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In this paper, the neutral 2SC phase of color superconductivity is investigated in the presence of a magnetic field and for diquark coupling constants and baryonic densities that are expected to characterize neutron stars. Specifically, the behavior of the charged gluons Meissner masses is investigated in the parameter region of interest, taking into account, in addition, the contribution of a rotated magnetic field. It is found that up to moderately high diquark coupling constants the mentioned Meissner masses become tachyonic independently of the applied magnetic-field amplitude, hence signalizing the chromomagnetic instability of this phase. To remove the instability, the restructuring of the system ground state is proposed, which now will be formed by vortices of the rotated charged gluons. These vortices boost the applied magnetic field, having the most significant increase for relatively low applied magnetic fields. Finally, considering that with the stellar rotational frequency observed for magnetars a field of the order of 10^8 G can be generated by dynamo effect, we show that by the boosting effect just described the field can be amplified to 10^17 G that is in the range of inner core fields expected for magnetars. Thus, we conclude that the described mechanism could be the one responsible for the large fields characterizing magnetars if the cores of these compact objects are formed by neutral 2SC matter.