Departures from jeans' escape rate for H and He in the earth's atmosphere

It has long been recognized that thermal, or gravitational, escape must perturb the velocity distribution function of an escaping species so that Jeans' classic escape rate cannot be strictly correct. The magnitude of the appropriate correction remained unknown. Three recent statistical (Monte Carlo) investigations of this problem have produced such discordant correction factors as to prompt yet another such study, reported here. Major differences in approach are (1) realistic atom-atom elastic scattering cross-sections are used instead of an isotropic approximation and (2) program efficiency is increased dramatically by studying the virtual trajectories of atoms missing from the atmosphere instead of the real atoms comprising the atmosphere. Excellent agreement is achieved with one of the previous investigations; the escape rates of hydrogen and helium from the Earth's atmosphere are typically 70–75 per cent and 97–99 per cent of the Jeans rate, respectively.