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A study is made of the saturation mechanism of a single superradiant spike of radiation in a Free Electron Laser. A one-dimensional (1D) computer model is developed using the Puffin, un-averaged FEL simulation code, which allows sub-radiation wavelength evolution of both the spike radiation field and the electron dynamics to be modelled until the highly non-linear saturation process of the spike is observed. Animations of the process from the start to the end of the interaction are available. The resultant saturated spike duration is at the sub-wavelength scale and has a broad spectrum. The electrons passing through the spike can both lose and gain energy many times greater than that of the normal non-pulsed FEL interaction. A saturation mechanism is proposed and tested via a simple analysis of the 1D FEL equations. The scaling results of the analysis are seen to be in good agreement with the numerical results. A simple model of three dimensional diffraction effects of the radiation is applied to the results of the 1D simulations. This greatly reduces longer wavelengths of the power spectrum, which are seen to be emitted mainly after the electrons have propagated through the spike, and is seen to be in qualitative agreement with recent experimental results., Comment: Submitted to Results in Physics

Free-electron lasers (FELs) operate at wavelengths from millimeter waves through hard x-rays. At x-ray wavelengths, FELs typically rely on self-amplified spontaneous emission (SASE). Typical SASE emission contains multiple temporal "spikes" which limit the longitudinal coherence of the optical output; hence, alternate schemes that improve on the longitudinal coherence of the SASE emission are of interest. In this paper, we consnider electron bunches that are shorter than the SASE spike separation. In such cases, the spontaneously generated radiation consists of a single optical pulse with better longitudinal coherence than is found in typical SASE FELs. To investigate this regime, we use two FEL simulation codes. One (MINERVA) uses the slowly-varying envelope approximation(SVEA) which breaks down for extremely short pulses. The second (PUFFIN) is a particle-in-cell (PiC) simulation code that is considered to be a more complete model of the underlying physics and which is able to simulate very short pulses. We first anchor these codes by showing that there is substantial agreement between the codes in simulation of the SPARC SASE FEL experiment at ENEA Frascati. We then compare the two codes for simulations using electron bunch lengths that are shorter than the SASE slice separation. The comparisons between the two codes for short bunch simulations elucidate the limitations of the SVEA in this regime but indicate that the SVEA can treat short bunches that are comparable to the cooperation length., Comment: 8 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1906.01996

An optics-free method is proposed to generate X-ray radiation with spatially variant states of polarization via an afterburner extension to a Free Electron Laser (FEL). Control of the polarization in the transverse plane is obtained through the overlap of different coherent transverse light distributions radiated from a bunched electron beam in two consecutive orthogonally polarised undulators. Different transverse profiles are obtained by emitting at a higher harmonic in one or both of the undulators. This method enables the generation of beams structured in their intensity, phase, and polarization - so-called Poincar\'e beams - at high powers with tunable wavelengths. Simulations are used to demonstrate the generation of two different classes of light with spatially inhomogeneous polarization - cylindrical vector beams and full Poincar\'e beams., Comment: 10 pages, 3 figures