Two-component cosmological plasmas

We generalize our previous work to perform a detailed study of the modes of a two-component cosmological plasma. We are interested in the analytical form of modes not obtainable by our one-component and magnetohydrodynamical treatments, for example, ion-sound modes. These types of modes may be found in an electron-proton plasma, both in the radiation-dominated era and in the post-recombination era. We use the fluid equations previously derived in the nonrelativistic limit, with an external background magnetic field. We search for modes both with the field neglected and explicitly contained, but pay more attention to the field-free modes in this paper. The ion mass corrections to Langmuir modes are obtained, and the new ion-sound mode is studied in detail. Particular attention is paid to deriving an analytical form for the perturbed number densities and obtaining the redshifted observable frequencies from this. The differences in redshift of the various quantities that enter in constructing the modes, depending on whether the dynamics is dominated by matter or radiation, are illustrated. We also briefly explore the two-component transverse mode. As a prelude to possible further work, we derive the equations for longitudinal magnetoplasma modes and indicate the expected outcome for the solutions. Finally we present a general analytical method for finding leading asymptotic forms for any mode covered by our formalism. [S0556-2821(97)01124-7].