  In this work, we mainly concern the limiting behavior of the electromagnetic
field of two species Vlasov-Maxwell-Botlzmann system in diffusive limits. As
knudsen numbers goes to zero, the electric magnetic and magnetic field may
perserve or vanish. We verify rigorously Navier-Stokes, Navier-Stokes-Poisson
and Navier-Stokes Maxwell limit of the two species Vlasov-Maxwell-Boltzmann
system on the torus in three dimension. The justification is based on the
unified and uniform estimates of solutions to the dimensionless
Vlasov-Maxwell-Boltzmann. The uniform estimates of solutions are obtained by
employing the hypocoercivity of the linear Boltzmann operator and constructing
a equation containing damping term of electric field.
