The first pass of the Cassini orbiter near the A and B rings of Saturn, formed mainly by H2O ice particles, revealed the presence of an ionosphere composed of O+ and O2+ ions. Such a result suggests the existence of an atmospheric halo made up of molecular oxygen surrounding the rings. It is produced by solar UV radiation-induced decomposition of ice releasing molecular oxygen which does not stick on the surface at the relevant temperatures. A Monte Carlo model of the atmosphere/ionosphere ring system that uses test-particles and incorporates chemical processes and transport of both neutrals and plasma ions is developed. Published ion data from the ion mass spectrometer (IMS) experiment were used as constraint and the model provides a very satisfactory fit between simulated O+ and O2+ ion densities and those measured along Cassini trajectory.