Method of integral equations for dust particles of finite size

Abstract

In this paper we make use of the earlier proposed pseudopotential model of interaction of dusty plasma particles, which correctly takes into account the finite size of the dust particles in the framework of classical plasma electrodynamics in the random-phase approximation. The potential thus constructed differs significantly from the widely used Yukawa (Debye-Hückel) potential at sufficiently large values ​​of the screening parameter, which is explained by the engagement of different boundary conditions at the surface of dust particles. The proposed pseudopotential model is applied to determine the radial distribution functions and the static structural factors of dust particles by the method of integral equations. In particular, the Ornstein-Zernike relation in the hypernetted-chain approximation with the bridge functions for the point-like particles is numerically solved. Since the dimensions of the dust particles are assumed to be finite, the calculations are also carried out within the framework of the combined method of integral equations, which is based on the determination of the correlation functions for the system of hard spheres within the Percus-Yevick equation with further transition to a model of solid charged balls studied within the modified hypernetted-chain approximation. The results show that at high packing fractions, the radial distribution functions and the static structural factors exhibit more significant peaks in comparison with the simple Ornstein-Zernike relation in the hypernetted-chain approximation, which indicates the formation of short-range and long-range orders in the arrangement of dust particles at rather large values of their coupling.