  This work tackles the diffusive limit for the Vlasov-Poisson-Fokker-Planck
model. We derive a priori estimates which hold without restriction on the
phase-space dimension and propose a strong convergence result in a L2 space.
Furthermore, we strengthen previous results by obtaining an explicit
convergence rate arbitrarily close to the (formal) optimal rate, provided that
the initial data lies in some Lp space with p large enough. Our result holds on
bounded time intervals whose size grow to infinity in the asymptotic limit with
explicit lower bound. The analysis relies on identifying the right set of
phase-space coordinates to study the regime of interest. In this set of
coordinates the limiting model arises explicitly.
