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