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In this paper, we report results of simulations, in the framework of both EuPRAXIA cite{Walk2017} and EuPRAXIA@SPARC_LAB cite{Ferr2017} projects, aimed at delivering a high brightness electron bunch for driving a Free Electron Laser (FEL) by employing a plasma post acceleration scheme. The boosting plasma wave is driven by a tens of SI{}{terawatt} class laser and doubles the energy of an externally injected beam up to GeV{1}. The injected bunch is simulated starting from a photoinjector, matched to plasma, boosted and finally matched to an undulator, where its ability to produce FEL radiation is verified to yield $O( um{e11})$ photons per shot at m{2.7}.
Plasma driven particle accelerators represent the future of compact accelerating machines and Free Electron Lasers are going to benefit from these new technologies. One of the main issue of this new approach to FEL machines is the design of the trans
A model of a Free Electron Laser operating with an elliptically polarised undulator is presented. The equations describing the FEL interaction, including resonant harmonic radiation fields, are averaged over an undulator period and generate a general
Existing FEL facilities often suffer from stability issues: so electron orbit, transverse electron optics, electron bunch compression and other parameters have to be readjusted often to account for drifts in performance of various components. The tun
The density matrix in the Lindblad form is used to describe the behavior of the Free-Electron Laser (FEL) operating in a quantum regime. The detrimental effects of the spontaneous emission on coherent FEL operation are taken into account. It is shown
The spectacular development of Laser-Plasma Accelerators (LPA) appears very promising for a free electron laser application. The handling of the inherent properties of those LPA beams already allowed controlled production of LPA-based spontaneous und