  The structure of the Meissner effect in a current-carrying cylindrical wire
with arbitrary disorder is studied using a numerical procedure that is exact
within the semiclassical approximation. A distribution of currents is found
that is non-monotonous as a function of the radial coordinate. For high
currents, a robust gapless superconducting state develops at the surface of
both clean and dirty leads. Our calculation provides a quantitative theory of
the critical current in realistic wires.
