TeV Cosmic-Ray Anisotropy from the Magnetic Field at the Heliospheric   Boundary
  We performed numerical calculations to test the suggestion by Desiati & Lazarian (2013) that the anisotropies of TeV cosmic rays may arise from their interactions with the heliosphere. For this purpose, we used a magnetic field model of the heliosphere and performed direct numerical calculations of particle trajectories. Unlike earlier papers testing the idea, we did not employ time-reversible techniques that are based on Liouville's theorem. We showed numerically that for scattering by the heliosphere the conditions of Liouville's theorem are not satisfied and the adiabatic approximation and time-reversibility of the particle trajectories are not valid. Our results indicate sensitivity to the magnetic structure of the heliospheric magnetic field, and we expect that this will be useful for probing this structure in future research. 
Vanessa L\'opez-Barquero, S. Xu, P. Desiati, A. Lazarian, N. V.   Pogorelov, H. Yan
astro-ph.HE astro-ph.EP