  We derive and solve a Boltzmann equation governing the cosmological evolution
of the number density of current carrying cosmic string loops, whose
centrifugally supported equilibrium configurations are also referred to as
vortons. The phase space is three-dimensional and consists of the time
variable, the loop size, and a conserved quantum number. Our approach includes
gravitational wave emission, a possibly finite lifetime for the vortons and
works with any initial loop distribution and for any loop production function.
We then show how our results generalize previous approaches on the vorton
excess problem by tracking down the time evolution of the various
sub-populations of current-carrying loops in a string network.
