  Dense quark matter is expected to behave as a type-II superconductor at
strong coupling. It was previously shown that if the strange quark mass $m_s$
is neglected, magnetic domain walls in the so-called 2SC phase are the
energetically preferred magnetic defects in a certain parameter region.
Computing the flux tube profiles and associated free energies within a
Ginzburg-Landau approach, we find a cascade of multi-winding flux tubes as
"remnants" of the domain wall when $m_s$ is increased. These flux tubes exhibit
an unconventional ring-like structure of the magnetic field. We show that flux
tubes with winding numbers larger than one survive for values of $m_s$ up to
about 20% of the quark chemical potential. This makes them unlikely to play a
significant role in compact stars, but they may appear in the QCD phase diagram
in the presence of an external magnetic field.
