Grain charging rate in high ion concentrated dusty plasma using Langevin-dynamic simulations

Grain charging is modeled in instances wherein the ions are dense and strongly coupled: $\Gamma_{i}\mathrm{\equiv }\frac{e^{\mathrm{2}}}{\mathrm{4}\pi \varepsilon _{o}n_{i}^{\mathrm{-}\frac{\mathrm{1}}{\mathrm{3}}}k_{B}T_{i}}\mathrm{>1}$. Langevin Dynamics is used to simulate the motion of multiple ions around a negatively charged grain in a periodic domain for $\mathrm{\sim }{\mathrm{10}}^{\mathrm{1}}\mathrm{-}{\mathrm{10}}^{\mathrm{5}}\mathrm{\thinspace }Pa$. The ion flux coefficient is calculated using the grain-ion collision time distribution and the grain-ion pair correlation function $g^{\left( \mathrm{2} \right)}\mathrm{(}r\mathrm{)}$ is used to deduce the influence of the ion space charge on the collision of individual ions with the grain during charging. In addition to $\Gamma_{i}$, the ion flux coefficient is influenced by the diffusive Knudsen number $Kn_{D}\mathrm{\equiv }\frac{\sqrt {m_{i}k_{B}T_{i}} }{f_{i}n_{i}^{\mathrm{-}\frac{\mathrm{1}}{\mathrm{3}}}}$ (an ion-neutral gas interaction parameter) and $\chi_{p}\mathrm{\equiv }\frac{a_{p}}{n_{i}^{\mathrm{-}\frac{\mathrm{1}}{\mathrm{3}}}}$ (that compares the size of the grain to the mean inter-ion spacing). We also demonstrate that an effective grain-ion potential computed using $g^{\left( \mathrm{2} \right)}\mathrm{(}r\mathrm{)}$ according to the effective potential theory accurately describes the grain-ion dynamics in a binary framework for $\Gamma_{i}\mathrm{<\sim 20}$, without the need to simulate multiple ions. Ion concentration has a significant effect across different ion coupling regimes and the analysis of the pair-correlation functions reveals the perturbation of ion structure in the plasma by the presence of grains. We hope our model development will spark experimental validation efforts.