  We analyze a simple macroscopic model describing the evolution of a cloud of
particles confined in a magneto-optical trap. The behavior of the particles is
mainly driven by self--consistent attractive forces. In contrast to the
standard model of gravitational forces, the force field does not result from a
potential; moreover, the non linear coupling is more singular than the coupling
based on the Poisson equation. We establish the existence of solutions, under a
suitable smallness condition on the total mass, or, equivalently, for a
sufficiently large diffusion coefficient. When a symmetry assumption is
fulfilled, the solutions satisfy strengthened estimates (exponential moments).
We also investigate the convergence of the $N$-particles description towards
the PDE system in the mean field regime.
