  We study the asymptotic regime of strong electric fields that leads from the
Vlasov-Poisson system to the Incompressible Euler equations. We also deal with
the Vlasov-Poisson-Fokker-Planck system which induces dissipative effects. The
originality consists in considering a situation with a finite total charge
confined by a strong external field. In turn, the limiting equation is set in a
bounded domain, the shape of which is determined by the external confining
potential. The analysis extends to the situation where the limiting density is
non-homogeneous and where the Euler equation is replaced by the Lake Equation,
also called Anelastic Equation.
