Kinetic theory of Jeans instability of a dusty plasma

A kinetic theory of the Jeans instability of a dusty plasma has been developed in the present work. The effect of grain charge fluctuations due to the attachment of electrons and ions to the grain surface has been considered in the framework of Krook's collisional model. We demonstrate that the grain charge fluctuations alter the growth rate of the gravitational collapse of the dusty plasma. The Jeans length has been derived under limiting cases, and its dependence on the attachment frequency is shown. In the absence of gravity, we see that the damping rate of the dust acoustic mode is proportional to the electron-dust collision frequency.