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The FEL integral equation is reviewed here and is studied under different contexts, accounting for diverse physical regimes. We include higher order harmonics and saturation effects, and explain the origin of scaling relations, widely exploited to describe either FEL dynamics or nonnlinear harmonic generation.

The possibility of extending the tunability of Free-Electron Lasers towards short wavelengths has been explored through the design of devices conceived to enhance the mechanisms of nonlinear harmonic generation. In this respect, different schemes of operation have been suggested in the past, such as harmonic seeding, bi-harmonic undulators, and two-beam self-seeding devices. In this paper, we discuss how these methods can be merged into a tool, extending the performance of FEL devices.

International audience; The fourth generation of synchrotron radiation sources, commonly referred to as the Free Electron Laser (FEL), provides an intense source of brilliant X-ray beams enabling the investigation of matter at the atomic scale with unprecedented time resolution. These sources require the use of conventional linear accelerators providing high electron beam performance. The achievement of chirped pulse amplification allowing lasers to be operated at the Terawatt range, opened the way for the Laser Plasma Acceleration (LPA) technique where high energy electron bunches with high current can be produced within a very short centimeter-scale distance. Such an advanced acceleration concept is of great interest to be qualified by an FEL application for compact X-ray light sources. We explore in this paper what the LPA specificities imply on the design of the undulator, part of the gain medium. First, the LPA concept and state-of-art are presented showing the different operation regimes and what electron beam parameters are likely to be achieved. The LPA scaling laws are discussed afterwards to better understand what laser or plasma parameters have to be adjusted in order to improve electron beam quality. The FEL is secondly discussed starting with the spontaneous emission, followed by the different FEL configurations, the electron beam transport to the undulator and finally the scaling laws and correction terms in the high gain case. Then, the different types of compact undulators that can be implemented for an LPA based FEL application are analyzed. Finally, examples of relevant experiments are reported by describing the transport beamline, presenting the spontaneous emission characteristics achieved so far and the future prospects.

The theory of Generalized Bessel Functions is reviewed and their application to various problems in the study of electro-magnetic processes is presented. We consider the cases of emission of bremsstrahlung radiation by ultra-relativistic electrons in linearly polarized undulators, including also exotic configurations, aimed at enhancing the harmonic content of the emitted radiation. The analysis is eventually extended to the generalization of the FEL pendulum equation to treat Free Electron Laser operating with multi-harmonic undulators. The paper aims at picking out those elements supporting the usefulness of the Generalized Bessel Functions in the elaboration of the theory underlying the study of the spectral properties of the bremsstrahlung radiation emitted by relativistic charges, along with the relevant flexibility in accounting for a large variety of apparently uncorrelated phenomenolgies, like multi-photon processes, including non linear Compton scattering.

We discuss a hybrid Free Electron Laser (FEL) architecture operating with a RF undulator provided by a powerful Cyclotron Auto-Resonance Maser (CARM). We outline the design elements to operate a compact X-ray device. We review the essential aspects of wave undulator FEL theory and of CARM devices.

European physical journal special topics 229(24), 3675 - 4284 (2020). doi:10.1140/epjst/e2020-000127-8, This report presents the conceptual design of a new European research infrastructure EuPRAXIA. The concept has been established over the last four years in a unique collaboration of 41 laboratories within a Horizon 2020 design study funded by the European Union. EuPRAXIA is the first European project that develops a dedicated particle accelerator research infrastructure based on novel plasma acceleration concepts and laser technology. It focuses on the development of electron accelerators and underlying technologies, their user communities, and the exploitation of existing accelerator infrastructures in Europe. EuPRAXIA has involved, amongst others, the international laser community and industry to build links and bridges with accelerator science — through realising synergies, identifying disruptive ideas, innovating, and fostering knowledge exchange. The Eu-PRAXIA project aims at the construction of an innovative electron accelerator using laser- and electron-beam-driven plasma wakefield acceleration that offers a significant reduction in size and possible savings in cost over current state-of-the-art radiofrequency-based accelerators. The foreseen electron energy range of one to five gigaelectronvolts (GeV) and its performance goals will enable versatile applications in various domains, e.g. as a compact free-electron laser (FEL), compact sources for medical imaging and positron generation, table-top test beams for particle detectors, as well as deeply penetrating X-ray and gamma-ray sources for material testing. EuPRAXIA is designed to be the required stepping stone to possible future plasma-based facilities, such as linear colliders at the high-energy physics (HEP) energy frontier. Consistent with a high-confidence approach, the project includes measures to retire risk by establishing scaled technology demonstrators. This report includes preliminary models for project implementation, cost and schedule that would allow operation of the full Eu-PRAXIA facility within 8—10 years., Published by Springer, Heidelberg

