For an ordinary superconductor such as Lead, charge supercurrent gives rise to a magnetic field around the whole material for low enough currents. At large enough currents, the superconductor will either return to the normal phase, or will screen part of the magnetic field from the supercurrent through vorticies. Depending on which effect occurs, the superconductor would be considered type I or type II.
Recently I saw the article by Krishna Rajagopal and Frank Wilczek The Condensed Matter Physics of QCD. I am totally unfamiliar with QCD, but this got me thinking about color superconductors. In particular, a color-charged supercurrent would have to give rise to some sort of static/DC color or gluon field. However, I presume the strong interaction would mean such a static color field would cost huge amounts of energy, and would immediately give rise to either vorticies or some other mechanism to screen it. Alternatively, it could be that only color-neutral supercurrents/cooper pairs can exist because of the aforementioned energy cost.
So I want to ask, in a color superconductor can a color supercurrent possibly exist? If so, how does the rest of the superconductor respond?