We study how the presence of world-sheet currents affects the evolution of cosmic string networks, and their impact on predictions for the cosmic microwave background (CMB) anisotropies generated by these networks. We provide a general description of string networks with currents and explicitly investigate in detail two physically motivated examples: wiggly and superconducting cosmic string networks. By using a modified version of the CMBact code, we show quantitatively how the relevant network parameters in both of these cases influence the predicted CMB signal. Our analysis suggests that previous studies have overestimated the amplitude of the anisotropies for wiggly strings. For superconducting strings the amplitude of the anisotropies depends on parameters which presently are not well known - but which can be measured in future high-resolution numerical simulations.
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