Evolution of superconducting cosmic loops

The evolution of superconducting cosmic loops is studied numerically. The back reaction of the electromagnetic radiation on the string and the current is considered. It is shown that the infinitely thin string does not lead to a ‘‘renormalizable’’ back reaction, contrary to the case of a pointlike charge. However, a tentative formula for the electromagnetic back reaction is derived and several arguments are given to justify it. The full set of equations of motion for the string and the current is solved, both with and without the back reaction of the radiation. I discuss the stability of the current, the electromagnetic radiation, and the rate of particle production near the string. The main result is that the high-frequency modes of the current are very rapidly excited and the further evolution seems to be chaotic. This conclusion is based on the study of the Fourier spectrum of the current and an approximate computation of the largest Liapunov exponent, which turned out to be positive. For the current j≊0.005$j_{\max }$ particle production is the main mechanism of the dissipation of energy for small loops of size L≤${10}^7$ cm.