Dust-Acoustic Wave Dispersion in Thermal Dusty Plasmas at Weak and Moderate Couplings

The dispersion of dust-acoustic waves (DAWs) in weakly and moderately coupled thermal dusty plasmas is studied in the framework of the linear density-response formalism with the static local-field correction for interdust interactions. The plasma medium composition and the charge of dust particles are simultaneously determined within a recently developed chemical model (Physical Review E, vol. 101, 063203, 2020) based on minimizing the Helmholtz free energy of the system under investigation. Stemming from the generalized Poisson-Boltzmann equation, the renormalization procedure is consistently applied to derive an interdust screened potential that takes into account the finiteness of dust grains. Within the framework of the Ornstein-Zernike relationship in the hypernetted chain approximation, the static structure factor of the dust component is evaluated to manifest the appearance of local extrema on its wavenumber dependence, thereby indicating the short-range order formation in the arrangement of dust particles with respect to one another. It is shown that the DAW dispersion law is completely governed by the static structure factor and, therefore, exhibits a nonmonotonic dependence on the wavenumber as well. In the long-wavelength limit, the acoustic-like behavior of the DAW dispersion is strictly confirmed and the corresponding phase speed, reduced in units of the dust thermal velocity, is ultimately expressed via the static structure factor at zero wavenumber.