Ion attachment rates and collection forces on dust particles in a plasma sheath with finite ion inertia and mobility.

Ion attachment and ion drag to dust particles near the edge of a nonthermal plasma sheath are of interest to better understand how particles become trapped in such sheath regions. While electron-particle collisions in plasmas and sheaths can often be described by orbital motion limited theory, quantification of ion transport about dust particles in collisional sheath regions requires a distinct modeling approach. In this work, the dimensionless ion attachment coefficients and dimensionless collection forces on negatively charged particles are calculated using ion trajectory models accounting for an external electric field in a collisional sheath, ion inertia, and finite ion mobility. By considering both ion inertia and finite ion mobility, results apply for ion transport from the fully collisional regime into a regime of intermediate collisionality. Ion collection forces are calculated in two related limits; first, the nondissipative limit, wherein the dimensionless collection force function coincides with the dimensionless attachment coefficient (anticipated in the collisionless regime), and second, a dissipative limit, wherein neutral gas collisions dissipate ion momentum, which strongly affects the resulting collection force (anticipated in the fully collisional regime). We show that ion motion about a charged particle can be parametrized by the ion Stokes number, which is the ratio of ion inertia to gas resistance to motion and dimensionless electric field strength (the external field strength normalized by the electric field at the particle surface). At intermediate Stokes numbers (${10}^{1}--{10}^{2}$), ions adopt trajectories that are extremely sensitive to the initial ion-particle impact parameter. Plots of the resulting collision angle at fixed Stokes number and dimensionless field strength as a function of impact parameter contain multiple discontinuities. Nonetheless, we obtain smooth curves for the ion attachment rates and collection forces in both the nondissipative and fully dissipative limits. Increasing the ion Stokes number is found to significantly decrease the dimensionless ion attachment coefficients and ion collection forces in comparison to coefficients evaluated with expressions derived in the fully collisional limit. In all instances, including the dissipative limit, we find the ion collection force acts in the direction of ion migration. Neural network fits are utilized to parametrize the resulting attachment coefficients and ion collection forces, and we apply these fits to examine the charge levels on 1-\ensuremath{\mu}m radius particles in external fields in the $3\ifmmode\times\else\texttimes\fi{}{10}^{2}--3\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{0.16em}{0ex}}\mathrm{V}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}$ range and pressures in the $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}1}--5\ifmmode\times\else\texttimes\fi{}{10}^{1}$ Torr (66.7--6667 Pa) range. We find the charge level is strongly sensitive to both field strength and pressure in the plasma sheath, ranging from 6 \ifmmode\times\else\texttimes\fi{} ${10}^{3}$ to 1.8 \ifmmode\times\else\texttimes\fi{} ${10}^{4}$ over the conditions examined. Calculations are also used to demonstrate that the ion collection force can be sufficiently strong to trap particles not only close to the bottom electrode of a parallel-plate reactor, but also close to the top electrode, with a critical ion density required for trapping.