The influence of a dust size distribution on the dust-acoustic mode

A real dusty plasma is modelled by taking into account the size distribution of the dust particles. The influence of this distribution on the dust plasma frequency is examined for a power law distribution and for a normal distribution. The first is relevant in astrophysical applications (e.g. planetary rings, comets), while the latter can be used in laboratory plasmas (e.g. dust crystals). It is shown that the dust plasma frequency for a power law distribution exceeds the plasma frequency for mono-sized dust. A normal distribution will result in an increase of the dust plasma frequency. The corrections have been quantified for these two distributions and the change to the real part of the dispersion relation for the dust-acoustic wave is discussed.