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The effects of ion temperature are discussed in a two-ion electron plasma andfor a model applicable to the oscillating sheath theory that has recently beenmuch in the focus of researchers. The differences between the fluid and kineticmodels have been pointed out, as well as the differences between theapproximative kinetic description (which involves the expansion of the plasmadispersion function), and the exact kinetic description. It is shown that theapproximative kinetic description, first, can not describe the additionalacoustic mode which naturally exists in the plasma with an additional ionpopulation with a finite temperature, and, second, it yields an inaccurateLandau damping of the bulk ion acoustic mode. The reasons for these twofailures are described. In addition to this, a fluid model is presented that iscapable of capturing both of these features that are missing in theapproximative kinetic description, i.e., two (fast and slow) ion acousticmodes, and the corresponding Landau damping of both modes.

Ion thermal effects in oscillating multi-ion plasma sheath theory