  Vortex solutions to the classical field equations in a massive,
renormalizable U(1) gauge model are considered in (2+1) dimensions. A vector
field whose kinetic term consists of a Chern-Simons term plus a Stuekelberg
mass term is coupled to a scalar field. If the classical scalar field is set
equal to zero, then there are classical configurations of the vector field in
which the magnetic flux is non-vanishing and finite. In contrast to the
Nielsen-Olesen vortex, the magnetic field vanishes exponentially at large
distances and diverges logarithmicly at short distances. This divergence,
although not so severe as to cause the flux to diverge, results in the
Hamiltonian becoming infinite. If the classical scalar field is no longer equal
to zero, then the magnetic flux is not only finite, but quantized and the
asymptotic behaviour of the field is altered so that the Hamiltonian no longer
suffers from a divergence due to the field configuration at the origin.
Furthermore, the asymptotic behaviour at infinity is dependent on the magnitude
of the Stuekelberg mass term.
