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
On the basis of the generalized Poisson-Boltzmann equation derived from the Bogolyubov chain of equations for the equilibrium distribution functions in the pair correlation approximation, a general expression is proposed for the Helmholtz free energy of a system that contains any number of components and whose particles interact via arbitrary potentials. This opens up an extraordinary opportunity to simultaneously treat a whole range of physical effects including partial ionization, quantum effects of diffraction and electron degeneracy, short- and long-range interactions of charged particles with neutrals, finite size effects, etc. It is shown that all medium constituents are tied together in a single screening matrix, whose determinant and trace determine the excess contribution to the free energy. The approach developed is then applied to the problem of the ionization potential depression (IPD) leading to quite simple analytical expressions, which turn out to be useful for various practical purposes. In particular, for a single ionization from the neutral state the IPD is shown to significantly depend on the ionization degree such that it consists of the difference of charged and neutral contributions for a fully ionized plasma and turns non-zero for an almost neutral medium. On the other hand, for a multiple ionization process finite size effects of atoms and ions are demonstrated to be of great importance and accounted for in order to achieve good agreement with experimental data on the IPD under warm dense matter conditions.
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