields cause pressure depletion at the x-line

Pressure replenishment controls reconnection speed

Theory explains observed reconnection rate of ~0.1

Abstract

The rate of magnetic reconnection is of the utmost importance in a variety of processes because it controls, for example, the rate energy is released in solar flares, the speed of the Dungey convection cycle in Earth's magnetosphere, and the energy release rate in harmful geomagnetic substorms. It is known from numerical simulations and satellite observations that the rate is approximately 0.1 in normalized units, but despite years of effort, a full theoretical prediction has not been obtained. Here, we present a first-principles theory for the reconnection rate in non-relativistic electron-ion collisionless plasmas, and show that the same prediction explains why Sweet-Parker reconnection is considerably slower. The key consideration of this analysis is the pressure at the reconnection site (i.e., the x-line). We show that the Hall electromagnetic fields in antiparallel reconnection cause an energy void, equivalently a pressure depletion, at the x-line, so the reconnection exhaust opens out, enabling the fast rate of 0.1. If the energy can reach the x-line to replenish the pressure, the exhaust does not open out. In addition to heliospheric applications, these results are expected to impact reconnection studies in planetary magnetospheres, magnetically confined fusion devices, and astrophysical plasmas.