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