  This paper is concerned with the large-time behavior of solutions to the
Cauchy problem on the two-fluid Euler-Maxwell system with collisions when
initial data are around a constant equilibrium state. The main goal is the
rigorous justification of diffusion phenomena in fluid plasma at the linear
level. Precisely, motivated by the classical Darcy's law for the nonconductive
fluid, we first give a heuristic derivation of the asymptotic equations of the
Euler-Maxwell system in large time. It turns out that both the density and the
magnetic field tend time-asymptotically to the diffusion equations with
diffusive coefficients explicitly determined by given physical parameters.
Then, in terms of the Fourier energy method, we analyze the linear dissipative
structure of the system, which implies the almost exponential time-decay
property of solutions over the high-frequency domain. The key part of the paper
is the spectral analysis of the linearized system, exactly capturing the
diffusive feature of solutions over the low-frequency domain. Finally, under
some conditions on initial data, we show the convergence of the densities and
the magnetic field to the corresponding linear diffusion waves with the rate
$(1+t)^{-5/4}$ in $L^2$ norm and also the convergence of the velocities and the
electric field to the corresponding asymptotic profiles given in the sense of
the geneneralized Darcy's law with the faster rate $(1+t)^{-7/4}$ in $L^2$
norm. Thus, this work can be also regarded as the mathematical proof of the
Darcy's law in the context of collisional fluid plasma.
