In a one-dimensional plasma-sheath system representing a concave quasistati
onary electric potential typical of a negatively charged system, oscillatio
ns 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 aco
ustic waves are dominant; a high and a low frequency mode. By deriving a li
near differential equation with a dissipation and an ion flow, and taking f
or granted the sheath width and the distribution of ion flow velocity, the
dispersion relation for a finite length system can be calculated. The simul
ation 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 asymmet
ry of boundary conditions and by the dissipative effect. (C) 2000 American
Institute of Physics. [S1070-664X(00)00603-0].