Multiple spatial scaling and the weakcoupling approximation. Part 1. General formulation and equilibrium theory
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 twoparticle distribution functions in the limit as the plasma parameter goes to zero. Because the reformulated cluster expansion permits retention of essential twoparticle collisional information in the limiting equations, while simultaneously retaining the wellestablished Debyescale 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 twoparticle equilibrium correlation function is used to calculate the interaction energy and the equation of state. The limiting equation for the equilibrium threeparticle correlation function is then developed, and a formal solution is obtained.
 Publication:

Journal of Plasma Physics
 Pub Date:
 April 1976
 DOI:
 10.1017/S0022377800019747
 Bibcode:
 1976JPlPh..15..223K
 Keywords:

 Bbgky Hierarchy;
 Bogoliubov Theory;
 Equilibrium Equations;
 Plasma Physics;
 Scaling Laws;
 Correlation;
 Debye Length;
 Distribution Functions;
 Equations Of State;
 Thermodynamic Equilibrium;
 Plasma Physics