Shear instability in magnetised collisional dusty plasmas

The relative motion of the lighter, magnetised plasma component against charged dust is at the heart of Hall electric field in dusty plasmas. The presence of charged dust causes very low frequency waves in both unmagnetised as well as magnetised medium. However, collisional process in dusty medium strongly influences the diffusion of magnetic field. Therefore, it should be anticipated that plasma--dust collision, by unfreezing the magnetic flux from the dusty fluid, may open new channels through which free shear energy (if it is available in the plasma) can flow to waves. We shall show that the non-thermal character of the plasma particles which manifests itself as Hall diffusion of the magnetic field facilitates the shear flow driven instability. It is important to distinguish it from well know shear driven Kelvin-Helmholtz instability. Unlike KHI where transverse magnetic field quenches the growth rate, this new, Hall effect driven shear instability is solely due to the transverse relative drift of the plasma particles against charged dust and disappears in the absence of magnetic field.