Background: Neutron star outer cores contain superfluid neutrons and superconducting protons. Their mutual interaction, mediated by vortex–flux-tube dynamics, affects both the rotational and magnetic evolution of the star. Understanding the structure and energetics of these topological defects is therefore relevant for models of glitch dynamics and magnetic field evolution.

Methods: We model the neutron–proton system with a two-component Ginzburg–Landau framework, treating neutrons as a neutral condensate and protons as a charged one. By solving the coupled Ginzburg–Landau equations, we obtain the modified core profiles of vortices and flux tubes and quantify how inter-species coupling alters their structure. The corresponding interaction energies are computed to characterise mixed configurations.

Results: The numerical calculations identify regimes in which vortices and flux tubes attract (i.e., display pinning behaviour) or repel, depending on the coupling parameters of the two condensates. Furthermore, we identify constraints on the choice of coupling parameters required to achieve stable configurations for this system.

Conclusions: A microscopically calibrated two-component Ginzburg–Landau model can reproduce key mesoscopic features of vortex–flux-tube interactions in the outer core. While our model is phenomenological, it shows that the resulting forces may be of sufficient magnitude to influence glitch dynamics as well as the coupled rotational–magnetic evolution of neutron stars.