A kinetic description for low frequency longitudinal waves in a dust plasma including charge fluctuations

A kinetic description is presented here for the study of low frequency elec trostatic waves in a dusty plasma including the effect of charge fluctuatio ns on the dust grains. The kinetic description uses the charge on the grain s as a dynamical variable as a generalization of the usual kinetic model to describe the charge fluctuation effects. When properly carried out it lead s to the appearance of a new term in the dispersion relation arising out of the kinetic treatment of charge fluctuations. This new term strongly modif ies the known dust plasma modes such as the dust acoustic modes, dust-Coulo mb mode, etc., as well as leads to new modes of oscillation in the zero wav e number limit both in the tenuous and dense plasma regimes (determined ent irely by charging and discharging frequencies of the grain as a capacitance ), which may be called as "grain capacitance oscillations." Because of the presence of such a frequency of oscillation, the possibility is also pointe d out of a reflection of dust-acoustic wave from the region of increasing p lasma density very much analogous to the reflection of a plasma wave in a r egion of increasing plasma density. There is also found the existence in th e tenuous plasma regime of a new purely oscillatory and purely damped "dust hybrid" mode with a frequency as a geometric mean of the new term-modified dust acoustic wave frequency and discharging frequency. (C) 2000 American Institute of Physics. [S1070-664X(00)03409-1].