We present a model to describe the dynamical evolution of the delocali
zed electrons in a simple metal cluster during and following the passa
ge of a charged particle at intermediate energies. Assuming a mean-fie
ld approximation we solve the Vlasov equation by combining the test-pa
rticle method and the numerical resolution of the Poisson equation at
each time step. This method allows one to use a large number of test p
articles and to obtain a reliable behavior of the one-body phase-space
density over more than 20 fs. The rate and features of fast electron
emission are predicted.