Self-amplified spontaneous emission (SASE) free electron laser (FEL) devices have disclosed an unexpected interplay between the laser intensity growth and regions of the electron bunch of the order of the coherence length. They are usually identified with the bunch slice and contribute to the laser dynamics with their own characteristics. The dynamical effects inducing geometrical and phase space misalignment of bunch slice in X-ray operating FELs can be traced back to a plethora of phenomena, both in the Linac accelerating section or inside the beam transport optic magnet. They are responsible for spoiling of the beam projected qualities and, if not corrected properly, induce an increase of the saturation length and a decreasing of the output power. We discuss the inclusion of these effects in models employing scaling formulae.

Effects producing gain dilution in Free Electron Laser devices are well documented. We develop here a unified point of view allowing the introduction of space charge effects, along with the gain deterioration due to inhomogeneous broadening contributions and discuss the relevant interplay. We outline future developments and comment on the possibility of including in the formalism effects of quantum mechanical nature., 10 pages, 7 figures

Over the past 90 years, particle accelerators have evolved into powerful and widely used tools for basic research, industry, medicine, and science. A new type of accelerator that uses plasma wakefields promises gradients as high as some tens of billions of electron volts per meter. This would allow much smaller accelerators that could be used for a wide range of fundamental and applied research applications. One of the target applications is a plasma-driven free-electron laser (FEL), aiming at producing tunable coherent light using electrons traveling in the periodic magnetic field of an undulator. In this work, the plasma-based electron beams with the most promising qualities, designed in the framework of EuPRAXIA, are analyzed in terms of the FEL performance.

We study the small signal regime of Cyclotron Auto-Resonance Maser (CARM), using different computational tools. The analysis is motivated by the necessity of an accurate benchmarking of the design parameter for the CARM device under construction at ENEA Frascati center. The main goal is that of comparing the results from three different procedures, the analytical formulation and two different numerical items: the home-made code GRAAL (Gyrotron Radiation Auto-Resonance Amplification Laser) and the, commercially available, software package CST. We prove the substantial consistence between the different methods and comment on the reasons leading to the discrepancies. The extension to the non-linear regime is finally touched on.

We present an analysis of the FEL performances of several working points belonging to three different classes of electron beams driven by the same infrastructure: two high flux working points are relevant to the operation with a linac up to 1 GeV, while both LWFA and PWFA beams have been considered at this same energy for low charge operation. Soft X rays in single spike mode with fluxes up to 10 12 electrons per shot have been found.

The term Free Electron Laser (FEL) will be used, in this paper, to indicate a wide collection of devices aimed at providing coherent electromagnetic radiation from a beam of “free” electrons, unbound at the atomic or molecular states. This article reviews the similarities that link different sources of coherent radiation across the electromagnetic spectrum from microwaves to X-rays, and compares the analogies with conventional laser sources. We explore developing a point of view that allows a unified analytical treatment of these devices, by the introduction of appropriate global variables (e.g. gain, saturation intensity, inhomogeneous broadening parameters, longitudinal mode coupling strength), yielding a very effective way for the determination of the relevant design parameters. The paper looks also at more speculative aspects of FEL physics, which may address the relevance of quantum effects in the lasing process.

This review paper is devoted to the understanding of free-electron lasers (FEL) as devices for fundamental physics (FP) studies. After clarifying what FP stands for, we select some aspects of the FEL physics which can be viewed as fundamental. Furthermore, we discuss the perspective uses of the FEL in FP experiments. Regarding the FP aspects of the FEL, we analyze the quantum electrodynamics (QED) nature of the underlying laser mechanism. We look for the truly quantum signature in a process whose phenomenology is dominated by classical effects. As to the use of FEL as a tool for FP experiments we discuss the realization of a device dedicated to the study of non-linear effects in QED such as photon–photon scattering and shining-through-the-wall experiments planned to search for dark matter candidates like axions. © 2018 Elsevier B.V.

