Ion oscillations in a one dimensional plasma-sheath system are simulated by the aid of the convective scheme, combining the kinetic equation with the Poisson equation. The frequency spectra of the ion current through a cathode reveal to us that two modes of ion acoustic wave are dominant; a high frequency mode and the fundamental mode. By using a linearized differential equation the appearance of the two modes is corroborated. As the nonlinear phenomena on the fundamental mode, excitation of sub-harmonics is observed if the gas pressure concerned with ionization is changed. A model equation of nonlinear oscillation including the ponderomotive force term caused by the high frequency mode is introduced, and sub-harmonics and period-doubling bifurcations are shown by using the growth rate with the flow velocity obtained in our linear theory.
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