Using a two-fluid description of a large, magnetized, self-gravitating plasma cloud, we derive a fully nonlinear system of equations for electrostatic and gravitational potentials. In the regime when nonlinear effects, arising from the particle drift, are dominating over the gravitational condensation, we obtain a stationary solution in the form of travelling double vortex, with the charge separation being localized to the vortex core, and its immediate surroundings. Density perturbation has a long range spatial extend, in the form of alternating condensations and rarefactions with the typical scale length of the order of Jeans' critical length. Influence of higher order effects, and their role in the gravitational contraction of the vortex, is discussed.