In a one-dimensional plasma-sheath system representing a concave quasistationary electric potential typical of a negatively charged system, oscillations of ion are simulated by the aid of a convective scheme useful for weakly ionized plasma, and are theoretically investigated. The frequency spectra of the ion current through a cathode reveal to us that two modes of ion acoustic waves are dominant; a high and a low frequency mode. By deriving a linear differential equation with a dissipation and an ion flow, and taking for granted the sheath width and the distribution of ion flow velocity, the dispersion relation for a finite length system can be calculated. The simulation results, such as the reinforcement of the low frequency mode and the suppression of the high frequency mode, are satisfactorily corroborated by the linear theory. The instabilities of the waves are caused by the asymmetry of boundary conditions and by the dissipative effect.
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