  We present analytic and numerical results for the evolution of currents on
superconducting strings in the classical $U(1) \times U(1)$ model. We derive an
energy functional for the currents and charges on these strings, establishing
rigorously that minima should exist in this model for loops of finite size
(vortons) if both charge and current are present on the worldsheet. We then
study the stability of the currents on these strings, and we find an analytic
criterion for the onset of instability (in the neutral limit). This limit
specifies a lower maximal current than previous heuristic estimates. We
conclude with a discussion of the evolution of loops towards their final vorton
state in the model under consideration.
