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Multiple spatial scaling and the weak-coupling approximation. I. General formulation and equilibrium theory

Journal Article:

Abstract

Multiple spatial scaling is incorporated in a modified form of the Bogoliubov plasma cluster expansion; then this proposed reformulation of the plasma weak-coupling approximation is used to derive, from the BBGKY Hierarchy, a decoupled set of equations for the one-and two-particle distribution functions in the limit as the plasma parameter goes to zero. Because the reformulated cluster expansion permits retention of essential two-particle collisional information in the limiting equations, while simultaneously retaining the well-established Debye-scale relative ordering of the correlation functions, decoupling of the Hierarchy is accomplished without introduction of the divergence problems encountered in the Bogoliubov theory, as is indicated by an exact solution of the limiting equations for the equilibrium case. To establish additional links with existing plasma equilibrium theories, the two-particle equilibrium correlation function is used to calculate the interaction energy and the equation of state. The limiting equation for the equilibrium three-particle correlation function is then developed, and a formal solution is obtained.
Authors:
Kleinsmith, P E [1] 
  1. Carnegie-Mellon Univ., Pittsburgh, Pa. (USA)
Publication Date:
Apr 01, 1976
Product Type:
Journal Article
Reference Number:
AIX-07-269724; ERA-02-015458; EDB-77-022310
Resource Relation:
Journal Name: J. Plasma Phys.; (United Kingdom); Journal Volume: 15:pt.2
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; INHOMOGENEOUS PLASMA; BBGKY EQUATION; WEAK-COUPLING MODEL; BOGOLYUBOV METHOD; DEBYE LENGTH; EQUILIBRIUM; PLASMA; SCALING; DIFFERENTIAL EQUATIONS; EQUATIONS; MATHEMATICAL MODELS; NUCLEAR MODELS; 700105* - Fusion Energy- Plasma Research- Plasma Kinetics-Theoretical- (-1987)
OSTI ID:
7241518
Country of Origin:
United Kingdom
Language:
English
Other Identifying Numbers:
Journal ID: CODEN: JPLPB
Submitting Site:
INIS
Size:
Pages: 223-238
Announcement Date:

Journal Article:

Citation Formats

Kleinsmith, P E. Multiple spatial scaling and the weak-coupling approximation. I. General formulation and equilibrium theory. United Kingdom: N. p., 1976. Web.
Kleinsmith, P E. Multiple spatial scaling and the weak-coupling approximation. I. General formulation and equilibrium theory. United Kingdom.
Kleinsmith, P E. 1976. "Multiple spatial scaling and the weak-coupling approximation. I. General formulation and equilibrium theory." United Kingdom.
@misc{etde_7241518,
title = {Multiple spatial scaling and the weak-coupling approximation. I. General formulation and equilibrium theory}
author = {Kleinsmith, P E}
abstractNote = {Multiple spatial scaling is incorporated in a modified form of the Bogoliubov plasma cluster expansion; then this proposed reformulation of the plasma weak-coupling approximation is used to derive, from the BBGKY Hierarchy, a decoupled set of equations for the one-and two-particle distribution functions in the limit as the plasma parameter goes to zero. Because the reformulated cluster expansion permits retention of essential two-particle collisional information in the limiting equations, while simultaneously retaining the well-established Debye-scale relative ordering of the correlation functions, decoupling of the Hierarchy is accomplished without introduction of the divergence problems encountered in the Bogoliubov theory, as is indicated by an exact solution of the limiting equations for the equilibrium case. To establish additional links with existing plasma equilibrium theories, the two-particle equilibrium correlation function is used to calculate the interaction energy and the equation of state. The limiting equation for the equilibrium three-particle correlation function is then developed, and a formal solution is obtained.}
journal = {J. Plasma Phys.; (United Kingdom)}
volume = {15:pt.2}
journal type = {AC}
place = {United Kingdom}
year = {1976}
month = {Apr}
}