Collisional plasma sheath model

TLDR

The effects of ion collisionality on the plasma sheath are revealed by a two‑fluid model. A two‑fluid model with a power‑law ion–neutral collision cross section is solved numerically and analytically to map how sheath width and ion impact energy depend on collisionality across collisionless, transition, and collisional regimes. The transition regime centers at a sheath width of five mean‑free paths for sheath width and at about half a mean‑free path for ion impact energy in the constant mean‑free‑path case.

Abstract

The effects of ion collisionality on the plasma sheath are revealed by a two-fluid model. In contrast to previous work, the ion–neutral collision cross section is modeled using a power law dependence on ion energy. Exact numerical solutions of the model are used to determine the collisional dependence of the sheath width and the ion impact energy at the wall. Approximate analytical solutions appropriate for the collisionless and collisionally dominated regimes are derived. These approximate solutions are used to find the amount of collisionality at the center of the transition regime separating the collisionless and collisional regimes. For the constant ion mean-free-path case, the center of the transition regime for the sheath width is at a sheath width of five mean-free paths. The center of the transition regime for the ion impact energy is at a sheath width of about one-half of a mean-free path.