The combined effect of slippage and energy spread in self-amplified-spontaneous-emission Free Electron Laser devices, operating in single spike regime, may impose limitations on the relevant performance. If the slippage is larger than the electron bunch length, the saturated power is significantly reduced. We provide a simple scaling formula capable of parameterizing the effect in terms of the device parameter and discuss possible mechanisms allowing the power output optimization. © 2018 Elsevier GmbH

On the wake of the results obtained so far at the SPARC_LAB test-facility at the Laboratori Nazionali di Frascati (Italy), we are currently investigating the possibility to design and build a new multi-disciplinary user-facility, equipped with a soft X-ray Free Electron Laser (FEL) driven by a ∼ 1 GeV high brightness linac based on plasma accelerator modules. This design study is performed in synergy with the EuPRAXIA design study. In this paper we report about the recent progresses in the on going design study of the new facility. On the wake of the results obtained so far at the SPARC\_LAB test-facility at the Laboratori Nazionali di Frascati (Italy), we are currently investigating the possibility to design and build a new multi-disciplinary user-facility, equipped with a soft X-ray Free Electron Laser (FEL) driven by a $\sim$1 GeV high brightness linac based on plasma accelerator modules. This design study is performed in synergy with the EuPRAXIA design study. In this paper we report about the recent progresses in the on going design study of the new facility.

The efficiency of Free Electron Laser (FEL) Oscillator devices is a fairly complicated function of the various parameters which characterize the device itself. We explore the relevant dependences by the use of the scaling formulas describing the FEL Oscillator dynamics and providing the relevant design elements. We obtain a quantitative dependence of the efficiency on the key FEL parameters (small signal gain coefficient, saturation intensity, electron beam qualities…) and discuss the use of the results obtained in the paper as a further element for the FEL Oscillator optimization. © 2018 Elsevier B.V.

'Charged Beam Dynamics, Particle Accelerators and Free Electron Lasers' summarises different topics in the field of accelerators and of Free Electron Laser (FEL) devices. It explains how to design both an FEL device and the accelerator providing the driving beam. Covering both theoretical and experimental aspects, this book allows researchers to attempt a first design of an FEL device.

'Charged Beam Dynamics, Particle Accelerators and Free Electron Lasers' summarises different topics in the field of accelerators and of Free Electron Laser (FEL) devices. It explains how to design both an FEL device and the accelerator providing the driving beam. Covering both theoretical and experimental aspects, this book allows researchers to attempt a first design of an FEL device.

'Charged Beam Dynamics, Particle Accelerators and Free Electron Lasers' summarises different topics in the field of accelerators and of Free Electron Laser (FEL) devices. It explains how to design both an FEL device and the accelerator providing the driving beam. Covering both theoretical and experimental aspects, this book allows researchers to attempt a first design of an FEL device.

'Charged Beam Dynamics, Particle Accelerators and Free Electron Lasers' summarises different topics in the field of accelerators and of Free Electron Laser (FEL) devices. It explains how to design both an FEL device and the accelerator providing the driving beam. Covering both theoretical and experimental aspects, this book allows researchers to attempt a first design of an FEL device.

We have considered a novel scheme of wave undulator FEL. The system employs a recirculated radiation pulse serving as undulator provided by a high power laser. Non conventional electron acceleration schemes promise nowadays high gradient acceleration yielding the GeV on the scale of few centimeters, however these solutions might solve the problem of the accelerator length, but not that associated with the saturation length and thus of the length of the undulator, which remains on the order of tens of meters. The option of wave-undulator based FEL might provide a valid solution in the future. © 2017 Elsevier B.V.

The high gain free electron laser (FEL) equation is a Volterra type integro-differential equation amenable for analytical solutions in a limited number of cases. In this note, a novel technique, based on an expansion employing a family of two variable Hermite polynomials, is shown to provide straightforward analytical solutions for cases hardly solvable with conventional means. The possibility of extending the method by the use of expansion using different polynomials (two variable Legendre like) expansion is also discussed. © 2017 by the authors.

We take advantage of previous research in the field of cyclotron auto resonance maser (CARM) and undulator-based free electron laser (U-FEL) sources to establish a common formalism for the relevant description of the underlying physical mechanisms. This strategy is aimed at stressing the deep analogies between the two devices and at providing a practical tool for their study based on the use of well-Tested scaling formulae developed independently for the two systems. © Cambridge University Press 2017.

The development of a microwave tube providing high output power (1 MW) at a high frequency (250 GHz) with high efficiency of the beam-wave power conversion is a challenging task. A great deal of theoretical and experimental efforts is directed toward such a goal. A promising powerful source of microwave radiation is the cyclotron autoresonance maser (CARM) oscillator. In this paper, we revisit the well-known physical models in a way, which is suitable for their implementation in the numerical tools for computer-aided design and optimization of a CARM operating at high frequency. The analysis developed by us is an attempt directed toward the realization of an adequate design tool for the development of CARM devices. © 1963-2012 IEEE.

