The ion-beam dynamics is simulated for a bounded dusty plasma with the immobile dust particles. Since there is no dust motion, the growth of an instability is induced dominantly from the Pierce instability, but the beam motion is also greatly influenced by the Debye-shielding thermal electrons whose densities are determined from the Boltzmann relation. The analytic calculation of a dispersion relation shows the nonexistence of a uniform equilibrium which is confirmed by simulations. A period-doubling route to chaos is observed and the various nonlinear oscillations are classified in view of a diagnostic parameter which is applied to many other beam systems.
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Hur et al. (1999) studied this question.
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