Electrostatic two-dimensional numerical simulations of a radially symmetric barium injection experiment show that ions created by solar UV irradiation are electrostatically bound to the electrons which remain tied to the field lines on which they are created. Two possible instabilities are identified, but neither of them causes the barium plasma cloud to polarize in a way that would allow the plasma to keep up with the neutrals. In a second model the velocity of the neutrals was allowed to be a function of the azimuthal angle. In this case a portion of the cloud did polarize in a way that allowed a portion of the plasma to detach and move outward at the approximate speed of the neutrals. No rapid detachment was found when only the density of the neutrals was given an azimuthal asymmetry.