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Neutron stars, and magnetars in particular, are known to host the strongestmagnetic fields in the Universe. The origin of these strong fields is a matterof controversy. In this preliminary work, via numerical simulations, we study,for the first time in non-ideal general relativistic magnetohydrodynamic(GRMHD) regime, the growth of the magnetic field due to the action of themean-field dynamo due to sub-scale, unresolved turbulence. The dynamo process,combined with the differential rotation of the (proto-)star, is able to producean exponential growth of any initial magnetic seed field up to the valuesrequired to explain the observations. By varying the dynamo coefficient weobtain different growth rates. We find a quasi-linear dependence of the growthrates on the intensity of the dynamo. Furthermore, the time interval in whichexponential growth occurs and the growth rates also seems to depend on theinitial configuration of the magnetic field.

General Relativistic Mean-field Dynamo Model for Proto-neutron Stars