Grounded on the premise that dust particles are charged hard balls, the analysis in Davletov et al. (Contrib. Plasma Phys., vol. 56, 2016, 308) provides an original pseudopotential model of intergrain interaction in complex (dusty) plasmas. This accurate model is engaged herein to consistently treat the finite-size effects from the process of dust particle charging to determination of the thermodynamic quantities and the dust-acoustic wave dispersion in the strongly coupled regime. The orbital motion limited approximation is adopted to evaluate an electric charge of dust grains immersed in a neutralizing background of the buffer plasma. To account for finite dimensions of dust particles, the radial distribution function is calculated within the reference hypernetted-chain (RHNC) approximation to demonstrate a well-pronounced short-range order formation at rather large values of the coupling parameter and the packing fraction. The evaluated excess pressure of the dust component is compared to the available theoretical approaches and the simulation data and is then used to predict the dust-acoustic wave (DAW) dispersion in the strongly coupled regime under the assumption that the dust particles charge varies in the course of propagation. In contrast to many previous investigations, it is demonstrated for the first time ever that for DAWs the charge variation of dust particles should necessarily be taken into account while evaluating the dust isothermal compressibility.

Based on the previously developed pseudopotential model of the dust particles interaction, which takes into account both the finite size and screening effects, the equilibrium distribution functions are investigated in a broad range of plasma parameters. The treatment stems entirely from the renormalization theory of plasma particles interactions which leads to the so-called generalized Poisson-Boltzmann equation. In particular, an analytical expression for the static structure factor of the dust particles is proposed and its non-monotonic behavior in the hyper-netted chain approximation is found in a specified domain of plasma parameters to indicate the formation of short- or even long-range order in the system.

The aim of the present study is to determine the impact the finite size of dust particles has on the static and dynamic characteristics of the dust component of a plasma.Taking into account both the finite dimensions of dust grains and the plasma screening, a model expression is chosen for the interdust interaction potential. The static structure factor of dust particles is evaluated by iteratively solving the reference hypernetted-chain approximation, which inherently contains the hard sphere model handled within the Percus-Yevick closure. The self-consistent method of moments is then engaged to relate the static and dynamic structure factors by assuming that the second derivative of the dynamic structure factor with respect to the frequency vanishes at the origin. Thus, an analytical expression for the dynamic structure factor is validated over quite a broad domain of dusty plasma non-ideality and grains packing fraction. The calculated spectrum of dust-acoustic waves reveals the appearance of the roton minimum, which becomes less pronounced when the packing fraction of dust particles rises. It is also predicted that the wavenumber position of the roton minimum is de facto independent of the size of dust particles. New analytical expressions for the dust-acoustic wave spectrum and decrement of damping are proposed and thoroughly checked. K E Y W O R D Sdust-acoustic waves, dusty plasmas, dynamic structure factor, method of moments

An approach is presented to derive a pseudopotential model of interaction between dust particles that simultaneously takes into account the polarization, finite size and screening effects. The consideration starts from the assumption that the dust particles are hard balls made of a conductive material such that their mutual interaction and interaction with the electrons and ions of the buffer plasma can analytically be interpreted within the method of image charges. Then, the renormalization theory of plasma particles interaction, leading to the so-called generalized Poisson-Boltzmann equation, is applied to obtain the interaction potential of two isolated dust grains immersed into the buffer plasma of electrons and ions. After that the Ornstein-Zernike relation in the hyper-netted chain approximation (HNC) is numerically solved to study the radial distribution function and the static structure factor of the dust grains. In doing so the system of hard balls is actually replaced by a system of point-like charges with properly adjusted number density in the form of van der Waals correction. A straightforward comparison is made with the Monte-Carlo simulation to find a fairly good agreement for the radial distribution function at relatively high dust couplings.

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