High potential, near free molecular regime Coulombic collisions in aerosols and dusty plasmas

Determination of the particle charge in aerosols and dusty plasmas requires an accurate calculation of the particle-ion collision kernel taking into account the particle-ion Coulombic coupling and ion-neutral gas molecule collisions. While the effect of Coulombic interactions of any strength is described accurately in the continuum limit and free molecular limit, an accurate physical description at intermediate collisional regimes remains elusive. Specifically, the Coulomb influenced collisions between oppositely charged particles and ions have evaded accurate theoretical description in the past. We use Langevin dynamics (LD) calculations to infer the non-dimensional collision kernel H as a function of the electrostatic potential energy to thermal energy ratio ΨE and the diffusive Knudsen number KnD, the index of ion-neutral collisionality in a finite pressure system. The LD approach yields a simple, approximate treatment of particle charging in the entire ion-neutral collision regime under the assumption that Z≡mimg→∞, where mi is the mass of an ion and mg is the mass of the background gas molecules. We show that the Gumbel distribution accurately describes the underlying distribution of H calculated using LD. The effect of high ion concentrations (at which screening of particle by free charges in space is important) on H is parameterized through a non-dimensional screening length parameter SD. Analysis of the dependence of the distribution parameters on ΨE, KnD, and SD leads to a regression for H that is valid for 0<ΨE≤60 and KnD≤2000 plasmas. Inter-comparison of current model with select models from the literature shows that the current model and the model published by Gatti and Kortshagen (that assumes Z→0) yield similar predictions for a wide range of ΨE, KnD, and SD.