Variational Study of Ordinary and Superconducting Cosmic Strings

We use a variational approach to study Abelian vortices, both the ordinary and bosonic superconducting varieties. We present accurate results for the energy per length. For superconducting strings we map out the parameter space of solutions, quantify the critical current, discuss the quench transition, and investigate the possibility of static solutions where electromagnetic stresses balance the string tension.