Influence of dust mass distributions on generalized Jeans-Buneman instabilities in dusty plasmas

The linear dispersion law is given for a generalized Jeans-Buneman instability in the presence of a dust mass distribution. It is shown that this instability is easier to evoke when a reasonable power law mass distribution for the dust grains is assumed than for the mono-sized dust case. For Boltzmann distributed ions and electrons the dust-acoustic mode and the unstable Jeans mode are modified due to the self-gravitation and mass distribution. The frequency of the dust-acoustic mode is increased. For long wavelengths, a new stable mode occurs, due only to the dust mass distribution. The growth rate of the Jeans instability is increased, and the mode is extended beyond the usual wavelength domain. For high values of k a new instability arises, which is called the dust distribution instability.