Electron Acceleration by Multiple Fast Fermi Reflections at Earth’s Bow Shock

The generation of energetic particles in the Universe is an important topic in astrophysical and space physics. Although the diffusive shock acceleration has been acknowledged to play an essential role in particle acceleration, the injection problem has not been well resolved yet. Using measurements from the Magnetospheric Multiscale spacecraft, we report unexpected spiky enhancements of energetic electron flux in the upstream region of the Earth’s bow shock. Such enhancements are then demonstrated to result from the accelerated electron population by shock reflection. Meanwhile, the magnetic field exhibits no variations except an increase in radius of curvature. Based on the results above, we uncover the underlying acceleration scenario. When the interplanetary magnetic field with a proper curvature approaches the bow shock, the two ends of a magnetic field line may touch the shock front earlier than its middle part. Magnetic mirror points form at the two field-line-shock intersections. The solar wind electrons are therefore trapped and bounce between two mirror points. Eventually, these electrons undergo fast Fermi reflection several times and gain substantial energies. The spacecraft observation of accelerated electrons is reproduced with a numerical method based on the reflection model. Such an acceleration process may be a potential solution to the injection problem.