  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.
