Magnetic Field Effect on Neutral Color Superconductivity as a Mechanism to Boost the Inner Magnetic Field of Magnetars

In this paper, we review the impact of a strong magnetic field on the neutral two-flavor color superconducting (2SC) phase of dense quark matter. Using a Nambu–Jona–Lasinio (NJL) model approach in the mean-field approximation, we first solve the gap equations for the diquark condensate Δ and the electric chemical potential μe under a uniform external magnetic field, and discuss the coupled evolution of the chiral and diquark order parameters. We then evaluate the field-dependent Meissner masses of the rotationally charged gluons for a wide range of densities and moderate diquark coupling strengths. Combining the “zero-mode problem” mechanism with the neutrality condition, we show that the gluon masses become tachyonic, even at moderate magnetic field values, signaling a chromomagnetic instability in density regions where the system was stable at zero field. This instability can be resolved through the restructuring of the ground state with the formation of a gluon vortex condensate. A remarkable consequence of the vortex configuration is the paramagnetic amplification of the in-medium magnetic field: seed fields of the order 1015 G can be enhanced by up to two orders of magnitude, reaching ∼1017 G, precisely the range predicted for magnetar cores. We compare this microscopic mechanism with the conventional dynamo explanation and discuss how it offers a plausible explanation for the extremely high magnetic fields expected to be realized in magnetar interiors.