  The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a
viscous plasma with vanishing viscosity coefficients in the half-space
$\mathbb{R}^{3}_{+}$ is rigorously proved under a Navier-slip boundary
condition for velocity and the Dirichlet boundary condition for electric
potential. This is achieved by establishing the nonlinear stability of the
approximation solutions involving the strong boundary layer in density and
electric potential, which comes from the break-down of the quasi-neutrality
near the boundary, and dealing with the difficulty of the interaction of this
strong boundary layer with the weak boundary layer of the velocity field.
