Direct Acceleration of Pickup Ions at the Solar Wind Termination Shock: The Production of Anomalous Cosmic Rays

We have modeled the injection and acceleration of pickup ions at the solarwind termination shock and investigated the parameters needed to produce theobserved Anomalous Cosmic Ray (ACR) fluxes. A non-linear Monte Carlo techniquewas employed, which in effect solves the Boltzmann equation and is notrestricted to near-isotropic particle distribution functions. This techniquemodels the injection of thermal and pickup ions, the acceleration of theseions, and the determination of the shock structure under the influence of theaccelerated ions. The essential effects of injection are treated in a mostlyself-consistent manner, including effects from shock obliquity, cross-fielddiffusion, and pitch-angle scattering. Using recent determinations of pickupion densities, we are able to match the absolute flux of hydrogen in the ACRsby assuming that pickup ion scattering mean free paths, at the terminationshock, are much less than an AU and that modestly strong cross-field diffusionoccurs. Simultaneously, we match the flux ratios He$^{+}$/H$^{+}$ orO$^{+}$/H$^{+}$ to within a factor $\sim 5$. If the conditions of strongscattering apply, no pre-termination-shock injection phase is required and theinjection and acceleration of pickup ions at the termination shock is totallyanalogous to the injection and acceleration of ions at highly obliqueinterplanetary shocks recently observed by the Ulysses spacecraft. The factthat ACR fluxes can be modeled with standard shock assumptions suggests thatthe much-discussed "injection problem" for highly oblique shocks stems fromincomplete (either mathematical or computer) modeling of these shocks ratherthan from any actual difficulty shocks may have in injecting and acceleratingthermal or quasi-thermal particles.Comment: 15 pages including 1 table and 10 figures, AASTeX emulateapj format, accepted for publication in The Astrophysical Journa