  Neutron stars, and magnetars in particular, are known to host the strongest
magnetic fields in the Universe. The origin of these strong fields is a matter
of 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 the
mean-field dynamo due to sub-scale, unresolved turbulence. The dynamo process,
combined with the differential rotation of the (proto-)star, is able to produce
an exponential growth of any initial magnetic seed field up to the values
required to explain the observations. By varying the dynamo coefficient we
obtain different growth rates. We find a quasi-linear dependence of the growth
rates on the intensity of the dynamo. Furthermore, the time interval in which
exponential growth occurs and the growth rates also seems to depend on the
initial configuration of the magnetic field.
