Shock-drift acceleration of interstellar pickup protons at the solar wind termination shock

The numerical model of the shock-drift acceleration of interstellar pick-up protons at the solar wind termination shock is presented taking into account multiple reflections of the particles at and passing through the shock. The processes of the multiple interactions with the shock are possible due to pitch-angle scattering in the upstream and downstream parts of the solar wind flow. The model takes into account variations of the magnetic field direction near the shock front connected with its three-dimensional shape. The main advantage of the model is the self-consistent treatment of protons and interstellar hydrogen atoms, which interact with each other through the resonant charge exchange process. The model gives very simple and natural resolution of so-called injection problem for anomalous cosmic rays. The shock-drift acceleration can explain the fluxes of the anomalous cosmic rays measured at the Voyager 1/2 spacecraft after the termination shock crossings.