Derivation from the B.B.G.K.Y.-hierarchy of a completely convergent collision integral for a fully ionized plasma, pt. 1

A spatially uniform approximation for the binary correlation function is derived from the so called Born-Bogolyobov-Green-Kirkwood-Yvon theory with an explicit evaluation of the accuracy of the result. No use is made of ad hoc truncations of the open set of hierarchy equations, or of inconsistent power series expansions in the plasma parameter. Functional forms that are only valid in thermodynamic equilibrium are also not used. The resulting expression for the free energy in thermodynamic equilibrium is shown to be finite and in agreement with equilibrium theory. The resulting collision integral converges completely and is used to calculate the high-frequency electrical conductivity in a spatially homogeneous plasma