STATISTICAL MECHANICAL THEORY OF DENSE PLASMAS.
Scientific rept. for 1 Jul 64-30 Jun 65 (Interim),
AERONAUTICAL RESEARCH ASSOCIATES OF PRINCETON INC N J
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The physical and mathematical tools are developed for the analysis of the behavior of plasmas for which the given Bogolubov conditions do not hold. The higher order terms in these conditions for all observable quantities depend on three- and four-body correlations. The authors show that a direct calculation with Bogolubovs technique leads to divergent results. They introduce a method believed to be a far-reaching generalization of Bogolubovs. The emphasis of the classical analysis, in terms of sharply localized particle collisions, is shifted by the method to an analysis of the time scales on which the phenomena evolve. This shift leads to a new view of kinetic equations. An analysis is given of the three-body correlations which relies on the solution of the three-body problem for hard spheres. They also obtain in closed form the nth order term in the Bogolubov expansion. They then introduce an externally controlled test particle in order to probe into the properties of these correlations and to develop rigorously the corresponding statistical theory. As an application of their theory, they obtain the complete solution for the lowest order distribution function in one dimension which coincides exactly with the non-linear Debye-Huckel theory. Next they prove that three-body correlations appear one order sooner than when the test particle is absent. The transition to the macroscopic or fluid description is carried out by an appropriate expansion, and the transient behavior is given of the important moments. Finally, correlation functions among many particles are discussed. Author
- Physical Chemistry
- Plasma Physics and Magnetohydrodynamics