The effective dielectric constant of plasmas:effects of screening

The object of this work is to calculate the effective dielectric constant tensor of a warm plasma made of non point-like ions in an electron gas whose screening length is much larger than the inter-ionic and inter-electronic distances. In this disordered medium, a proper treatment of the screening effects is proposed, and developed in the case of an ionic electromagnetic response described through an ad hoc dielectric constant. Here the latter is extracted from the ion RPA response. In the linear regime in ion density, one obtains a new mixing law for the dielectric constant. It's transverse part is compared with the Maxwell Garnett mixing law. In this paper one also gives the basis for its companion, where the complete calculation of the ionic scattering matrix will allow one to go further in ion density using a liquid-like 2-point correlation function to describe the ionic disorder.