Heliospheric modulation conditions were unusually quite during the last solar minimum activity between Solar Cycles 23/24. Fortunately, the PAMELA space-experiment measured six-month averaged Galactic positron spectra for the period July 2006 to December 2009, over an energy range of 80 MeV to 30 GeV, which is important for solar modulation. The highest level of Galactic positrons was observed at Earth during the July-December 2009 period. A well-established, comprehensive three-dimensional (3D) numerical model is applied to study the modulation of the observed positron spectra. This model had been used previously to understand the modulation of Galactic protons and electrons also measured by PAMELA for the same period. First, a new very local interstellar spectrum for positrons is constructed, using the well-known GALPROP code together with the mentioned PAMELA observations. The 3D model is used to distinguish between the dominant mechanisms responsible for the heliospheric modulation of Galactic positrons, and to understand the effect of particle drift during this unusual minimum in particular, which is considered diffusion dominant, even though particle drift still had a significant role in modulating positrons. Lastly, the expected intensity of Galactic positrons during an A>0 polarity minimum, with similar heliospheric conditions than for 2006-2009, is predicted to be higher than what was observed by PAMELA for the 2006-2009 unusual minimum.

The local interstellar spectra (LIS's) for galactic cosmic rays (CR's) cannot be directly observed at the Earth below certain energies, because of solar modulation in the heliosphere. With Voyager 1 crossing the heliopause in 2012, in situ experimental LIS data below 100 MeV/nuc can now constrain computed galactic CR spectra. Using galactic propagation models, galactic electron, proton and light nuclei spectra can be computed, now more reliably as very LISs. Using the Voyager 1 observations made beyond the heliopause, and the observations made by the PAMELA experiment in Earth orbit for the 2009 solar minimum, as experimental constraints, we simultaneously reproduced the CR electron, proton, Helium and Carbon observations by implementing the GALPROP code. Below about 30 GeV/nuc solar modulation has a significant effect and a comprehensive three-dimensional (3D) numerical modulation model is used to compare the computed spectra with the observed PAMELA spectra possible at these energies. Subsequently the computed LIS's can be compared over as wide a range of energies as possible. The simultaneous calculation CR spectra with a single propagation model allows the LIS's for positrons, Boron and Oxygen to also be inferred. This implementation of the most comprehensive galactic propagation model (GALPROP), alongside a sophisticated solar modulation model to compute CR spectra for comparison with both Voyager 1 and PAMELA observations over a wide energy range, allows us to present new self-consistent very LIS's (and expressions) for electrons, positrons, protons, Helium, Carbon, Boron and Oxygen for the energy range of 3 MeV/nuc to 100 GeV/nuc.

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Simultaneous and continuous observations of galactic cosmic-ray electrons (e −) and positrons (e +) from the PAMELA and AMS02 space experiments are most suitable for numerical modeling studies of the heliospheric modulation of these particles below 50 GeV. A well-established comprehensive three-dimensional modulation model is applied to compute full spectra for e − and e + with the purpose of reproducing the observed ratio e +/e − for a period that covers the previous long and unusual deep solar minimum activity and the recent maximum activity phase, including the polarity reversal of the solar magnetic field. For this purpose, the very local interstellar spectra for these particles were established first. Our study is focused on how the main modulation processes, including particle drifts, and other parameters, such as the three major diffusion coefficients, evolved and how the corresponding charge-sign dependent modulation subsequently occurred. The end result of our effort is the detailed reproduction of e +/e − from 2006 to 2015, displaying both qualitative and quantitative agreement with the main observed features. Particularly, we determine how much particle drift is needed to explain the time dependence exhibited by the observed e +/e − during each solar activity phase, especially during the polarity reversal phase, when no well-defined magnetic polarity was found.

We study solar modulation of galactic cosmic rays (GCRs) during the deep solar minimum, including the declining phase, of solar cycle 23 and compare the results of this unusual period with the results obtained during similar phases of the previous solar cycles 20, 21, and 22. These periods consist of two epochs each of negative and positive polarities of the heliospheric magnetic field from the north polar region of the Sun. In addition to cosmic ray data, we utilize simultaneous solar and interplanetary plasma/field data including the tilt angle of the heliospheric current sheet. We study the relation between simultaneous variations in cosmic ray intensity and solar/interplanetary parameters during the declining and the minimum phases of cycle 23. We compare these relations with those obtained for the same phases in the three previous solar cycles. We observe certain peculiar features in cosmic ray modulation during the minimum of solar cycle 23 including the record high GCR intensity. We find, during this unusual minimum, that the correlation of GCR intensity is poor with sunspot number (R = -0.41), better with interplanetary magnetic field (R = -0.66), still better with solar wind velocity (R = -0.80) and much better with the tilt angle of the heliospheric current sheet (R = -0.92). In our view, it is not the diffusion or the drift alone, but the solar wind convection is the most likely additional effect responsible for the record high GCR intensity observed during the deep minimum of solar cycle 23.