Type I superconductivity of protons in neutron stars

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 successive domains of normal and superconducting regions. The Gibbs free-energy is found in the case in which the normal domains form cylindrical tubes coaxial with the neutron vortex. The minimum of the energy functional corresponds to a tube radius a similar to 0.1-0.5b, where b is the outer radius of the neutron vortex. The magnetic field within the tube is of the order of 5 x 10(14) G.