  In the setting of general initial data and whole space we perform a rigorous
analysis of the quasineutral limit for a hydrodynamical model of a viscous
plasma with capillarity tensor represented by the Navier Stokes Korteweg
Poisson system. We shall provide a detailed mathematical description of the
convergence process by analyzing the dispersion of the fast oscillating
acoustic waves. However the standard acoustic wave analysis is not sufficient
to control the high frequency oscillations in the electric field but it is
necessary to estimates the dispersive properties induced by the capillarity
terms. Therefore by using these additional estimates we will be able to
control, via compensated compactness, the quadratic nonlinearity of the stiff
electric force field. In conclusion, opposite to the zero capillarity case
\cite{DM12} where persistent space localized time high frequency oscillations
need to be taken into account, we show that as $\lambda \to 0$, the density
fluctuation $\rho^{\lambda}-1$ converges strongly to zero and the fluids
behaves according to an incompressible dynamics.
