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This work extends our previous two-dimensional self-consistent model of the cosmic rays interacting with the solar wind to include anomalous cosmic rays. As before, energetic particles are described kinetically using a Parker equation. The model includes diffusion, convection, and drift effects, as well as shock and compression acceleration and expansion cooling by nonuniform solar wind flow. A new numerical model has been developed featuring an adaptive-mesh refinement algorithm to accommodate small diffusive length scales of low-energy shock-accelerated particles. We show that anomalous cosmic rays have only a minor effect on the termination shock during the time near solar minima. Specifically, cosmic-ray gradients cause the subshock to move away from the Sun by about 1 AU with its compression ratio decreasing by about 5% compared to the reference case without cosmic-ray effects. We also study the effect of solar wind slowdown by charge exchange downstream of the termination shock, producing compressive flow in this region and resulting in additional acceleration of anomalous cosmic rays in the heliosheath. For the first time, spectra calculated with our self-consistent model show a good agreement with the cosmic-ray data from the two Voyager spacecraft, giving more confidence in the model predictions than the previous parametric studies.

Do Anomalous Cosmic Rays Modify the Termination Shock?