Monte Carlo study of the escape of a minor species

The understanding of some important space-physics problems (e.g., the Jeans escape of light atoms from a planetary atmosphere and the ion escape in the terrestrial polar wind) is related to the problem of the escape of a minor species through a nonuniform background. This latter problem was studied for different interparticle collision models (Maxwell molecule and hard sphere), for different minor-to major-species mass ratios, and for different values of the escape velocity (${\mathit{v}}_{\mathit{c}}$). The gravitational force was simulated by a critical escape velocity (${\mathit{v}}_{\mathit{c}}$), and the Lorentz forces were ignored. First, a simple variable change was used to transform the problem into a simpler one where the background medium is uniform. This simplified problem, which is similar to the ‘‘Milne’’ problem, was solved by a Monte Carlo simulation. In the collisionless region and for the case of zero escape velocity (${\mathit{v}}_{\mathit{c}}$=0), the velocity distribution function of the minor species (${\mathit{f}}_{\mathit{t}}$) showed large deviations from a Maxwellian, with large temperature anisotropy (parallel temperature less than the perpendicular temperature) and asymmetry in the parallel direction (upward tail), for both of the collision models. In the collision-dominated region the normalized density gradient was found to be independent of the mass ratio for the Maxwell molecule collision. For the hard-sphere cross section, it was reduced by a mass-ratio-dependent factor. This is due to the heat-flow contribution to the momentum balance, which vanishes only for the former collision model. The Monte Carlo results were compared with the moment-equations approach and the direct solution of the Boltzmann equation. This comparison confirms that the Monte Carlo method is a viable alternative and complementary to other techniques, especially in recent years, due to the large increase in the available computation power.