  We suggest a new mean field dynamo model in anomalous MagnetoHydroDynamics
(AMHD) accounting for the mean spin (polarization) of the magnetized chiral
(ultrarelativistic) plasma of a neutron star (NS). For simplicity we consider a
non-superfluid NS with its rigid rotation neglecting also any matter turbulence
(convection) within a star. On this way, we recover the Chiral Magnetic Effect
(CME) as a possible source for the amplification of a seed, sufficiently strong
magnetic field, $B\sim 10^{13}\,\text{G}$, up to values $B\gtrsim
10^{18}\,\text{G}$ in old NS's, having ages $t\gtrsim 10^6\,\text{yr}$. The
important issue in AMHD model suggested is the continuous evolution of the
chiral imbalance providing the CME for these ages, $\partial_t\mu_5 (t)\neq 0$,
in spite of the fast spin-flip in Coulomb collisions in the dense NS plasma
that leads to vanishing $\mu_5\to 0$ at an earlier epoch in the corresponding
protoneutron star. In contrast to the conventional mean-field dynamos, the
dynamo drivers in the model are produced due to magnetic field generated at the
previous stages of stellar evolution. It makes our model basically nonlinear.

High Energy Astrophysical Phenomena;High Energy Physics - Phenomenology