The Classical Binary and Triplet Distribution Functions for Two Component Plasma

Abstract

The equilibrium properties of a multi‐component plasma of charged particles that interact through the coulomb and short‐range potentials are investigated. In particular, this article presents density expansions of the reduced distribution functions for more particles, our calculations are based on the Bogoliubov‐Born‐Green‐Kirkwood‐Yvon (BBGKY) hierarchy, we used the results to calculate the binary and triplet distribution functions. We obtained the analytical form of the classical triplet distribution functions for two component plasma; one of them is based on the Kirkwood superposition approximation (KSA) which is consisting of the assumption that the potential in a set of three particles is the sum of the three pair potentials, this is equivalent to assuming that the triplet distribution function is the product of the three radial distribution functions, and the other form is calculated by integration the triplet distribution function (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Quantum Binary and Triplet Distribution Functions of Plasma by using Green's Function

“…We obtained two forms of the triplet distribution function one of them is based on KSA; in which the triplet distribution function is the product of the three binary distribution functions, the other form is calculated by BBGKY hierarchy equation. [2] for one and two component plasma respectively. But we observe the different behavior in the curve of F ei because the attraction force between the different charges.…”

“…Fig. [2] for one component plasma. The corresponding temperatures and densities are T=10 6 Kelvin, n = 10 23 cm −3 .…”

“…The corresponding temperatures and densities are T=10 6 Kelvin, n = 10 23 cm −3 . [2] for two component plasma. 2 The comparison between the binary distribution function for our results (Eq.…”

“…Owing to Kirkwood Superposition Approximation (KSA), we can get the triplet distribution function in the following form [2] F abc = F ab (r)F bc (r )F ac (r ) Owing to Kirkwood Superposition Approximation (KSA), we can get the triplet distribution function in the following form [2] F abc = F ab (r)F bc (r )F ac (r )…”

“…Kraeft et al [4] have calculated binary distribution function and Effective Potentials. Falkenhagen et al [5] and Eisa [2] have calculated the classical binary and triplet distribution functions for two component plasma by using the method of Slater Sum and effective potential in quantum statistical mechanics. All the authors who have used the method of Slater Sum are near to the classical limit in their calculations.…”