  In this paper we present the first analytic model for vorton formation. We
start by deriving the microscopic string equations of motion in Witten's
superconducting model, and show that in the relevant chiral limit these
coincide with the ones obtained from the supersonic elastic models of Carter
and Peter. We then numerically study a number of solutions of these equations
of motion and thereby suggest criteria for deciding whether a given
superconducting loop configuration can form a vorton. Finally, using a recently
developed model for the evolution of currents in superconducting strings we
conjecture, by comparison with these criteria, that string networks formed at
the GUT phase transition should produce no vortons. On the other hand, a
network formed at the electroweak scale can produce vortons accounting for up
to 6% of the critical density. Some consequences of our results are discussed.
