Electrostatic interactions and stability of dusty plasmas and the multicomponent Ornstein–Zernike equation

Using the Ornstein–Zernike integral fluid equation for multi-component plasma, the dielectric properties and thermodynamical stability of dusty plasmas are studied. For the most non-ideal dust plasma subsystem, a transition to the one-component approximation is carried out. It is shown that the effective pseudopotential for determining the correlation functions in the selected subsystem should not include the contribution of this subsystem to the screening constant but also take into account the condition of total plasma quasineutrality. It is demonstrated that when the coupling parameter of the dust subsystem is smaller than unity, Γ00 < 1, the interaction potential between the charged plasma particles is fairly well described by the Debye potential with a full screening constant. For Γ00 > 1, the static dielectric function in the long wavelength domain becomes negative, and this domain expands when Γ00 increases. This leads to the appearance of attraction of particles with charges of the same sign and repulsion of particles with charges of the opposite sign. In this case, both the total pressure and the isothermal compressibility in the entire studied range of the coupling parameter Γ00 < 250 remain positive, but the isothermal compressibility of the dust subsystem becomes negative at Γ00 ≈ 2 within the studied range of variation of the plasma parameters. The sign of the derivative of the chemical potential with respect to the total number of dust particles, the positiveness of which is the third condition for the thermodynamic stability, is shown to coincide with the sign of the isothermal compressibility of the dust subsystem. Therefore, it is concluded that the equilibrium dusty plasma at Γ00 > 2 is thermodynamically unstable.