  We report on a study of the evolution of magnetic fields of neutron stars,
driven by the expulsion of magnetic flux out of the proton superconducting core
of the star. The rate of expulsion, or equivalently the velocity of outward
motion of flux-carrying proton-vortices is determined from a solution of their
equation of motion. A determination of the effective forces on the fluxoids
moving through the quantum liquid interior of neutron stars is however
confronted with many ambiguities about the properties of this special case of
superconductivity in the nature. Also, the behaviour of the fluxoids at the
core boundary, and the subsequent evolution of the expelled flux within the
highly conductive surrounding crust, are other related issues that have not
been so far explored in any great details.

Superconductivity;Astrophysics