  We perform a rigorous analysis of the quasineutral limit for a hydrodynamical
model of a viscous plasma represented by the Navier Stokes Poisson system in
$3-D$. We show that as $\lambda\to 0$ the velocity field $u^{\lambda}$ strongly
converges towards an incompressible velocity vector field $u$ and the density
fluctuation $\rho^{\lambda}-1$ weakly converges to zero. In general the limit
velocity field cannot be expected to satisfy the incompressible Navier Stokes
equation, indeed the presence of high frequency oscillations strongly affects
the quadratic nonlinearities and we have to take care of self interacting wave
packets. We shall provide a detailed mathematical description of the
convergence process by using microlocal defect measures and by developing an
explicit correctors analysis. Moreover we will be able to identify an explicit
pseudo parabolic pde satisfied by the leading correctors terms. Our results
include all the previous results in literature, in particular we show that the
formal limit holds rigorously in the case of well prepared data.
