Charge fluctuations and Hall effect in dusty plasmas

In a magnetized dusty plasma, Hall effect can arise due to collisional processes when, e.g., ion-dust collision decouples the ions from the magnetic field. In this case, due to the dust stoppage of the ions, the Hall electric field can be generated over large scales. The same collisional processes are also responsible for dust charge fluctuations. Therefore, the Hall effect and dust charge fluctuations are intricately linked to each other through the same mechanism. The inertial scale over which the Hall effect is dynamically important depends not only on the value of the grain charge times the ratio of the grain to the plasma (ion) number densities but also on the ratio of the ion-dust to the electron-dust collision frequencies. This scale can become arbitrarily large when these collision frequencies are comparable. We show that the charge dynamics, though linked to the Hall scale, does not directly affect the low frequency waves in the medium. Since charge fluctuation modifies the length scale over which Hall operates, the normal mode in such a medium is only indirectly affected although wave suffers weak damping due to collision.