Probability density function model equation for particle charging in a homogeneous dusty plasma - art. no. 036405

In this paper, we use the direct interaction approximation (DIA) to obtain an approximate integrodifferential equation for the probability density fun ction (PDF) of charge (q) on dust particles in homogeneous dusty plasma. Th e DIA is used to solve the closure problem which appears in the PDF equatio n due to the interactions between the phase space density of plasma particl es and the phase space density of dust particles. The equation simplifies t o a differential form under the condition when the fluctuations in phase sp ace density for plasma particles change very rapidly in time and is correla ted for very short times. The result is a Fokker-Planck type equation with extra terms having third and fourth order differentials in q, which account for the discrete nature of distribution of plasma particles and the intera ction between fluctuations. Approximate macroscopic equations for the time evolution of the average charge and the higher order moments of the fluctua tions in charge on the dust particles are obtained from the differential PD F equation. These equations are computed, in the case of a Maxwellian plasm a, to show the effect of density fluctuations of plasma particles on the st atistics of dust charge.