  A theoretical framework is presented which allows to quantitatively predict
the final stationary state achieved by a non-neutral plasma during a process of
collisionless relaxation. As a specific application, the theory is used to
study relaxation of charged-particles beams. It is shown that a fully matched
beam relaxes to the Lynden-Bell distribution. However, when a mismatch is
present and the beam oscillates, parametric resonances lead to a core-halo
phase separation. The approach developed accounts for both the density and the
velocity distributions in the final stationary state.
