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The generation of Free Electron Laser (FEL) radiation relies on the extraction of electromagnetic energy from kinetic energy of a relativistic electron beam by propagating it along the axis of a periodic lattice of alternating magnetic dipolar fields, known as undulator. This forces the beam to undulate transversally, thus causing the electrons to emit electromagnetic radiation. The fundamental wavelength emitted is proportional to λu/γ 2 , where λu is the undulator period, typically a few centimeters long, and γ is the relativistic Lorentz factor of the electrons, which typically reaches several thousand for X-ray emission. The main figures of merit of an FEL are extremely high brilliance, close to full transverse and longitudinal coherence, a bandwidth approaching the Fourier limit and a stable and well characterized temporal structure in the femtosecond time domain. We can identify two general ways to generate X-rays with an FEL. The Self Amplified Spontaneous Emission (SASE) [1–4] relies on the interaction of electrons and photons that are emitted by the electron beam itself. The electron bunching that generates the coherent emission of radiation starts to grow from the natural noise of the initial electron distribution. For this reason, the SASE output radiation is relatively poor in longitudinal coherence. In the High Gain Harmonic Generation (HGHG) scheme [5–11], instead, the initial energy modulation is driven by an external seed laser. It is then transformed into density bunching in a dispersive section inserted in the undulator chain. In this case, the output FEL properties reflect the high longitudinal coherence of the seed laser.

Design and Simulation Challenges of a Linac-Based Free Electron Laser in the Presence of Collective Effects