Modelling of `barrier' modulation for cosmic ray protons in the outer heliosphere

Voyager and Pioneer spacecraft observations over 22 years and out to ∼82 AU have found two particular features of cosmic ray proton modulation in the heliosphere: (1) Markedly different behavior for minimum modulation conditions between the radial intensity profiles for periods of opposite magnetic polarities. (2) Most of the residual modulation for these periods was found to take place in the outer heliosphere, near and beyond where the termination shock (TS) is expected to be, and seems to differ for the two polarity cycles. Since contemporary models do not provide satisfactory quantitative explanations for these features, they are studied with a numerical model including a solar wind TS, a heliosheath and drifts. Results show interesting features caused by the TS and the heliosheath which differ markedly for the two polarity cycles, with energy and with increasing solar activity.