Charge-velocity-dependent one-scale linear model

We apply a recently developed formalism to study the evolution of a current-carrying string network under the simple but generic assumption of a linear equation of state. We demonstrate that the existence of a scaling solution with nontrivial current depends on the expansion rate of the Universe, the initial root-mean-square current on the string, and the available energy-loss mechanisms. We find that the fast expansion rate after radiation-matter equality will tend to rapidly dilute any preexisting current, and the network will evolve towards the standard Nambu-Goto scaling solution (provided there are no external current-generating mechanisms). During the radiation era, current growth is possible provided the initial conditions for the network generate a relatively large current and/or there is significant early string damping. The network can then achieve scaling with a stable nontrivial current, assuming large currents will be regulated by some leakage mechanism. The potential existence of current-carrying string networks in the radiation era, unlike the standard Nambu-Goto networks expected in the matter era, could have interesting phenomenological consequences.