  The form and stability of quantum vortices in Bose-Einstein condensates with
attractive atomic interactions is elucidated. They appear as ring bright
solitons, and are a generalization of the Townes soliton to nonzero winding
number $m$. An infinite sequence of radially excited stationary states appear
for each value of $m$, which are characterized by concentric matter-wave rings
separated by nodes, in contrast to repulsive condensates, where no such set of
states exists. It is shown that robustly stable as well as unstable regimes may
be achieved in confined geometries, thereby suggesting that vortices and their
radial excited states can be observed in experiments on attractive condensates
in two dimensions.
