Study Of Magnetorotational Instability In Viseous Dusty Plasnlas With Three-component Model

The magnetorotational instability (MRI), is a fluid instability that arises when the angular velocity of a magnetized fluid decreases as the distance from the rotation center increases. It is thought that plasma turbulence and angular momentum transport in accretion discs arise from MRI, where a magnetic field destabilizes a rotating velocity field which decreases outwardly.The MRI in axisymmetric rotating dusty plasmas which with viscous effects is investigated by means of a three-component model MRI with a vertical weak magnetic field in this paper. Starting from the three-fluid equations and Maxwell’s equations, we derive the general linear dispersion relation governing local MRI. The dust rotational flow is assumed to have the same angular velocity with ions and electrons, and short-wave approximation (krr>>1) is considered to simplify the results. We base our analysis on the results of previous studies, but differ from those which assumed the dust grains were too heavy to mobile, and investigate MRI in dusty plasmas by considering viscosity dissipative effects in a rotating Couette flow using a three-fluid model in the present paper. we obtain the general local dispersion relation in high-frequency approximation (Ωe>>ω>> Ω>>Ωi>>Ωd) in order that the perturbation frequency larger than the ion cyclotron frequency.The dispersion relation is discussed in detail of two special cases by contrast, without viscosity and dust effects respectively. The numerical results demonstrate that a rotating plasma is always unstable due to MRI. See from the diagram, we get that both the viscosity and dust effects can prevent the MRI growth, and the dust-induced effects are shown to be especially significant.