a Model of Fermi Acceleration at Shock Fronts with an Application to the Earth's Bow Shock

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Abstract

A model of first-order Fermi acceleration at shock fronts is developed. A hydromagnetic shock is assumed to be propagating toward an isolated magnetic mirror in an otherwise uniform magnetic field which is not parallel to the shock front. The behavior of an ensemble of particles trapped between the mirror and the shock is studied, and a description of the balance of particle injection into the trapping region, loss through the shock or mirror, and energy gain is obtained. Injection criteria are discussed, and an attractive source of particles eligible for acceleration is shown to be the quasi-thermalized plasma behind the shock, a small fraction of which may leak out in front of the shock and be accelerated. Application of the model to the Earth's bow shock leads to an attractive model for the energetic electron pulses which have been observed outside of the magnetosphere. If a small fraction of the 1-keV electrons in the quasi-thermalized plasma behind the shock escape to the region in front of the bow shock, many quantitative features of the observed pulses are explained by a model in which each pulse is due to the acceleration of these electrons by a mirror approaching the bow shock. In particular, the observed cutoff in >30-keV pulses a few Earth radii beyond the shock is readily explained. The model predicts, further, that the cutoffs for more energetic particles should be at smaller distances from the shock. The observed energy spectra are in excellent agreement with the model. 8ome critical observations are suggested.

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