  We explore the possibility of generating large-scale magnetic fields from
second-order cosmological perturbations during the pre-recombination era. The
key process for this is Thomson scattering between the photons and the charged
particles within the cosmic plasma. To tame the multi-component interacting
fluid system, we employ the tight coupling approximation. It is shown that the
source term for the magnetic field is given by the vorticity, which signals the
intrinsically second-order quantities, and the product of the first order
perturbations. The vorticity itself is sourced by the product of the
first-order quantities in the vorticity evolution equation. The magnetic fields
generated by this process are estimated to be $\sim 10^{-29} $Gauss on the
horizon scale at the recombination epoch. Although our rough estimate suggests
that the current generation mechanism can work even on smaller scales, more
careful investigation is needed to make clear whether it indeed works in a wide
range of spatial scales.
