Maximum entropy principle and coherent harmonic generation using a single-pass free-electron laser

Single-pass free-electron lasers constitute an example of systems with long-range interactions. The light-particle interplay leading to the power growth and successive relaxation towards a quasi-stationary state is governed by the Vlasov equation. A maximum entropy principle inspired to Lynden-Bell's theory of “violent relaxation" for the Vlasov equation can be invoked to analytically characterize the behaviour of the saturated system. In particular, we here concentrate on the case of coherent harmonic generation obtained from an externally seeded free-electron laser and provide a simple strategy to predict the laser intensity as well as the final electron-beam energy distribution