Jeans instability of a dusty plasma

We study the linear and the nonlinear stages of the Jeans instability of charged grains with mass ${\mathit{m}}_{\mathit{d}}$ and charge ${\mathit{q}}_{\mathit{d}}$ in the regime ${\mathit{Gm}}_{\mathit{d}}^2$/${\mathit{q}}_{\mathit{d}}^2$≊O(1). Various conditions for stable electrostatic levitation, condensation, and dispersion of grains in the plasma background are obtained. The nonlinear solutions show that there is a condensation of grains even when the effect of self-gravity is annulled by self-electrostatic repulsion. Astrophysical situations relevant to the results are briefly discussed.