Correlations in plasmas: I. Ternary correlations

The kinetic stage of an interacting, multi-component system is studied using Bogoliubov's formalism including terms up to the second orde formalism including terms up to the second order in interaction strength λ, but to all orders in nλ, n being the density. It is shown that the second order s-particle distribution function can be expressed in terms of zero and first order binaiy and zero order ternary correlation functionals. This functional form is also shown to be deducible in a prescribed manner from the so-called cluster expansion series of the equilibrium theory. The latter observation provides a means for guessing the structures of the higher order distribution functionals. The equations satisfied by the first order binary and zero order ternary correlation functionals are derived. They constitute a coupled set of equations determining the second order contribution to the kinetic equation. Explicit expressions are found for the correlation functions when the one-particle distribution function is Maxwellian. The results, in this case, are in agreement with those obtained from the equilibrium theory.