A chemical model of a three-component dusty plasma

Abstract

A chemical model of a three-component dusty plasma consisting of electrons, protons, and dust particles is developed. The number density of protons is assumed to be fixed, and the absorption of electrons by dust particles is considered as bound states, determined by the work function of the electrons. An expression is obtained for the free energy of the system, which includes the ideal and excess parts. The contribution of interactions between particles is considered in the framework of the generalized Poisson-Boltzmann integro-differential equation obtained from the Bogolyubov chain of equations for the equilibrium distribution functions in the pair correlation approximation. This equation is easily solved and transformed into a system of algebraic equations by using Fourier transformation and delta function properties. For perform numerical calculations, the Coulomb potential was chosen as the interaction of electrons and protons with each other in the absence of a plasma medium, and an identical potential for the interaction of dust particles, corrected for finite size. Numerical calculation show that the free energy of a three-component dusty plasma is a function of a single parameter and has a pronounced minimum, which can be used to evaluate the electric charge of dust particles immersed into a buffer plasma.