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 kappa(z) is a function of position in the sheath through its dependence on the ion distribution f(v,z). We show that kappa(z) is determined by basic sheath parameters, such as the ion-to-neutral-species-mass ratio m/M, the mean free paths lambda-e and lambda-c for elastic scattering and charge transfer, and the ion distribution f0(v) = f(v,0) at the presheath-sheath boundary. When m/M greater-than-or-equal-to 1 or lambda-c << lambda-e, the Monte Carlo models indicate that kappa(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.