What is the average density of solar wind particles that produce the aurora?

Well..the average density of particles that reach the Earth from a solar flare or coronal ejection event is probably of the order of a few hundred particles per cubic centimeter or less. The ordinary solar wind has a density of 5 - 10 atoms per cubic centimeter. But auroral 'sub-storms' are produced when the particles trapped in the Earth's magnetotail are accelerated into the north and south auroral regions. This happens because the solar magnetic field carried by the plasma that reaches the Earth, interacts with the geotail magnetic field. A 'reconnection' event then occurs, and like the snapping of a rubber band, some of the geotail magnetic field lines snap back into the inner magnetosphere. Charged particles carried along for the ride are accelerated to very high energies in the 5 - 6000 volt range, and when these slam into the upper atmosphere the electrons excite the oxygen and nitrogen atoms to produce red green and blue lights.