Acceleration of ACRs at the termination shock: 2-AD simulations

When Voyagers' crossed the termination shock (TS) in 2004 and 2007 the spectrum of anomalous cosmic rays (ACRs) did not unfold to a smooth power law at the shock. ACR uxes continued to increase into the heliosheath and ACR spectra unfolded gradually as Voyagers advanced deeper into the heliosheath. This finding can be interpreted in terms of field-topology, i.e the connection between the Parker spiral field and the blunt termination shock. We consider a two-dimensional model with an offset circle representing the blunt termination shock. Field lines wound in a Parker spiral cross the TS multiple times. We present simulation results with changing the shock strength and injection rate along the shock. We find that the flux of few MeV ACRs turn out sensitive to the injection rate at the nose and quite insensitive to the injection rate at the flank and tail regions. We also perform a backward calculation tracing the history of few MeV ACRs. Our results indicate that most of these ACRs, including ACRs in the tail, were likely be injected at the nose of the TS.