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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.

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Global modulation studies with comprehensive numerical models contribute meaningfully to the refinement of very local interstellar spectra (VLISs) for cosmic rays. Modulation of positrons and anti-protons are investigated to establish how the ratio of their intensity, and with respect to electrons and protons, are changing with solar activity. This includes the polarity reversal of the solar magnetic field which creates a 22-year modulation cycle. Modeling illustrates how they are modulated over time and the particle drift they experience which is significant at lower kinetic energy. The VLIS for anti-protons has a peculiar spectral shape in contrast to protons so that the total modulation of anti-protons is awkwardly different to that for protons. We find that the proton-to-anti-proton ratio between 1–2 GeV may change by a factor of 1.5 over a solar cycle and that the intensity for anti-protons may decrease by a factor of ~2 at 100 MeV during this cycle. A composition is presented of VLIS for protons, deuteron, helium isotopes, electrons, and particularly for positrons and anti-protons. Gaining knowledge of their respective 11 and 22 year modulation is useful to interpret observations of low-energy anti-nuclei at the Earth as tests of dark matter annihilation.