A long-standing problem in the study of space and astrophysical plasmas is to explain the production of energetic electrons as magnetic fields ‘reconnect’ and release energy. In the Earth's magnetosphere, electron energies reach hundreds of thousands of electron volts (refs 1–3), whereas the typical electron energies associated with large-scale reconnection-driven flows are just a few electron volts. Recent observations further suggest that these energetic particles are produced in the region where the magnetic field reconnects4. In solar flares, upwards of 50 per cent of the energy released can appear as energetic electrons5,6. Here we show that electrons gain kinetic energy by reflecting from the ends of the contracting ‘magnetic islands’ that form as reconnection proceeds. The mechanism is analogous to the increase of energy of a ball reflecting between two converging walls—the ball gains energy with each bounce. The repetitive interaction of electrons with many islands allows large numbers to be efficiently accelerated to high energy. The back pressure of the energetic electrons throttles reconnection so that the electron energy gain is a large fraction of the released magnetic energy. The resultant energy spectra of electrons take the form of power laws with spectral indices that match the magnetospheric observations.
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This work was supported by the NSF/DOE programme in plasma science, by NASA through the Supporting Research and Technology and the Sun-Earth Connections Theory programmes, through CMPD, a DOE FSC, and through CISM, an NSF STC. Computations were carried out in part at the National Energy Research Scientific Computing Center. Author Contributions J.F.D., M.S. and M.A.S. identified the Fermi mechanism; J.F.D. carried out the particle simulations of reconnection, obtained the solutions of the transport equation and wrote the paper; and M.S. and H.C. carried out the bubble and test particle simulations, respectively. All of the authors discussed the results and commented on the paper.
Derivation of the powerlaw spectrum. The notes outline the derivation the solution of the particle transport equation in the limit in which the back-pressure from energetic particles can be neglected. The resulting solution in Eq. (4) of the paper takes the form of a power-law at high energy.
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Space Science Reviews (2017)