Partial differential equations of evolution: By J. Bartak, L. Hermann, V. Lovicar and O. Vejvoda. Pp. 261. Ellis Horwood, London. 1991. £41.00

Abstract

A numerical model for the solar modulation of cosmic rays, based on the solution of a set of stochastic differential equations (SDEs), is used to illustrate the effects of modifying the heliospheric magnetic field, particularly in the polar regions of the heliosphere. SDE-based models are well suited for such studies so that new insights are gained. To this end, the differences in the modulation brought about by each of three choices for the heliospheric magnetic field, i.e. the unmodified Parker field, the Smith–Bieber modified field, and the Jokipii–Kóta modified field, are studied as typical well-known cases. It is illustrated that although both these modifications change the Parker field satisfactorily in the polar regions of the heliosphere, the Smith–Bieber modification is more effective in reducing cosmic ray drift effects in these regions. The features of these two modifications, as well as the effects on the solar modulation of cosmic rays, are illustrated qualitatively and quantitatively. In particular, it is shown how the Smith–Bieber modified field is applied in a cosmic ray modulation model to reproduce observational proton spectra from the PAMELA mission during the solar minimum of 2006–2009. These SDE-based results are compared with those obtained in previous studies of this unusual solar minimum activity period and found to be in good qualitative agreement.