Non-Maxwellian effects associated with the thermal escape of a planetary atmosphere

The velocity distribution function of a minor gaseous constituent escaping from a planetary atmosphere is perturbed from the equilibrium Maxwell-Boltzmann distribution function, There is a depletion in the high energy portion of the distribution function. The escape flux is consequently somewhat less than the Jeans flux obtained assuming complete equilibrium. The non-Maxwellian velocity distribution function for an escaping constituent is calculated with a Boltzmann equation modified by the addition of an isotropic sink term. The effects due to diffusion of particles and heat conduction are neglected. A discrete ordinate method which requires little computational time is employed in the solution of the Boltzmann equation. The corrections to the Jeans flux calculated in this way are compared with the results obtained with the Monte-Carlo techniques. The corrections for the escape of H and He from Earth, H from Mars and H₂ from Titan are calculated. The reductions in the Jeans flux are largest for a light escaping gas and for small escape parameters. The depletion of fast particles also results in the cooling of the minor component below the temperature of the background gas. This effect is also studied for the escape of H from Earth.