Out-of-equilibrium mean-field dynamics of a model for wave-particle interaction

The out-of-equilibrium mean-field dynamics of a model for wave-particle interaction is investigated. Such a model can be regarded as a general formulation for all those applications where the complex interplay between particles and fields is known to be central, e.g., electrostatic instabilities in plasma physics, particle acceleration, and free-electron lasers (FELs). The latter case is here assumed as a paradigmatic example. A transition separating different macroscopic regimes is numerically identified and interpreted by making use of the so-called violent-relaxation theory. In the context of free-electron lasers, such a theory is shown to be effective in predicting the saturated regime for energies below the transition. The transition is explained as a dynamical switch between two metastable regimes, and is related to the properties of a stationary point of an entropic functional.