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In this paper, we present some results of previous works on Alfvén waves in a dusty plasma in different astrophysical and space regions by taking into account the effect of superthermal particles on the dispersive characteristics. We show that the presence of dust and superthermal particles sensibly modify the dispersion of Alfvén waves. The competition between different damping processes of kinetic Alfvén waves and Alfvén cyclotron waves is analyzed. The nonlinear evolution of Alfvén waves to chaos is reviewed. Finally, we discuss some applications of Alfvén waves in the auroral region of space plasmas, as well as stellar winds and star-forming regions of astrophysical plasmas. [ABSTRACT FROM AUTHOR]

A kinetic description is used to analyze wave propagation in dusty plasmas, taking into account the fluctuation of the charge of the dust particles due to inelastic collisions with electrons and ions. The case of propagation of waves exactly parallel to the external magnetic field and Maxwellian distributions for the electrons and ions in the equilibrium is considered, and a parametric analysis of the dispersion relation is performed. The investigation emphasizes particularly the effects of dust density, radius of dust particles, ion temperature, ratio between electron and ion temperatures, ion density, and ambient magnetic field, on the solutions of the dispersion relation. The analysis shows the possibility of occurrence of coupling between waves in the whistler branch and waves in the branch of circularly polarized waves, in the presence of the dust particles. [ABSTRACT FROM AUTHOR]

Using a completely kinetic description to analyze wave propagation in dusty plasmas, the case of propagation of waves exactly parallel to the external magnetic field and Maxwellian distributions for electrons and ions in the equilibrium is considered. A model for the charging process of dust particles which depends on the frequency of inelastic collisions between dust particles and electrons and ions is used. The dispersion relation and damping rates for Alfvén waves are obtained. For the numerical solutions, the average value of the inelastic collision frequency is used as an approximation. The results show that the presence of dust particles with variable charge in the plasma produces significant additional damping of the Alfvén wave. A novel process of mode coupling of low-frequency waves is demonstrated to occur due to the presence of dust particles. [ABSTRACT FROM AUTHOR]