Modeling of Elastic Collisions between High Energy and Slow Neutral Atoms

In the plumes of Hall thrusters and ion thrusters, high energy neutral atoms are created as a result of the charge exchange interaction between exhaust ions and neutral atoms exiting the discharge region. Proper modeling of fast atoms is important for assessing spacecraft-plume interaction in space as well as facility interactions for ground tests. Many numerical models for Hall thrusters approximate the collisions between the high energy and slow atoms via the variable hard sphere (VHS) model, even though the VHS parameters necessary for scattering angle calculations cannot be determined properly due to the lack of viscosity data at high energies. In order to more accurately approximate such collisions, the applicability of the classical approach has been examined in simulations for both a low temperature 1D normal shock and a high energy ion beam experiment. For the low temperature shock, the VHS model outperforms the classical scattering model in speed and accuracy, while it is possible to obtain a nearly accurate shock profile using the classical approach with the semi-empirical HFD-B2 potential for xenon atoms. For the ion beam experiment, the result obtained with the classical approach is clearly more accurate over the VHS model result due to the lack of validity of the VHS model for high energy collisions. However, the classical scattering model is inherently more expensive compared to the VHS model. The computational intensity can be reduced by using the minimum required cross-section to cover the finite scattering region and the means of interpolation from pre-computed scattering angles at ranges of impact parameters and energies. Alternatively, the scattering angle calculation can be performed, without sacrificing much accuracy, with a simpler representation for the interatomic potential and reduced number of integration points when approximating the classical scattering equation with the Gauss-Mehler formula.