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The out-of-equilibrium mean-field dynamics of a model for wave-particleinteraction is investigated. Such a model can be regarded as a generalformulation for all those applications where the complex interplay betweenparticles and fields is known to be central, e.g., electrostatic instabilitiesin plasma physics, particle acceleration and free-electron lasers (FELs). Thelatter case is here assumed as a paradigmatic example. A transition separatingdifferent macroscopic regimes is numerically identified and interpreted bymaking use of the so-called violent relaxation theory. In the context offree-electron lasers, such a theory is showed to be effective in predicting thesaturated regime for energies below the transition. The transition is explainedas a dynamical switch between two metastable regimes, and is related to theproperties of a stationary point of an entropic functional.

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