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

Abstract

A kinetic description is presented here for the study of low frequency electrostatic waves in a dusty plasma including the effect of charge fluctuations on the dust grains. The kinetic description uses the charge on the grains as a dynamical variable as a generalization of the usual kinetic model to describe the charge fluctuation effects. When properly carried out it leads to the appearance of a new term in the dispersion relation arising out of the kinetic treatment of charge fluctuations. This new term strongly modifies the known dust plasma modes such as the dust acoustic modes, dust-Coulomb mode, etc., as well as leads to new modes of oscillation in the zero wave number limit both in the tenuous and dense plasma regimes (determined entirely 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 pointed out of a reflection of dust-acoustic wave from the region of increasing plasma density very much analogous to the reflection of a plasma wave in a region of increasing plasma density. There is also found the existence in the 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.