Monte Carlo simulation of the terrestrial hydrogen exosphere

Abstract

Methods for Monte Carlo simulation of planetary exospheres have evolved from early work on the lunar atmosphere, where the regolith surface provides a well defined exobase. A major limitation of the successor simulations of the exospheres of Earth and Venus is the use of an exobase surface as an artifice to separate the collisional processes of the thermosphere from a collisionless exosphere. In this paper a new generalized approach to exosphere simulation is described, wherein the exobase is replaced by a barometric depletion of the major constituents of the thermosphere. Exospheric atoms in the thermosphere-exosphere transition region, and in the outer exosphere as well, travel in ballistic trajectories that are interrupted by collisions with the background gas, and by charge exchange interactions with ionospheric particles. The modified simulator has been applied to the terrestrial hydrogen exosphere problem, using velocity dependent differential cross sections to provide statistically correct collisional scattering in H-O and H-H + interactions. Global models are presented for both solstice and equinox over the effective solar cycle range of the Fx0.7 index (80 to 230). Simulation results show significant differences with previous terrestrial exosphere models, as well as with the H distributions of the MSIS-86 thermosphere model. IntroductionJeans [1916, p. 342] suggested that atmospheric escape could be approximated as the rate of thermal evaporation from a spherical surface "of such radius that collisions outside it are very infrequent." The nonescaping atoms above this surface form an exosphere. Common wisdom embraces the notion that the exobase for hydrogen escape is located where the mean free path of hydrogen equals the scale height of atomic oxygen and that this level effectively separates the hydrodynamic processes of the thermosphere from free ballistic transport in the exosphere.In the classical view of a collisionless planetary exosphere, atoms leaving the exobase have a Maxwellian distribution of velocities. Those on the high-energy tail of the distribution with velocities greater than V/•2GM/r) escape from the planet, while the rest travel through the exosphere in ballistic trajectories and return to the exobase. Owing to the tendency of ballistic atoms to travel vertical and lateral distances that are proportional to the exobase temperature, the exosphere acts as a lateral diffusion channel superimposed on the top of the thermosphere, and the equilibrium distribution of atomic concentration at the exobase tends to vary approximately as T -•/•' [Hodges and Johnson, 1968]. Merging of thermosphere and exosphere transport occurs at the altitude where the coefficient of molecular diffusion becomes equal to that for the exospheric diffusion channel, which is the product of the scale height and the mean atomic speed [Hodges, 1972]. This transition is at a substantially higher altitude (about 2 oxygen scale heights) than the exobase for Jeans' escape. The exospheric diffusion analogy works well to descr...

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