  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.
