Microscopic theory of the long-wavelength modes of two component plasmas and ionic liquids: I. The transverse modes

The long wavelength modes of a system of two kinds of particles are studied starting from first principles while accounting for the presence of Coulomb interactions. It is shown that in order to cope with the Coulomb singularity the use of two-fluid hydrodynamical variables is indicated. Microscopic expressions for the various hydrodynamical modes as well as a number of interspecies relaxation modes are obtained for arbitrary density and coupling. In this paper only the transverse modes are considered. The results for the longitudinal modes as well as their contribution to a number of correlation functions will be considered in two compagnon papers.