Kinetic effects of the dust charge fluctuations on the instability of dust ion-acoustic waves

In this paper, a kinetic description is used to derive the perturbed dust grain currents carried by the plasma particles, taking into account dust charge fluctuations. The longitudinal dielectric permittivity and the dispersion relation of dust ion-acoustic waves in an unmagnetized dusty plasma are obtained. It is shown that the dust charge fluctuations effectively modify the damping rate of these waves, which can lead to an excitation of instability in plasma. This instability is due to the thermal velocity of the plasma particles and dust charge fluctuations. It is different from the instability due to the drift speed of the plasma particles. It is found that there is a critical wave number above which these waves are unstable. In addition, the growth rate of these waves is numerically investigated for different plasma parameters. The present theory is applicable in astronomers and space scientists working on dusty plasmas, especially planetary ring systems and cometary tails, where dust charge fluctuations are important.