  Using a generally covariant Electro-Vortic (magnetofluid) formalism for
relativistic plasmas, the dynamical evolution of a generalized vorticity (a
combination of the magnetic and kinematic parts) is studied in a cosmological
context. We derive macroscopic vorticity and magnetic field structures that can
emerge in spatial equilibrium configurations of the relativistic plasma. These
fields, however, evolve in time. These magnetic and velocity fields fields are
self-consistently sustained in a diamagnetic state in the expanding Universe,
and do not require an external seed for their existence. In particular, we
explore a special class of magnetic/velocity field structures supported by a
plasma in which the generalized vorticity vanishes. We derive a highly
interesting characteristic of such "superconductor--like" fields in a
cosmological plasmas in the radiation--era in early Universe. In that case, the
fields grow proportional to the scale factor, establishing a deep connection
between the expanding universe and the primordial magnetic fields.
