  I investigate solutions to the Euclidean Einstein-matter field equations with
topology $S^1 \times S^2 \times R$ in a theory with a massless periodic scalar
field and electromagnetism. These solutions carry winding number of the
periodic scalar as well as magnetic flux. They induce violations of a
quasi-topological conservation law which conserves the product of magnetic flux
and winding number on the background spacetime. I extend these solutions to a
model with stable loops of superconducting cosmic string, and interpret them as
contributing to the decay of such loops.