We discuss a new method for the production of trains of FEL radiation pulses based on the FEL emission driven by a comb-like electron beam. In addition, we present recent experimental results on the two color FEL emission as generated at the SPARC_LAB facility: a train of two short (

Exploration of the mutual scattering of photons in vacuum is considered as a fundamental test of the quantum electrodynamics theory. In this connection, we propose a "double" free-electron laser oscillator as a possible device for head-on photon-photon collisions. The device is conceived to comprise two undulator sections within the same cavity, where then two laser beams are produced by two counterpropagating electron beams. The latter are in turn exploited to produce gamma photons by backward Compton scattering of the intracavity FEL radiation itself. A preliminary analysis of the collision rate of the backscattered photons is presented specifically at the maximum of the relevant cross section. © 2013 Elsevier B.V.

We present a procedure based on the combined use of analytical and numerical tools, useful for understanding the relative interplay between the various components of a free electron laser (FEL) self-amplified spontaneous emission (SASE) device. We take as reference case the Sorgente Pulsata Auto-amplificata di Radiazione Coerente (SPARC) experiment to analyze how electron beam transverse matching conditions affect the lasing conditions itself and discuss the possibility of implementing new configurations. In particular we show that the procedure can be extended to account for the effect of an on line inserted cavity, with the role of inducing a transverse longitudinal correlation allowing a transfer of the longitudinal and transverse emittance. We discuss the associated benefit on the FEL operation, with particular reference to the nonlinear harmonic generation. The possibility of completing the tool with regards to the beam degradation effects due to CSR is briefly accounted for. © 1965-2012 IEEE.

We develop a self-consistent general purpose code modelling the storage ring free electron laser devices. The code accounts for the beam longitudinal dynamics and the laser pulse propagation and is capable of reproducing the wealth of phenomenology associated with the laser–electron beam interplay and provides a deeper understanding of the mechanisms underlying the role of the laser in the suppression of instabilities of longitudinal type.

Free-electron laser (FEL) operations in a storage ring operating in a low emittance and reduced momentum compaction factor setting are here presented with reference to the experimental case of Super-ACO. The new working point of the storage ring has been optimized by renouncing to the standard double achromatic feature of the magnetic optics. This makes possible the laser dynamics to benefit from high particle density conditions together with a particular regime of beam dynamics whose peculiarity is to correlate the longitudinal and horizontal oscillations in the laser interaction region. In such a new configuration, the Super-ACO two-bunches dynamics has been experimentally characterized and analyzed in comparison with analogous experimental results corresponding to standard machine operations. For a low emittance and a reduced momentum compaction factor, the calculated small signal gain of the laser results to be enhanced because of the increased particle density. Passing from the nominal to the low emittance setting of the storage ring, variations of the measured beam life-time have been observed by reason of either the increased particle density or the effect of the laser heating. Useful indications about the dependence of the laser saturation mechanism on the modified regime of the beam dynamics can be obtained from the analysis of the beam life-time. In spite of the dependence of the beam orbit on the energy spread in the laser interaction region, the typical non-equilibrium distribution of the laser intensity—the so-called detuning curve—has been observed also in correspondence of the new operation point of the storage ring. Finally, the average laser power measured at the equilibrium has been analyzed and theoretically interpreted.

We analyze the behavior of Free Electron Laser (FEL) oscillators operating in the deep saturated regime and point out the formation of sub-peaks of the optical pulse. They are very stable configurations, having a width corresponding to a coherence length. We speculate on the physical mechanisms underlying their growth and attempt an identification with FEL mode locked structures associated with Super Modes. Their impact on the intra-cavity nonlinear harmonic generation is also discussed along with the possibility of exploiting them as cavity out-coupler., Comment: 28 pages

Free electron lasers operating with two colors are promising devices for applications. The relevant modelization has provided a good understanding of the underlying physics. In this paper we present an analysis of the experimental results obtained at SPARC-LAB concerning seeded two-colors free electron laser (FEL) operation. The use of an ad hoc developed semi-analytical model based on the small-signal FEL integral equation reproduces most of the observed phenomenology. The paper discusses the reliability of the proposed method, the range of validity and its possible improvement. © 2016, American Physical Society. All rights reserved.

We investigate the working conditions of Free Electron Lasers operating in the SASE regime with wave undulators. We provide general scaling criteria and corroborate them with appropriate numerical simulations.

