The Role of the Electron Mass in Damping Chiral Magnetic Instability in   Supernova and Neutron Stars
  We show that the nonzero electron mass plays a critical role in determining the magnetic properties of neutron stars, making it impossible to generate the chiral charge density needed to trigger a strong chiral magnetic instability during the core collapse of supernovae. This instability has been proposed as a plausible mechanism for generating extremely large helical magnetic fields in neutron stars at their birth; the mechanism relies on the generation of a large non-equilibrium chiral charge density via electron capture reactions that selectively deplete left-handed electrons during core-collapse and the early evolution of the protoneutron star. Our calculation shows that the electron chirality violation rate induced by Rutherford scattering, despite being suppressed by the smallness of the electron mass relative to the electron chemical potential, is still fast compared to the weak interaction electron capture rate. The resulting asymmetry between right and left-handed electron densities is therefore never able to attain an astrophysically relevant magnitude. 
Dorota Grabowska, David B. Kaplan, Sanjay Reddy
hep-ph astro-ph.HE nucl-th