Dispersion relation for dust charge fluctuations of multi-ion dusty plasma

In this paper, we show that dust particles embedded in plasmas may show charge variations in response to fluctuations in the oscillatory currents of the plasma species. The fluctuating electrodynamics of dusty plasmas determine the dynamic forces of the charging procedures related to plasma currents. By applying the fluid model of plasma, dispersion relations for dust-acoustic and dust-ion-acoustic modes are derived while incorporating various dust parameters, such as dust-neutral collisions, dust charge fluctuations, and dust self-gravitation in a multi-species plasma consisting of electrons, positive ions, and negative ions. The influence of negative ions on the multi-component dusty plasma, along with several limiting cases, is examined through different forms of dispersion relations. The general dielectric response function is derived using the fluid treatment of each component of the dusty plasmas. The results obtained from this are relevant to numerous space plasma environments, such as astrophysical situations, cometary plasmas, planetary rings, and the interstellar medium.