Nonlinear phenomena of the ion acoustic wave in a negatively charged plasma-sheath system are observed in the simulation with a convective scheme described by a two-dimensional phase space, and are theoretically analyzed. Subharmonics of a fundamental mode are excited and show the bifurcation phenomena when the intensity of the ion source relating to the ionization is increased. A reversed electric field from the cathode to anode reveals that the ponderomotive force due to a high frequency mode pushes the ions toward the cathode. A nonlinear coupling of two modes through the ponderomotive force is a key idea to construct the model. Nonlinear dynamical model equations involving the coupling of the two modes and an interaction of the sheath with the two modes, i.e., two nonlinear effects, are proposed. The period-doubling bifurcations of the fundamental mode are examined by using the same growth rates with the flow velocity as in our previously published linear theory.
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