The amplification of magnetic fields during the radiation era

During the radiation era, the relative motion of the proton fluid and the electron–photon fluid generates a small magnetic field. Cosmic turbulence can amplify that seed field, but the extent of the amplification has not been certain. This paper addresses the amplification issue afresh. Spectral techniques are used to solve an evolutionary equation for a linear combination of magnetic field and vorticity. When the field is extracted, one finds that it has not grown beyond 10−9 Gauss, in order of magnitude. Thus, at the onset of recombination, the field is still too small to be dynamically significant, nor can it be responsible, by itself, for present-day intergalactic fields of any substantial magnitude.