Behavior of magnetic fields around the cosmic recombination

Several mechanisms have been proposed to generate primordial magnetic fields and it is often assumed that magnetic fields are not affected by a sharp drop in ionization rate due to the cosmic recombination. We investigate the validity of the assumption by studying the behavior of magnetic fields and fluid motion around recombination. Fluid equations including the effect of recombination are considered for protons, electrons and neutral hydrogens separately, combining Maxwell equations. We find that the residual ionization rate required for the conservation of magnetic field at cosmological scales is about $10^{-10}$, which is much smaller than the standard value $\sim 10^{-4}$. Further we will show the acceleration of protons and electrons in the process of recombination which conpensates the decrease in the carrier of electric current in order to preserve electric current and then magnetic fields.