Generalized magnetohydrodynamic equations for partially ionized dusty magnetoplasmas: Derivation and applications

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Abstract
A comprehensive investigation of electromagnetic wave and instability phenomena in partially ionized, magnetized dusty plasmas has been carried out. By employing the multi‐fluid balance equations along with the Maxwell equations, a compact set of coupled field equations for the cases in which the dust grains are either robust (vd=0) or dynamic is derived. These systems of partial differential equations are used to study wave phenomena and resistive tearing mode instabilities analytically as well as by means of numerical simulations. For robust dust grains, it is shown that coupled sound‐Alfvén waves can appear even in the absence of ion‐neutral collisions. The unstable tearing modes are coupled to convective drift modes, if the dust number density is inhomogeneous. In the induction equation two new source terms for self‐generation of magnetic fields can be identified. In parameter regimes that are characterized by dynamic dust grains, the low‐frequency phenomena develop on timescales that are governed by the dust particle inertia rather than the ion inertia, as it is the case in dust‐free plasmas. The results of this investigation should be useful in understanding the properties of low‐frequency electromagnetic wave phenomena and the formation of coherent structures in dusty magnetoplasmas whose main constituents are negatively charged dust grains, singly charged positive ions, and neutrals.