Abstract: This paper describes a model for the return flux of neutral and charged particles to a satellite in geosynchronous earth orbit. For neutral particles, the main return flux mechanisms is back-scattering via self-collisions among molecules outgassed or vented from the satellite; whereas for charged particles, the main mechanism is electrostatic re-attraction of ionized outgassed or vented molecules to a negatively charged satellite. Computer codes that simulate spacecraft charging typically contain a 3D charged particle trajectory-tracking procedure that, in principle, could be used for contamination studies. In practice, however, it is difficult to obtain quantitative results on the return flux distribution by this method. This makes such a code impractical to use as an engineering tool for identifying contamination problems reliably and evaluating corrective measures through simulation. To achieve a practical engineering tool, we prose an alternative to the particle tracking technique. We treat the problem for both neutral and charged particles in a unified manner by direct numerical solution to the Boltzmann equation in the BGK approximation. The feasibility of this approach is demonstrated by favorable numerical results presented for the simplified geometry of a spherical spacecraft. !12
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