Magnetic fields generated by turbulence during the radiation dominated era

There are two classical papers (Matsuda, Sato and Takeda, 1971; Harrison, 1973) in which magnetic fields were considered to be generated by turbulence in the radiation dominated universe. There is also a close relation between vorticity and magnetic fields, $\vec{B}\,$ = - (mc/e)$\vec{\omega}\,$ (where $\vec{\omega}\,$ is the vorticity) which was deduced by Batchelor (1950) and considered again by Kulsrud et al. (1997) as an extension of a previous study by Biermann. The deduction is based on the surprising similarity between the vorticity and the induction equations. With similar initial conditions, both magnitudes, vorticity and magnetic fields, should evolve similarly. Viscosity has a different behaviour, because there is a saturation of vorticity, but the above equation could be used in other astrophysical problems. In the epoch of radiation domination, however, we will present arguments against this, so that this equation probably does not hold.