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Precise measurements of the time-dependent intensity of the low energy ($<50$ GeV) galactic cosmic rays are fundamental to test and improve the models which describe their propagation inside the heliosphere. Especially, data spanning different solar activity periods, i.e. from minimum to maximum, are needed to achieve comprehensive understanding of such physical phenomenon. The minimum phase between the 23$^{rd}$ and the 24$^{th}$ solar cycles was peculiarly long, extending up to the beginning of 2010 and followed by the maximum phase, reached during early 2014. In this paper, we present proton differential spectra measured from January 2010 to February 2014 by the PAMELA experiment. For the first time the galactic cosmic ray proton intensity was studied over a wide energy range (0.08-50 GeV) by a single apparatus from a minimum to a maximum period of solar activity. The large statistics allowed the time variation to be investigated on a nearly monthly basis. Data were compared and interpreted in the context of a state-of-the-art three-dimensional model describing the galactic cosmic rays propagation through the heliosphere., Comment: article, 4 figures. Accepted for publication on The Astrophysical Journal Letters (January 2018)

Since the beginning of the space exploration era, solar activity was observed at its lowest level during 2006 to 2009. During this period, the PAMELA space experiment observed spectra for galactic cosmic rays, specifically for protons, electrons and positrons over a wide energy range, during what is called an A < 0 solar magnetic polarity cycle. Drift theory predicts a difference in the behaviour for these oppositely charge particles during A < 0 cycles. An opportunity was thus created to study the predicted charge-sign-dependent modulation, also now for very quiet heliospheric conditions. A comprehensive three-dimensional, drift modulation model has been used to study the solar modulation for cosmic rays in detail with extensive comparison to the observed PAMELA spectra for the mentioned period. First, this was done for protons and secondly for electrons, as already published, to test and to authenticate the modelling approach and then to come to a better understanding and appreciation of the underlying physics, such as diffusion and drift theory. The results were also used to make predictions of how cosmic rays are differently modulated down to low energies (1 MeV) for the two magnetic polarity cycles of the Sun, and what role drifts play in this process. All computed solutions are based on new very local interstellar spectra, now also done for positrons. This report is focussed on detailed aspects of the solar modulation of positrons during the extraordinary quiet solar modulation period from 2006 to 2009. For the first time, a meaningful modulation factor in the heliosphere is computed for positrons, from 50 GeV down to 1 MeV, as well as the electron to positron ratios as a function of time and rigidity for the mentioned period., Comment: 8 pages, 5 figures

A numerical model for the solar modulation of cosmic rays, based on the solution of a set of stochastic differential equations, is used to illustrate the effects of modifying the heliospheric magnetic field, particularly in the polar regions of the heliosphere. To this end, the dfferences 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-Kota modified field, are studied. It is illustrated that both the Jokipii-Kota and Smith-Bieber modifications are effective in modifying the Parker field in the polar regions. In addition, it is argued that the modification of Smith and Bieber is based on observational evidence and has a firm physical basis, while these motivations are lacking in the case of the Jokipii-Kota modification. From a cosmic ray modulation point of view, we found the Smith-Bieber modification to be the most suitable choice for modifying the heliospheric magnetic field. The features and effects of these three modifications are illustrated both qualitatively and quantitatively. It is also shown how the Smith-Bieber modified field can be applied in cosmic ray modulation models to reproduce observational cosmic ray proton spectra from the PAMELA mission during the solar minimum of 2006 - 2009. These results are compared with those obtained in previous studies of this unusual solar minimum activity period and found to be in good qualitative agreement., Comment: 25 pages, 11 figures