Electrostatic modes and instabilities in nonideal dusty plasmas with sheared flows and grain charge fluctuations

The combined effects of nonideal contributions and grain charge fluctuations on the propagation of low-frequency electrostatic modes, such as the dust-acoustic waves and drift waves, as well as on the excitation of (parallel) Kelvin–Helmholtz instabilities in a dusty inhomogeneous magnetoplasma are investigated. In the low-frequency regime, dust-acoustic waves and drift waves are recovered with modifications due to the nonideal, as well as charge fluctuation contributions. Magnetized dusty plasmas support a dust temperature gradient-driven drift wave, which exists even in the absence of density inhomogeneities. In the dust gyro-frequency regime, the electrostatic dust cyclotron mode is modified by the transverse shear in the field-aligned flow. The other branch of the cyclotron mode becomes unstable when the shear flow exceeds a threshold value, which is determined by the ratio of the parallel to perpendicular component of the wave number. In general, the charge fluctuation leads to an overall decrease in the growth rate of the excited instability. For the Kelvin–Helmholtz configuration, the existence of a temperature gradient-driven instability that occurs when the relative flow speed between adjacent layers exceeds a critical value is shown. The latter is found to be much smaller than the dust-acoustic phase speed which is applicable for the density gradient-driven Kelvin–Helmholtz instability. On the other hand, the effects of the nonideal contributions in the two cases show quantitative behavior which are complementary to each other. For frequencies larger than the charging frequency, there is a net reduction in the growth rate of the instabilities due to the grain charge fluctuations.