Current-carrying string network evolution in an external magnetic field

Cosmic strings are topological defects arising in a variety of cosmological scenarios, as the Universe undergoes symmetry-breaking phase transitions, whose discovery would offer valuable insight into the high-energy physics that shaped the early Universe. To interpret such a detection, robust theoretical models are essential. The Velocity-dependent One-Scale (VOS) model is particularly prominent: it self-consistently treats the network as a thermodynamic system, characterizing its key properties, and predicting its large-scale evolution. This has recently been extended to include superconducting cosmic strings, which carry additional degrees of freedom, giving rise to the Charge-Velocity dependent One-Scale (CVOS) model. One limitation of the latter model is that it only included loss mechanisms for the charge and current. Here, we extend this model by phenomenologically including a possible energy source mechanism, specifically by allowing current-carrying strings interactions with an external magnetic field. We discuss how this coupling impacts the network's evolution, present and classify the physically allowed scaling solutions for this extended CVOS model, and comment on the different impacts of the external magnetic field on the evolution of the network's charge and current. Under our modeling assumptions, one of the ten physically plausible scaling solution enables the network to gain energy by this mechanism.