Nonlinear Dynamics of a Grain in a Discharge Plasma Sheath

Recently the dynamics of dust grains trapped in the sheath region of radio-frequency (rf) or dc plasma discharges under low pressure conditions has attracted the attention of the dusty plasma community. Several experiments have been performed in order to explore the dynamics of dust grains levitating above the negatively biased electrode. Under very low pressures, several experimental groups have observed the generation of self excited large amplitude vertical oscillations which arise by lowering either the background pressure or the plasma number density. In other experiments, the vertical oscillations have been driven by an external sinusoidal voltage applied to a wire in the sheath region. A theoretical model is presented that successfully describes the phenomenology in these various experiments including the observed self excited oscillations and nonlinear resonance oscillations.