Magnetic field amplification in cold dark matter anisotropic collapse

We use the Zel'dovich approximation to analyse the amplification of magnetic fields in gravitational collapse of cold dark matter during the mildly non-linear regime, and identify two key features. First, the anisotropy of collapse effectively eliminates one of the magnetic components, confining the field in the pancake plane. Secondly, in agreement with recent numerical simulations, we find that the shear anisotropy can amplify the magnetic field well beyond the isotropic case. Our results suggest that the magnetic strengths observed in spiral and disc galaxies today might have originated from seeds considerably weaker than previous estimates.