  In this work, the current stability is discussed for cosmic strings with the
bosonic superconductivity. A non-vanishing curvature of string generally induce
the quantum instability of the current-carrying particle. Its decay rates are
explored for various types of model parameters, curved string shapes, and decay
processes. As a cosmological application, the stability is examined for
superconducting strings in the string network and also for cosmic vortons by
evaluating their cosmological evolution. The zero mode and hence the vorton
cannot be stable in various cases, e.g., with a hierarchy between the
current-carrying particle mass off the string and the string tension or with
sizable couplings of the current-carrying particle to light species such as the
Standard Model particles.
