Current-carrying string loop motion: Limits on the classical description   and shocks
  The dynamical evolution of superconducting cosmic strings is much more complicated than that of simple Goto-Nambu strings. For this reason, there are only a few known analytical solutions and no numerical ones. The goal of this paper is to present numerical solutions for the dynamics of planar superconducting cosmic string loops. In most cases, a purely dynamical approach turns out to be insufficient to describe correctly the evolution of a loop due mainly to the appearance of shocks when spacelike currents are present and kinks for timelike currents, leading to yet unaccounted for quantum effects. The consequences of the quantum effects are mostly unknown at this time because the problem requires a dynamical field theory treatment. It is however likely that ultimately the result will be massive radiation in the form of charge carriers from the string. 
X. Martin and P. Peter