Electrostatic modes in dusty plasmas with continuous size distributions

When the dust plasma frequency, and hence the dust-acoustic velocity is computed for a dusty plasma containing charged grains with individual identities, three possibilities occur in a natural way. One form is based on the average over all dust grains of the ratio of the square of charge to mass, whereas a second one uses the average charge and the average mass. The difference between the two gives rise to a dust distribution mode. A third option is to describe dust grains of similar composition by a monodisperse model based on an average radius, that conserves overall charge density. The dust plasma frequency thus obtained is intermediate between those from the two other definitions, indicating that the use of a monodisperse description at this average size underestimates the mass effects of the distribution. These results are applied to power-law size distributions observed in planetary rings