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This study explores the dynamic evolution of dust electrical potential and plasma particle number densities with a focus on the charging of dust grains through electron and ion absorption, as described by the orbital motion limited (OML) theory. The initial model, which does not account for plasma particle sources and sinks, predicts that dust grains could eventually absorb all plasma particles, leading to a null electrical potential. To address this, we introduced source and sink terms considering a finite region of space in order to simulate real conditions. Our findings indicate that, with the inclusion of plasma particle flow into and out of the region, dust grains reach a stable, non-zero equilibrium potential and the electron and ion densities reach an equilibrium value. This equilibrium is dependent on the size of the region; larger regions result in lower plasma densities and more negative equilibrium potentials. For extensive regions, the dust potential initially mirrors the scenario without sources or sinks but eventually deviates, showing increasing negative values as the region size grows. This behavior is attributed to the electron source term surpassing the combined sink and absorption terms at certain intervals along time evolution., Comment: Submitted to Physics of Plasmas

In this work we investigate the characteristics of the group velocity of obliquely propagating Alfv\'en waves in a dusty plasma typical of a stellar wind. The dispersion relation is derived with the aid of the kinetic theory for a magnetized dusty plasma consisting of electrons and ions, with distribution of momenta described by a Maxwellian function. The dust particles are considered to be immobile and have all the same size; they are electrically charged by absorption of plasma particles via inelastic collisions and by photoionization. We numerically solve the dispersion relation and calculate the components of group velocity (along and transverse to the magnetic field) for the normal modes, namely the compressional and shear Alfv\'en waves (CAW and SAW). The results show that the direction of the group velocity of CAWs is greatly modified with the wave-vector direction. On the other hand, SAWs will present group velocity propagating practically along the magnetic field. The changes in dust parameters, such as number density and equilibrium electrical charge, may significantly change the waves' characteristics. It is seen that for sufficiently high dust to ion number density ratio, the SAWs may present perpendicular group velocity propagating in opposite direction to the perpendicular phase velocity, in a small interval of wavenumber values; we also notice that this interval may change, or even vanish, when the flux of radiation incident on the dust is altered, changing the equilibrium electrical charge of the grains., Comment: 10 pages, 9 figures. Monthly Notices of the Royal Astronomical Society, 2022

The characteristics of Alfv\'en waves propagating in a direction oblique to the ambient magnetic field in a stellar wind environment are discussed. A kinetic formulation for a magnetized dusty plasma is adopted considering Maxwellian distributions of electrons and ions, and immobile dust particles electrically charged by absorption of plasma particles and by photoionization. The dispersion relation is numerically solved and the results are compared with situations previously studied where dust particles were not charged by photoionization, which is an important process in a stellar wind of a relatively hot star. We show that the presence of dust causes the shear Alfv\'en waves to present a region of wavenumber values with zero frequency and that the minimum wavelength for which the mode becomes dispersive again is roughly proportional to the radiation intensity to which the dust grains are exposed. The damping rates of both shear and compressional Alfv\'en waves are observed to decrease with increasing radiation flux, for the parameters considered. For the particular case where both modes present a region with null real frequency when the radiation flux is absent or weak, it is shown that when the radiation flux is sufficiently strong, the photoionization mechanism may cause this region to get smaller or even to vanish, for compressional Alfv\'en waves. In that case, the compressional Alfv\'en waves present non zero frequency for all wavenumber values, while the shear Alfv\'en waves still present null frequency in a certain interval of wavenumber values, which gets smaller with the presence of radiation., Comment: 10 pages, 4 figures. Monthly Notices of the Royal Astronomical Society, 2022

Using a kinetic description of a homogeneous magnetized dusty plasma with Maxwellian distribution of electrons and protons and dust particles charged by inelastic collisions and by photoionization, we analyse the dispersion relation considering the case where waves and radiation propagate exactly parallel to the ambient magnetic field. The investigation emphasizes the changes that the photoionization process brings to the propagation and damping of the waves in a stellar wind environment, since Alfv\'en waves are believed to play a significant role in the heating and acceleration processes that take place in the wind. The results show that, in the presence of dust with negative equilibrium electrical charge, the Alfv\'en mode decouples into the whistler and ion cyclotron modes for all values of wavenumber, but when dust particles acquire neutral or positive values of electrical charge, these modes may couple for certain values of wavenumber. It is also seen that the whistler and ion cyclotron modes present null group velocity in a interval of small wavenumber, and that the maximum value of wavenumber for which the waves are non-propagating is reduced in the presence of the photoionization process. For very small values of wavenumber, the damping rates of the modes could change significantly from very small to very high values if the sign of the dust electrical charge is changed., Comment: 12 pages, 6 figures. Monthly Notices of the Royal Astronomical Society, 2021