Type-I superconductivity of protons and magnetic fields of pulsars

The magnetic structure of neutron vortices in the superfluid cores of neutron stars is determined assuming that the proton condensate forms a type-I superconductor. It is shown that the entrainment currents induced by the neutron vortex circulation cause the proton superconductor to break into normal and superconducting domains of cylindrical form coaxial with the neutron vortex. The minimum of the energy functional corresponds to a tube radius a(0.1 – 0.5) b, where b is the outer radius of the neutron vortex. The magnetic field within the tube is of the order of 5 × 10¹⁴ G.