Unified kinetic theory of plasma correlations

Abstract

A unified approach to the kinetic theory of correlations in a plasma is presented, based on the BBKGY hierarchy. The theory is applied to a one-component plasma with the Coulomb interaction modified to include effects of the background. Closed integro-differential equations in space, momentum and time are obtained for the two-particle correlation function in both the strong and weak coupling limits. To corroborate the theory, the formalism is applied in the equilibrium limit. In the weak-coupling domain, γ ≪ 1, the time-independent analysis returns the well-known linearized Debye-Hückel result, where γ is the plasma parameter. In the strong-coupling domain with γ ≥ 1, the resulting two-particle ‘total’ correlation function exhibits decaying oscillatory behaviour for particle separation of the order of the effective interparticle range. Exponential behaviour of the correlation function found for small values of particle separation agrees with previous results of statistical mechanics.