Energy spectrum of ions accelerated through Fermi process at the terrestrial bow shock

Abstract

The observed energy spectra of the upstream energetic ions (up to ∼ 150 keV per charge) are compared with the expectations from a first‐order Fermi acceleration process, i.e., a multiple reflection process between the bow shock and the upstream wave field. The escape of particles into the far upstream region (≳ several tens to 100 RE) is found important for the formation of the energy spectrum. The predicted energy spectrum has exponential dependence on energy like N(E)dE ∼ exp (− E/Ec)dE, which is consistent with the observation. One of the remarkable features of the observation, the invariance of the abundance ratios among various ion species when evaluated at the same energy per charge, can also be explained by the Fermi acceleration process: At the same energy per charge, the elementary acceleration process at the shock front is more efficient for particles of higher mass to charge ratio (M/Q), while the scattering process in the upstream waves is less efficient for these particles. It is shown that the above two effects compensate each other and make the energy spectra of accelerated particles independent of particle species when evaluated by energy per charge unit.