On the nature of the residual magnetic fields in millisecond pulsars

We consider the expulsion of proton fluxoids along neutron vortices from the superfluid/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 leave the superfluid core sliding along the neutron vortices on a timescale of about 107 years. An alternative possibility is that fluxoids are aligned with the vortices on the same timescale. As the result, non-aligned surface magnetic fields of millisecond pulsars can be sustained for $\ga$109 years only in case of a comparable dissipation timescale of the currents in the neutron star crust. This defines upper limits of the impurity concentration in the neutron star crust: $Q \la 0.1$ if a stiff equation of state determines the density profile