  In this talk I will discuss how the in-medium magnetic field can influence
the gluon dynamics in a three-flavor color superconductor. It will be shown how
at field strengths comparable to the charged gluon Meissner mass a new phase
can be realized, giving rise to Abrikosov's vortices of charged gluons. In that
phase, the inhomogeneous gluon condensate anti-screens the magnetic field due
to the anomalous magnetic moment of these spin-1 particles. This paramagnetic
effect can be of interest for astrophysics, since due to the gluon vortex
antiscreening mechanism, compact stars with color superconducting cores could
have larger magnetic fields than neutron stars made up entirely of nuclear
matter. I will also discuss a second gluon condensation phenomenon connected to
the Meissner instability attained at moderate densities by two-flavor color
superconductors. In this situation, an inhomogeneous condensate of charged
gluons emerges to remove the chromomagnetic instability created by the pairing
mismatch, and as a consequence, the charged gluonic currents induce a magnetic
field. Finally, I will point out a possible relation between glitches in
neutron stars and the existence of the gluon vortices.
