Applicability of a diffusion model to lateral transport in the terrestrial and lunar exospheres

Abstract

Kinetic theory is used to determine a series expansion of the vertical flux of particles in an exosphere in terms of time and space derivatives of particle concentration, exobase velocity, and temperature. For sufficiently large scale variations of these parameters in time and space, the series can be truncated to a form that is similar to a diffusion equation. Owing to this analogy, it is possible to unite the mathematical description of molecular diffusion, which governs thermospheric flow, and the corresponding exospherie equation by using effective transport coefficients which change smoothly with altitude through the transition from thermosphere to exosphere. A new definition of the exobase for lateral flow emerges from the analogy of exospherie and thermospheric diffusion, as the altitude where the horizontal mean free path length equals the mean horizontal extent of ballistic trajectories of the transported gas, as opposed to the scale height of the dominant gas which determines the exobase for escape. It is shown that the approximation of exospherie lateral flow as a diffusion process is applicable to global scale problems concerning terrestrial helium and heavier gases, and lunar gases heavier than helium. The diffusion model is not valid near the abrupt surface temperature change at the lunar terminator, but exact and diffusion solutions to an idealized terminator problem are found to differ importantly only near the terminator, implying that no global scale error accrues in the diffusion solution due to a localized region of its nonvalidity.