  We prove a global-in-time limit from the two-species Vlasov-Maxwell-Boltzmann
system to the two-fluid incompressible Navier-Stokes-Fourier-Maxwell system
with Ohm's law. Besides the techniques developed for the classical solutions to
the Vlasov-Maxwell-Boltzmann equations in the past years, such as the nonlinear
energy method and micro-macro decomposition are employed, key roles are played
by the decay properties of both the electric field and the wave equation with
linear damping of the divergence free magnetic field. This is a companion paper
of [N. Jiang and Y.-L. Luo, \emph{Ann. PDE} 8 (2022), no. 1, Paper No. 4, 126
pp] in which Hilbert expansion is not employed.

Analysis of PDEs