Effects of Dust on Amplitude Modulation of Kinetic Alfvén Waves

Abstract

Effects of dust on the amplitude modulation of two possible types of kinetic Alfvén waves, modified and dust kinetic Alfvén waves, in a magnetized dusty plasma have been investigated. The appropriate nonlinear dispersion relations of the amplitude modulation predict that the carrier kinetic Alfvén waves are modulationally unstable for long wave-length perturbations. It has been found that the parameter σ plays a significant role on the amplitude modulation of the waves, where σ is the ratio of the equilibrium number densities of the ions and the electrons and is a measure of the charge carried by the dust component. The maximum growth rate of the modulational instability increases with the parameter σ, whereas, the range of the perpendicular component of the modulation wavenumber K⊥ of the unstable wave remains almost constant for the case of dust kinetic Alfvén waves. On the other hand, the maximum growth rate is almost constant with σ, while the range of K⊥ of the unstable wave drastically decreases for the case of modified kinetic Alfvén waves.