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The rate of magnetic reconnection is of the utmost importance in a variety ofprocesses because it controls, for example, the rate energy is released insolar flares, the speed of the Dungey convection cycle in Earth'smagnetosphere, and the energy release rate in harmful geomagnetic substorms. Itis known from numerical simulations and satellite observations that the rate isapproximately 0.1 in normalized units, but despite years of effort, a fulltheoretical prediction has not been obtained. Here, we present afirst-principles theory for the reconnection rate in non-relativisticelectron-ion collisionless plasmas, and show that the same prediction explainswhy Sweet-Parker reconnection is considerably slower. The key consideration ofthis analysis is the pressure at the reconnection site (i.e., the x-line). Weshow that the Hall electromagnetic fields in antiparallel reconnection cause anenergy void, equivalently a pressure depletion, at the x-line, so thereconnection exhaust opens out, enabling the fast rate of 0.1. If the energycan reach the x-line to replenish the pressure, the exhaust does not open out.In addition to heliospheric applications, these results are expected to impactreconnection studies in planetary magnetospheres, magnetically confined fusiondevices, and astrophysical plasmas.

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