Electrical conductivity tensor of a Coulomb plasma

The frequency dependent electrical conductivity tensor of a fully ionized, two component plasma is calculated to first order in the plasma parameter, including the leading order finite wavelength corrections. The calculation is based upon the rigorously derived BBGKY hierarchy of equations, truncated to first order in the plasma parameter and linearized about a spatially homogeneous Maxwellian equilibrium. A kinetic equation is formed, assuming a stable plasma, by solving the second equation of the hierarchy for the perturbed pair correlation function is terms of the perturbed distribution function. This solution is accomplished for arbitrary frequencies and wavevectors by two separate techniques, the Guernsey integral equation method and the Dupree operator method, and the equivalence of the two results is demonstrated