We develop an analytic model to quantitatively describe the evolution of superconducting cosmic string networks. Specifically, we extend the velocity-dependent one-scale (VOS) model to incorporate arbitrary currents and charges on cosmic string world sheets under two main assumptions, the validity of which we also discuss. We derive equations that describe the string network evolution in terms of four macroscopic parameters: the mean string separation (or, alternatively, the string correlation length) and the root mean square velocity which are the cornerstones of the VOS model, together with parameters describing the averaged timelike and spacelike current contributions. We show that our extended description reproduces the particular cases of wiggly and chiral cosmic strings, previously studied in the literature. This VOS model enables investigation of the evolution and possible observational signatures of superconducting cosmic string networks for more general equations of state, and these opportunities will be exploited in a companion paper.

中文翻译：

---

载流弦的广义速度相关一阶模型

我们开发了一个分析模型来定量描述超导宇宙弦网络的演变。具体来说，我们扩展了速度相关的一阶（VOS）模型，在两个主要假设下将任意电流和电荷合并到宇宙弦世界表上，我们还将讨论其有效性。我们推导出用四个宏观参数描述弦网络演化的方程式：均弦间隔（或弦相关长度）和均方根根速度（它们是VOS模型的基础），以及描述弦网络演化的参数。平均时空和时空当前贡献。我们表明，我们的扩展描述再现了摆动和手性的特殊情况以前在文献中研究过的宇宙弦。这个VOS模型能够研究超导宇宙弦网络的演化和可能的观测特征，以获取更一般的状态方程，这些机会将在伴随论文中得到利用。