  We discuss the self-consistent dynamics of plasmas by means of hamiltonian
formalism for a system of $N$ near-resonant electrons interacting with a single
Langmuir wave. The connection with the Vlasov description is revisited through
the numerical calculation of the van Kampen-like eigenfrequencies of the
linearized dynamics for many degrees of freedom. Both the exponential-like
growth as well as damping of the Langmuir wave are shown to emerge from a phase
mixing effect among beam modes, revealing unexpected similarities between the
stable and unstable regimes.
