  Because of the semi-collisional nature of the solar wind, the collisionless
or exospheric approach as well as the hydrodynamic one are both inaccurate.
However, the advantage of simplicity makes them useful for enlightening some
basic mechanisms of solar wind acceleration. Previous exospheric models have
been able to reproduce winds that were already nearly supersonic at the
exobase, the altitude above which there are no collisions. In order to allow
transonic solutions, a lower exobase has to be considered, in which case the
protons are experiencing a non-monotonic potential energy profile. This is done
in the present work. In this model, the electron velocity distribution in the
corona is assumed non-thermal. Parametric results are presented and show that
the high acceleration obtained does not depend on the details of the
non-thermal distributions. This acceleration seems, therefore, to be a robust
result produced by the presence of a sufficient number of suprathermal
electrons. A method for improving the exospheric description is also given,
which consists in mapping particle orbits in terms of their invariants of
motion.
