The hydrodynamic equations for opposite polarity dust grains in a quasineutral magnetoplasma, together with Ampère’s law, are used to derive nonlinear equations for ultralow-frequency (in comparison with the dust gyrofrequency) dispersive dust Alfvén waves (DDAWs). In the linear approximation, the frequency of the DDAWs is obtained. The governing equations for the DDAWs admit a tearing instability as well as a dipolar vortex solution.
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P. K. Shukla (2004) studied this question.
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