Comparison of the integral equation method with the results of Monte Carlo simulations for the radial distribution functions of particles in dusty plasmas

Abstract

An original approach is proposed for the pseudopotential model of interaction between dust particles, which simultaneously takes into account their polarization, finite dimension and the screening phenomenon due to buffer plasma particles. The derivation starts from the assumption that the dust particles are conductive hard balls, so that their interaction and the interaction with the electrons and ions of the buffer plasma can be analytically interpreted in the framework of the charge image method. After that, the renormalization theory of the plasma particles interaction, leading to the so-called generalized Poisson-Boltzmann equation, is utilized to construct the interaction potential of two isolated dust grains in the buffer plasma of electrons and ions. Then, the Ornstein-Zernike relation in the hypernetted chain approximation is numerically solved and behavior of the radial distribution function of dust grains is regularly studied. The idea of consistent treatment of finite size effects demands that the system of hard spheres should actually be replaced by a system of point charges with some effective number density in which the van der Waals correction is thoroughly introduced. A direct comparison with the results of Monte Carlo simulations is made and fairly good agreement is found for the radial distribution function at relatively high values of the dust coupling parameter.