A linearized Fokker-Planck study of ion-eigenmodes in an unmagnetized pair-ion-electron plasma

Two kinds of ion-eigenmodes in an unmagnetized pair-ion-electron plasma, pair-ion-acoustic waves (PIAWs) and ion-Langmuir waves (ILWs), are investigated with Fokker-Planck description. The linearized negative- and positive-ion Fokker-Planck equations and linearized electron Vlasov equation are solved numerically as an eigenvalue problem. The frequencies and damping rates of PIAWs and ILWs are presented as a function of kλ, kλ_D, T_e/T, n_-/n₊, where k is the wave number, λ is the mean-free path of the positive ion, λ_D is the positive ion Debye length, T_e and T are electron and ion temperature, and n_-/n₊ is the ratio of negative ion density to positive ion density. It is found that the dispersion relations of PIAWs and ILWs are sensitive to the strength of ion-ion collisions. As kλ increases, it is shown that PIAWs evolve into ILWs smoothly at small negative ion concentration. For large n_-/n₊, PIAWs and ILWs, respectively, exist in a strong-collisional and rare-collisional region, and coexist in the intermediate regime at about kλ∼1. For comparison, hydrodynamic description and Vlasov description are also discussed. When the Landau damping is negligible, the two-fluid hydrodynamic description can give good results for ILWs if the friction forces between the negative and positive ions are included