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 ${\lambda }_{\mathit{e}}$ and ${\lambda }_{\mathit{c}}$ for elastic scattering and charge transfer, and the ion distribution ${\mathit{f}}_0$(v)=f(v,0) at the presheath-sheath boundary. When m/M≥1 or ${\lambda }_{\mathit{c}}$≪${\lambda }_{\mathit{e}}$, 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.