A numerical model has been developed for atomic hydrogen densities in the Titan hydrogen torus. The effects of occasional collisions were included in order to accurately simulate physical conditions inferred from the Voyager 1 and 2 Ultraviolet Spectrometer (UVS) results of Broadfoot et al. (1981) and Sandel et al. (1982). The model employed Lagrangian perturbation of orbital elements of hydrogen atoms launched from Titan and Monte-Carlo simulation of collisions and loss mechanisms. The torus is found to be azimuthally symmetric with the density sharply peaked at Titan's orbit, and decreasing rapidly in the outward and perpendicular directions and more gradually inward from 17 to 5 R(s). The energetic hydrogen atoms from Saturn's upper atmosphere, first predicted by Shemansky and Smith (1982), were also investigated. Collisions of these Saturnian atoms with the torus population do not contribute to the torus density, and will lead to a net loss of torus atoms if their launch speeds from Saturn extend above 40 km/sec. The Saturnian atoms produce a corona which was modelled using the theory of Chamberlain (1963). Based on the energetic hydrogen production rate given by Shemansky and Smith (1986), the coronal density at Saturn's exobase is taken to be 200 to 300 cm⁻³, decreasing to 3 or 4 cm⁻³ at 20 R(s). Without the coronal population, the torus model does not reproduce the Voyager 2 UVS Lyman α intensities because the hydrogen atoms are too closely confined toward Titan's orbital plane. The observations can be reproduced by a model that includes the corona and has central plane maxima of 62 cm⁻³ at Titan's orbit and 318 cm⁻³ at Saturn's exobase. The effect of Titan's exospheric temperature (T(E)) on torus structure is seen in the column abundances perpendicular to the central plane at radii of 5 to 15 R(s). Spacecraft observations of these column abundances should allow verification of T(E) to within about 100°K. Similar observations of other species expected to be present in the torus, such as H₂, N, and N₂, would indicate their approximate launch speeds from Titan and thus the relative importance of thermal and non-thermal loss mechanisms.

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