Electromagnetic self-interaction of superconducting cosmic strings

This paper explores the electromagnetic self-interaction of oscillating, superconducting cosmic string loops. A linear integral operator formalism is developed. To order $q^2$ (∼(1/137), this can be put in the form of an explicit transfer matrix that connects the electromagnetic state of a string at one time to its state exactly one mechanical period later. Numerical eigenmode analysis of this matrix determines the complete electromagnetic behavior of the loop. Most modes are radiatively damped. However, it is found that some loops have unstable modes: Alternating currents grow exponentially by dynamo self-interaction. This channel converts the mechanical energy of the string into electromagnetic fields.