Monte Carlo simulations of space-charge-limited ion transport through collisional plasma sheaths

Iterative Monte Carlo simulations are employed to study ion transport across the self-consistent electric field of a plasma sheath, under the influence of elastic collisions and charge-transfer reactions with ambient neutral species. Invoking arguments from kinetic theory, we express the retarding effect of encounters with neutral species as a ``dynamical friction'' force, proportional to the square of the mean ion velocity, whose coefficient {κ}(z) is a function of position in the sheath through its dependence on the ion distribution f(v,z). We show that {κ}(z) is determined by basic sheath parameters, such as the ion--to--neutral-species-mass ratio m/M, the mean free paths λₑ and λc for elastic scattering and charge transfer, and the ion distribution f₀(v)=f(v,0) at the presheath-sheath boundary. When m/M{≥}1 or λc{}λₑ, the Monte Carlo models indicate that {κ}(z) is a relatively weak function, amenable to approximation by simple functional forms using parameters estimated from the simulations. By substituting such approximations into a simple continuum description---consisting of coupled ordinary differential equations for the electric field and mean ion velocity---substantively accurate models of the sheath structure are obtained at nominal computational expense, for regimes ranging from the nearly collisionless to the collision-dominated extremes.