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We apply a recently developed formalism to study the evolution of acurrent-carrying string network under the simple but generic assumption of alinear equation of state. We demonstrate that the existence of a scalingsolution with non-trivial current depends on the expansion rate of theuniverse, the initial root mean square current on the string, and the availableenergy loss mechanisms. We find that the fast expansion rate afterradiation-matter equality will tend to rapidly dilute any pre-existing currentand the network will evolve towards the standard Nambu-Goto scaling solution(provided there are no external current-generating mechanisms). During theradiation era, current growth is possible provided the initial conditions forthe network generate a relatively large current and/or there is significantearly string damping. The network can then achieve scaling with a stablenon-trivial current, assuming large currents will be regulated by some leakagemechanism. The potential existence of current-carrying string networks in theradiation era, unlike the standard Nambu-Goto networks expected in the matterera, could have interesting phenomenological consequences.

Charge-velocity-dependent one-scale linear model