A first-principles theoretical model of the reconnection rate in non-steady magnetic reconnection

As a key parameter in magnetic reconnection, the reconnection rate determines the speed at which magnetic energy is converted into plasma kinetic energy. It is well established that the reconnection rate of collisionless magnetic reconnection is on the order of 0.1—a value sufficiently high to account for various explosive phenomena in space environments, such as solar flares and geomagnetic substorms. Recently, Lu et al. [Sci. Bull. 70, 2766 (2025)] proposed a first-principles theoretical model of the reconnection rate during non-steady collisionless reconnection in a Harris-type current sheet. As magnetic reconnection proceeds, the ion and electron outflows increase continuously over time. Plasma becomes depleted in the electron and ion diffusion regions, while the magnetic field piles up downstream, causing the opening angles of the diffusion regions to grow continuously. As a result, the reconnection rate rises progressively and eventually reaches a peak value, which is approximated as 0.2n0/nb (where n0 is the peak density in the current sheet and nb is the density of the background plasma) and exhibits no dependence on the ion-to-electron mass ratio. However, in that model, the ion and electron outflows are solely governed by the Lorentz force term. In the present paper, we additionally incorporate contributions from the electric field and pressure gradient terms and analyze their combined influence on the electron and ion outflows and then the peak reconnection rate. Our results indicate that the electric field and pressure gradient terms weaken electron and ion outflows, which, in turn, reduces the peak reconnection rate. In the new model, the peak reconnection rate is roughly 1/5 times that in Lu et al. [Sci. Bull. 70, 2766 (2025)], which scales approximately as 0.09n0/nb.