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It was just shown that the mass current of the protons contains the term rho_np v_n. However, conservation of momentum and energy further requires that the charge currents equal charge to mass ratios times mass currents. Thus, rho_np v_n appears in the charge current. Thus, the circulation of neutrons around a neutron vortex creates a magnetic field! Alpar, Langer, and Sauls were the first to show that each neutron vortex carries a magnetic flux equal to the usual quantum of flux times (m_p/m_n)(rho_np/rho_pp). Note that rho_pp is not an independent parameter, but given by rho_pp = rho_p - rho_np. Of course the effect presented here vanishes if the entrainment density vanishes.

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