First-order Fermi acceleration of the diffuse ion population near the earth's bow shock

The flux of 30-65 keV particles observed by the ISEE-3 200 earth radii upstream is shown to be an upstream escape of the energetic ions in the earth's bow shock. A formal solution to the transport equation for the distribution function of energetic particles upstream from an isotropic monoenergetic source of particles/sq cm at a plane shock where the plasma changes speed is found, and escape conditions are defined. The efficiency of the acceleration is calculated to depend on the charge/particle, and fluxes near and far upstream of the shock are described analytically. Any model which takes into account shock acceleration by diffusive scattering with significant escape losses produces the observed spectrum close to the shock. The escape loss upstream is demonstrated to control the spectrum and the variation of flux and anisotropy with distance from the shock.