  We show that the Standard Model electroweak interaction of ultrarelativistic
electrons with nucleons ($eN$ interaction) in a neutron star (NS) permeated by
a seed large-scale helical magnetic field provides its growth up to $\gtrsim
10^{15}\thinspace\text{G}$ during a time comparable with the ages of young
magnetars $\sim 10^4\thinspace\text{yr}$. The magnetic field instability
originates from the parity violation in the $eN$ interaction entering the
generalized Dirac equation for right and left massless electrons in an external
uniform magnetic field. We calculate the averaged electric current given by the
solution of the modified Dirac equation containing an extra current for right
and left electrons (positrons), which turns out to be directed along the
magnetic field. Such current includes both a changing chiral imbalance of
electrons and the $eN$ potential given by a constant neutron density in NS.
Then we derive the system of the kinetic equations for the chiral imbalance and
the magnetic helicity which accounts for the $eN$ interaction. By solving this
system, we show that a sizable chiral imbalance arising in a neutron protostar
due to the Urca-process $e^-_\mathrm{L} + p\to N + \nu_\mathrm{eL}$ diminishes
very rapidly because of a huge chirality flip rate. Thus the $eN$ term prevails
the chiral effect providing a huge growth of the magnetic helicity and the
helical magnetic field.
