The spatial distributions of hydrogen atoms emitted from the rings of Saturn with a range of emission speeds are simulated by a Monte Carlo technique. Basically two issues, one concerning the source strength and the other concerning the geometrical configuration (which is specifically discussed in the present work), have to be dealt with. For example, among the several possibilities, photosputtering might be discarded because of its low production yield of H atoms and the absence of time variation of the H Ly &agr; emission over the years. Interplanetary meteoroid impact could fail by a factor of 10 in providing the required emission rate of the ring hydrogen atmosphere if the conservative estimate for the impact vapor production rate is used; otherwise, it is an adequate source. Exospheric ejection of dissociated hydrogen fragments from the dayside disk is also promising, but we show that the global distribution of the hydrogen atoms in ballistic trajectories appears not to be in agreement with the reported Voyager UVS observations. Charge exchange interaction with the magnetospheric plasma has been found to be a significant loss mechanism of the ring atmosphere. In turn, the pitch angle distribution and thermal energy distribution of the corotating plasma could be strongly modified by the neutral atoms. The present study indicates that the loss rate of neutral particle via charge exchange could vary between 4¿1027 s-1 and 7¿1028 s-1.