Multiple-sheath and the time-dependent grain charge in a plasma with trapped ions

Multiple-sheath structures and the time-dependent dust grain-charge in a dusty plasma with the electron emission and trapped ions are investigated by numerical calculation. Trapped positive ions, electron emission beam and dust grains modify the shape of the sheath, enhance the space charge density and give rise to the triple-electric field structure. It is found that the effect of trapped ions plays an important role in the formation of the new electric field structure in the sheath and shorten the charging time.