Magnetic field instability driven by anomalous magnetic moments of massive fermions and electroweak interaction with background matter

It is shown that the electric current of massive fermions along the external magnetic field can be excited in the case when particles possess anomalous magnetic moments and electroweakly interact with background matter. This current is calculated on the basis of the exact solution of the Dirac equation in the external fields. It is shown that the magnetic field becomes unstable if this current is taken into account in the Maxwell equations. Considering a particular case of a degenerate electron gas, which can be found in a neutron star, it is revealed that the seed magnetic field can be significantly enhanced. The application of the results to astrophysics is also discussed.