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A numerical model for the solar modulation of cosmic rays, based on thesolution of a set of stochastic differential equations, is used to illustratethe effects of modifying the heliospheric magnetic field, particularly in thepolar regions of the heliosphere. To this end, the dfferences in the modulationbrought about by each of three choices for the heliospheric magnetic field,i.e. the unmodified Parker field, the Smith-Bieber modified field, and theJokipii-Kota modified field, are studied. It is illustrated that both theJokipii-Kota and Smith-Bieber modifications are effective in modifying theParker field in the polar regions. In addition, it is argued that themodification of Smith and Bieber is based on observational evidence and has afirm physical basis, while these motivations are lacking in the case of theJokipii-Kota modification. From a cosmic ray modulation point of view, we foundthe Smith-Bieber modification to be the most suitable choice for modifying theheliospheric magnetic field. The features and effects of these threemodifications are illustrated both qualitatively and quantitatively. It is alsoshown how the Smith-Bieber modified field can be applied in cosmic raymodulation models to reproduce observational cosmic ray proton spectra from thePAMELA mission during the solar minimum of 2006 - 2009. These results arecompared with those obtained in previous studies of this unusual solar minimumactivity period and found to be in good qualitative agreement.

The effect of magnetic field modifications on the modulation of cosmic rays in the heliosphere