Generation of Magnetic Field in the Pre-recombination Era

We study the possibility of generating magnetic fields during the evolution of electron, proton, and photon plasma in the pre-recombination era. We show that a small magnetic field can be generated in the second order of perturbation theory for scalar modes with adiabatic initial conditions. The amplitude of the field is $\text{la}{10}^{-30}\mathrm{G}$ at the present epoch for scales from sub-kpc to $\text{ga}100\mathrm{M}\mathrm{p}\mathrm{c}$.