The preacceleration of anomalous cosmic rays

The flux of energetic particles at the termination shock, preaccelerated at interplanetary shocks, is calculated using Voyager 2 measurements in the outer heliosphere and by assuming a subsequent r-2 radial dependence. The spectrum of particles accelerated at the termination shock is then determined using the above spectrum as a source in the steady state diffusion convection equation. The accelerated spectrum is then modulated back to 57 AU and compared with measured anomalous cosmic ray (ACR) fluxes. For injection energies, at the termination shock, of about 50 keV the computed ACR flux at 57 AU compares well with the measured flux. Calculations, however, suggest that the injection energy should be considerably higher than 50 keV. If this is the case then the calculated ACR flux is considerably lower than expected. Voyager 2 observations beyond 40 AU and subsequent modeling suggest that interplanetary shocks may become too weak to continue accelerating energetic particles. Their flux should then fall off faster than r-2 and hence the flux at the termination shock may then be insufficient to explain the observed ACR fluxes. Using the injection energies computed for various species and by assuming that injection and acceleration takes place directly at the termination shock, we find acceleration efficiencies and fluxes consistent with those calculated from ACR measurements in the outer heliosphere.