Electromagnetic back-reaction from currents on a straight string
  Charge carriers moving at the speed of light along a straight, superconducting cosmic string carry with them a logarithmically divergent slab of electromagnetic field energy. Thus no finite local input can induce a current that travels unimpeded to infinity. Rather, electromagnetic back-reaction must damp this current asymptotically to nothing. We compute this back-reaction and find that the electromagnetic fields and currents decline exactly as rapidly as necessary to prevent a divergence. We briefly discuss the corresponding gravitational situation. 
Jeremy M. Wachter and Ken D. Olum
astro-ph.CO