Aloha – The practical applications of solar sails powered by the protons, electrons and other charged particles generated by solar flares and solar storms appears to be on the near horizon (thank goodness as I used similar future technology for Salt of the Earth). It is a short article, but if interested you can find it at http://www.space.com/31063-electric-sail-solar-wind-space-exploration.html.
Accepting that this is an acceleration model, Earth to the Moon is problematic. However, this could put travel to the Sun, if you know how to tack to the Solar Wind at a mere four day journey once full acceleration was achieved. That’s two days to Mars. Of course it would probably take weeks to build such momentum, so let’s put a trip to Mars at two weeks. Of course one of the challenges we’d have to face for manned flights using this technology is that the very particles that would drive the ship would also sicken the crew.