  We investigate singly and doubly charged flux tubes in U(1) lattice gauge
theory. By simulating the dually transformed path integral we are able to
consider large flux tube lengths, low temperatures, and multiply charged
systems without loss of numerical precision. We simulate flux tubes between
static sources as well as periodically closed flux tubes, calculating flux tube
profiles, the total field energy and the free energy. Our main results are that
the string tension in both three and four dimensions scales proportionally to
the charge -- which is in contrast to previous lattice results -- and that in
four-dimensional U(1) there is an attractive interaction between flux tubes for
beta approaching the phase transition.
