Nodal expansions for strongly coupled classical plasmas

Abstract

The canonical equilibrium properties of classical Coulomb systems are investigated in 2 + ϵ dimensions for any value of the plasma parameter Λ ϵ = e 2 k BTλ ϵ D , through the nodal expansion of the two-particle correlation function g 2( r), wh ere e is the electronic charge, k B the Boltzmann constant, T the absolute temperature and λ D the Debye length. We first consider the one-component plasma (OCP) model. An attention is especially paid on the higher order bridge (non-convolution type) graphs. The long-ranged resummations of the convolution-like geometric series which build up the hypernetted chain (HNC) approximation are considered at length. The short-range resummations are also performed in view of their specific interest for evaluating the enhancement rates of nuclear reactions in Astrophysics and Fusion Physics. Next, we shall extend the classical nodal expansions to high-temperature OCP models in which the short distance interactions have to be corrected for the ħ ≠ 0 diffract ion effects. A second generalization concerns the high-temperature two-component plasma(TCP) model of point charges of opposite signs at high temperatures. In both cases, the bare Coulomb interaction is modified by a temperature-dependent effective interaction which allows for an entirely classical treatment of the small quantum corrections. Finally, the equilibrium properties of the TCP are used to work out the density corrections to the hydrodynamic (Bohm) diffusion transverse to an arbitrarily strong and static magnetic field.