On the screening condition in the core of neutron stars

Earlier, the screening condition in neutron star core has been formulated as equality of velocities of superconducting protons and the electrons $\mathbf{v}_p=\mathbf{u}_e$ at wavenumbers $q\ll\lambda^{-1}$ ($\lambda$ is the London penetration depth) and has been used to derive the force exerted by the electrons on a moving flux tube. By calculating the current-current response, I find that $\mathbf{v}_p\neq\mathbf{u}_e$ for $l^{-1}<q\ll\lambda^{-1}$ ($l$ is the electron mean free path). I show that at typical realistic parameters the electric field induced by a moving (relative to the electrons) flux tube is not screened by the electron currents. The implication is that the existing picture of the momentum exchange between the electrons and the flux tubes must be reassessed.