Analytic model of the ion angular distribution in a collisional sheath

An analytic model is developed for the ion angular distribution in a collisional sheath. In a previous study, the one-dimensional (normal to the sheath) ion velocity distribution was obtained under the assumption that charge exchange is the dominant ion-neutral collision mechanism. In the present model, we assume λscat≥λcx, where λscat and λcx are the mean free paths for ion-neutral elastic scattering and charge-exchange collisions, respectively. With this assumption, the angular distribution mainly arises from ions that strike the electrode after undergoing only one scattering collision following the last charge-exchange collision. Comparison of the analytic model with results obtained from a particle-in-cell simulation gives excellent agreement. Both the average angle of ions striking the electrode and the ratio of parallel to perpendicular ion flux at the electrode are shown to scale with the ratio of scattering to charge-exchange cross sections σscat/σcx.