Dynamics of superconducting strings with chiral currents
  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. 
J.J. Blanco-Pillado, Ken D. Olum and Alexander Vilenkin