Electromagnetic modes with the electric vector of the wave lying in the plane defined by the wave vector and the external d.c. electric field are studied theoretically in weakly ionized plasmas with several sorts of ions. The corresponding instability criteria are also given. The analysis is based on kinetic equations with BGK model collision integrais for the one-particle distribution functions of the charged constituents (electrons and all sorts of ions). The linear theory of perturbation is applied. Special attention is given to the long-wave domain (modal wavelengths much larger than the electron mean free path): it is in this domain that the instabilities are found to set in first as the electron drift is gradually increased. The increments of these instabilities are, however, smaller than in the short-wave domain which was mainly studied before. Apart from the modes which exist in weakly ionized plasmas with only one ion species, and which re-appear in the case studied here with somewhat altered characteristics, a new slow mode, specifie for multi-species weakly ionized plasmas, is found. Its phase velocity is below the electron thermal velocity, and its existence, as well as the conditions of excitation of the corresponding instability, depend on the plasma composition and non-isothermality (viz. the ratio Te/Ti). In some situations, two such modes are possible. The analysis of the instabilities is completed by a brief description of two (sometimes three) branches of ion acoustic instability, specific for the multi-species plasmas and propagating strictly along the direction of the external electric field.
The Effect of Dust Size Distribution on the Propagation of Electromagnetic Waves in a Weakly Ionized Dusty Plasma