Diffusive acceleration at the blunt termination shock

Voyager 1's recent and long-anticipated passage into the heliosheath contradicted the prediction that we would observe the source of anomalous cosmic rays accelerated by the termination shock. The observed energetic protons reveal a power-law spectrum below several MeV, but above several MeV the spectrum falls more sharply, and we observe the familiar bump caused by modulation of anomalous cosmic rays. This paper develops the theoretical framework to include the motions and drift of particles during diffusive shock acceleration at a three-dimensional (3-D) termination shock, including cross-field diffusion, and curvature and gradient drifts. Our model supports the concept of McComas and Schwadron that because of the termination shock's blunt structure with a strong nose-to-tail asymmetry, there should be a strong deficit of locally accelerated anomalous cosmic rays (ACRs) near the nose. With reasonable parameters for the scattering mean free path and the ratio of perpendicular to parallel diffusion, the model produces an energy spectrum that agrees well with the Voyager 1 observations near the termination shock. These parameters also lead to an acceleration time to 10 MeVof about 1 yr, which is comparable to previous estimates derived from the observed charge states of ACRs. Thus, we provide a theory for diffusive acceleration at the blunt termination shock. The predictions of this theory are consistent with Voyager 1's observations, showing a lack of ACRs accelerated near the nose of the termination shock and the ACR acceleration timescale derived from ACR charge states.