On the origin of quasi-stationary states in models of wave–particle interaction

In presence of long-range interactions, physics is very peculiar and a wide range of striking phenomena appear, like the emergence of long-live quasi-stationary states (QSSs). Wave–particle interaction (plasmas, Free Electron Lasers, etc.) represents an interesting example of a long-range system and provides a unique experimental ground to investigate the aforementioned universal features. In this paper we apply a general approach, based on the statistical mechanics of the Vlasov equation, to study the QSSs in a typical model of wave–particle interaction. Using Lynden-Bell “violent relaxation” theory, we characterize a first-order phase transition with truly non-equilibrium features. We analyze in some detail the coexistence region and the non-Gaussian momentum distributions.