A study of the time-dependent modulation of cosmic rays in the inner heliosphere
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A two-dimensional (2-D) time-dependent cosmic ray modulation model is used to calculate the modulation of cosmic-ray protons and electrons for 11-and 22-year modulation cycles using a compound approach to describe solar cycle related changes in the transport parameters. The compound approach was developed by Ferreira and Potgieter (2004) and incorporates the concept of propagation diffusion barriers, global changes in the magnetic field, time-dependent gradient, curvature and current-sheet drifts, and other basic modulation mechanisms. By comparing model results with 2.5 GV Ulysses observations, for both protons and electrons, it is shown that the compound approach results in computed intensities on a global scale compatible to observations. The model also computes the expected latitudinal dependence, as measured by the Ulysses spacecraft, for both protons and electrons. This is especially highlighted when computed intensities are compared to observations for the different fast latitude scan (FLS) periods. For cosmic ray protons a significant latitude dependence was observed for the first FLS period which corresponded to solar minimum conditions. For the second, which corresponded to solar maximum, no latitude dependence was observed as was the case for the third FLS period, which again corresponded to moderate to minimum solar activity. For the electrons the opposite occurred with only an observable latitude dependence in intensities for the third FLS period. It is shown that the model results in compatible intensities when compared to observations for these periods. Due to the success of the compound approach, it is also possible to compute charge-sign dependent modulation for 2.5 GV protons and electrons. The electron to proton ratio is presented at Earth and along the Ulysses trajectory. Lastly, it is also shown how the modulation amplitude between solar minimum and maximum depends on rigidity. This is investigated by computing cosmic ray intensities for both protons and electrons, not only at 2:5 GV, but also up to 7:5 GV. A refinement for the compound approach at higher rigidities is proposed.