On the nature of the residual magnetic fields in millisecond pulsars

We consider the expulsion of proton fluxoids along neutron vortices from th e super fluid/superconductive core of neutron star with weak (B < 10(10) G) magnetic field. The velocity of fluxoids is calculated from the balance of buoyancy, drag and crustal forces. We show, that the proton fluxoids can l eave the super fluid core sliding along the neutron vortices on a timescale of about 10(7) years. An alternative possibility is that fluxoids are alig ned with the vortices on the same timescale. As the result, non-aligned sur face magnetic fields of millisecond pulsars can be sustained for <greater t han or similar to>10(9) years only in case of a comparable dissipation time scale of the currents in the neutron star crust. This defines upper limits of the impurity concentration in the neutron star crust: Q less than or sim ilar to 0.1 if a stiff equation of state determines the density profile.