  We rederive, using an elementary formalism, the general solution to the
equations of motion for a superconducting string with a chiral (null) neutral
current, earlier obtained by Carter and Peter. We apply this solution to show
that the motion of such string loops is strictly periodic and analyze cusp-like
behavior and vorton solutions of arbitrary shape. We argue that this solution
can be used to approximately describe the dynamics of superconducting strings
with small non-chiral currents. We use this description to estimate the
electromagnetic radiation power from such strings.
