Suppression of the Kelvin–Helmholtz instability due to polarization force in nonuniform magnetized sheared dusty plasmas

Abstract

The Kelvin–Helmholtz (K–H) instability in a magnetized nonuniform velocity sheared dusty plasma is investigated accounting for the effects of dust polarization force due to inhomogeneity in background plasma number densities. A three-component fluid model for dusty plasma is formulated considering Boltzmann electron/ion fluids and flowing magnetized dust fluids whose dynamics are affected due to the presence of dust polarization force. A dispersion relation for the K–H instability is derived by applying normal mode analysis on the linearized perturbation equations of the system. It is found that the polarization parameter dependent dust acoustic mode significantly modifies the dispersion relation of the K–H instability. The critical shear required to excite the K–H instability (S > Scrit) decreases with an increase in the dust polarization parameter and dust cyclotron frequency. The growth rate of the K–H instability is observed to be suppressed due to the presence of the dust polarization parameter. The results have been discussed for experimental magnetized dusty plasmas, which shows that under considered parametric limits, one cannot ignore the presence of dust polarization force on the excitation of the K–H instability in dusty plasmas. The astrophysical consequences are also discussed in Saturn’s E-ring in the limiting case of varying dust grain size.

Kelvin–Helmholtz instability in sheared dusty plasma flows including dust polarization and ion drag forces

“…The above expression is explicitly valid for typical laboratory dusty plasmas with T e ? T i and taken into account for investigating the K-H instability in highly magnetized sheared dusty plasmas [43]. The dusty plasma environments of Saturn's rings are entirely different from the dusty laboratory plasmas.…”

“…Most recently, Prajapati and Boro [43] have investigated the effects of the dust polarization force on the suppression of the magnetic shear driven K-H instability in magnetized laboratory dusty plasmas. That work dealt with the problem of magnetic field-driven shear flow instability without considering ion drag force and generalized expression of the polarization force.…”

“…That work dealt with the problem of magnetic field-driven shear flow instability without considering ion drag force and generalized expression of the polarization force. In contrast to [43], in the present work, we have considered the effects of inertial ions, dust and ion streaming velocities, dust polarization force and ion drag force on the combined K-H and dust-ion two-stream instabilities in subsonic sheared dusty plasmas flows. A systematic study of the K-H instability starting from ordinary fluids to homogeneous dusty plasma and then inhomogeneous dusty plasma with dusty polarization and ion drag forces is presented.…”