  We study chiral vorton production for Witten-type superconducting string
models in the context of a recently developed analytic formalism. We delineate
three distinct scenarios: First, a low energy regime (including the electroweak
scale) where vortons can be a source of dark matter. Secondly, an intermediate
energy regime where the vorton density is too high to be compatible with the
standard cosmology (thereby excluding these models). Finally, a high energy
regime (including the GUT scale) in which no vortons are expected to form. The
vorton density is most sensitive to the order of the string-forming phase
transition and relatively insensitive to the current-forming transition. For a
second-order string transition, vorton production is cosmologically disastrous
for the range $10^{-28}\lsim G\mu \lsim 10^{-10}$ ($10^{5} GeV \lsim T_{c}
\lsim 10^{14} GeV$), while for the first-order case we can only exclude
$10^{-20}\lsim G\mu \lsim 10^{-14}$ ($10^{9} GeV \lsim T_{c} \lsim 10^{12}
GeV$). We provide a fitting formula which summarises our results.
