The Boltzmann Equation to Study the Escape of Light Atoms from Planetary Atmospheres

The atmosphere is bound to a planet by the planetary gravitational field. At high altitudes, light atoms such as hydrogen and helium can attain speeds in excess of the escape speed of the planet. These particles escape provided they suffer no further collision. In exospheric models, it is assumed that the escape flux is contributed only by particles moving outwards with a speed greater than the escape speed. The exospheric theory has served as a useful model for comparison with satellite and ground‐based measurements, but it presents limitations inherent to the collisionless approach. To study the transition region between the collision‐dominated and the collisionless domains of the neutral planetary atmospheres, it is necessary to use a model based on the solution of the Boltzmann equation. Such a model is presented in the present work to study the escape of light atoms from the terrestrial atmosphere through a background of oxygen atoms. The escape of hydrogen atoms out of the atmosphere of Mars is also discussed. A spectral method, initially developed to study the polar wind, is used to solve the Boltzmann equation. The effects of the planetary curvature and the gravitational force are taken into account. Two boundary conditions are imposed: one at the bottom and one at the top of the transition region. With this model, the velocity distribution function of the light atoms can be calculated at different altitudes. The density, flux, bulk velocity, and temperature profiles are obtained by calculating the moments of the velocity distribution function. The escape flux is found to be reduced compared with purely exospheric Jeans’ flux. The results are compared with those of the exospheric models, as well as with previous collisional models based on Monte Carlo simulations or on the Boltzmann equation with different assumptions.