Electrodynamics and dispersion properties of a magnetoplasma containing elongated and rotating dust grains

The electrodynamics and dispersion properties of a magnetized dusty plasma containing elongated and rotating charged dust grains are examined. Starting from an appropriate Lagrangian for dust grains, a kinetic equation for the dust grain and the corresponding equations of motion are derived. Expressions for the dust charge and dust current densities are obtained with the finite size (the dipole moment) of elongated and rotating dust grains taken into account. These charge and current densities are combined with the Maxwell-Vlasov system of equations to derive dispersion relations for the electromagnetic and electrostatic waves in a dusty magnetoplasma. The dispersion relations are analyzed to demonstrate that the dust grain rotation introduces new classes of instabilities involving various low-frequency waves in a dusty magnetoplasma. Examples of various unstable low-frequency waves include the electron whistler, the dust whistler, dust cyclotron waves, Alfven waves, electromagnetic ion-cyclotron waves, as well as lower-hybrid, electrostatic ion cyclotron, modified dust ion-acoustic waves, etc. Also found is a new type of unstable waves whose frequency is close to the dust grain rotation frequency. The present results should be useful in understanding the properties of low-frequency waves in cosmic and laboratory plasmas that are embedded in an external magnetic field and contain elongated and rotating charged dust grains