  We discuss generation of magnetic field from cosmological perturbations. We
consider the evolution of three component plasma (electron, proton and photon)
evaluating the collision term between elecrons and photons up to the second
order. The collision term is shown to induce electric current, which then
generate magnetic field. There are three contributions, two of which can be
evaluated from the first-order quantities, while the other one is fluid
vorticity which is purely second order. We compute numerically the magnitudes
of the former contributions and shows that the amplitude of the produced
magnetic field is about $\sim 10^{-19} {\rm G}$ at 10kpc comoving scale at
present. Compared to astrophysical and inflationary mechanisms for seed-field
generation, our study suffers from much less ambiguities concerning unknown
physics and/or processes.
