  In this paper we study a system inspired on certain SUSY breaking models and
on more recent Dark Matter scenarios. In our set-up, two Abelian gauge fields
interact via an operator that mixes their kinetic terms. We find the extended
Supersymmetric version of this system, that also generates a Higgs portal type
of interaction. We obtain and study both analytically and numerically, the
equations defining topologically stable string-like objects. We check our
results using two different approaches. Various technical details are
explicitly stated for the benefit of various readers.