The existence of a characteristic coherence length in SASE FEL Physics determines the lasing of different portions, namely the slices, of the electron bunch. Each slice may be characterized by different phase space properties, namely by not necessarily equal emittances and Twiss coefficients. This fact opens new questions on the strategies of beam matching and how the various portions of the beam contribute to the performances of the output radiation, including those associated with the transverse coherence. In this paper we discuss how the FEL intensity evolution and eventually the saturated power are affected either by the phase space distributions of the different slices and by the e-beam transport matching. The analysis we develop is based on a semi-analytical procedure having the advantages of providing reliable results, with an almost negligible computational effort. The drawback of the method is that of neglecting the field phase evolution and the slippage effects. The obtained results are compared with those obtained from other codes and with the recent data from the SPARC experiment.

We analyze the dynamics of Free Electron Laser (FEL) devices, operating with a bunched beam exhibiting a longitudinal phase space correlation. We show that the presence of an energy-position correlation term is responsible for very interesting effects like an enhancement of the peak output power, a shortening of the laser pulses and an increase of the non linearly generated harmonic intensities. We conjecture that the mechanism is due to a kind of energy tapering effect associated with the correlation. We discuss the difference of the dynamics with respect to an ordinary undulator tapering and the relative advantages.

We present the experimental evidence of the generation of coherent and statistically stable two-color free-electron laser radiation obtained by seeding an electron beam double peaked in energy with a laser pulse single spiked in frequency. The radiation presents two neat spectral lines, with time delay, frequency separation, and relative intensity that can be accurately controlled. The analysis of the emitted radiation shows a temporal coherence and a shot-to-shot regularity in frequency significantly enhanced with respect to the self-amplified spontaneous emission. © 2015 American Physical Society. © 2015 American Physical Society.

The theory of cyclotron autoresonance maser (CARM) is formulated in a free electron laser (FEL) like fashion. We get a one-to-one correspondence between the equations describing the two devices and show that the wealth of scaling relations developed for the FEL evolution can be exploited to describe the CARM dynamics too. © 1965-2012 IEEE.

We present the experimental evidence of the generation of coherent and statistically stable Free-Electron Laser (FEL) two color radiation obtained by seeding an electron double peaked beam in time and energy with a single peaked laser pulse. The FEL radiation presents two neat spectral lines, with time delay, frequency separation and relative intensity that can be accurately controlled. The analysis of the emission shows a temporal coherence and regularity in frequency significantly enhanced with respect to the Self Amplified Spontaneous Emission (SASE). © 2015 SPIE.

In this paper, we show that Cerenkov free electron laser oscillators can be studied using a treatment closely similar to that of the magnetic undulator counterpart. We prove that the saturation dynamics can be modeled by strictly similar formulae and that also for Cerenkov Free Electron Laser oscillator the saturation intensity is a quantity of paramount importance.

In this paper, we show that the pulse propagation effects in high gain single pass free electron laser dynamics, from small signal to saturation, can be accurately modelled by using semi-analytical formulae. The method, which extends previous results, allows a fast and reliable tool of analysis of these devices along with a deeper understanding of the underlying physics.

In this paper we will discuss the conditions under which the free-electron laser interaction in a storage ring may reinforce the effect of the Landau damping, thus leading to the suppression of different types of instabilities. The problem will be discussed both by making use of general arguments and referring to the specific examples.

This report is a primer introduction on the sources of coherent syncrotron radiation from FELs compared to conventional lasers. Even though the underlying mechanisms are different, FELs can be considered a laser source to all effects. In fact FEL is based on the stimulated emission of virtual photons by a relativistic electron beam, passing through an undulator/wiggler, much like conventional lasers exploit the stimulated emission by an atomic/molecular system on which a population inversion has been realized. FEL operation is illustrated by means of the usual set of parameters (gain, saturation intensity...) used to describe the functioning of conventional lasers.

The operation of the Super-ACO storage ring FEL using a harmonic RF cavity exhibits vertical instabilities, which are generally compensated with an increase of the chromaticity of the operating point. It has been previously reported that the FEL itself can compete, and even damps various types of electron beam instabilities. Here, we show that, when the FEL is operating, the threshold of appearance of the vertical instability is modified and that the FEL enlarges the zone of stable regime of the beam operation. Experiments showing the evolution of the chromaticity allowing the beam to be stable versus current are compared, in the presence of the FEL or for the natural beam operation.

A free electron laser oscillator-amplifier device, in which the modulating section was provided an optical-klystron oscillator, was discussed. It was observed that the output power in the amplifier and the relevant stability were functions of the oscillator intracavity power. It was found that optimum conditions for the output power in the amplifier were obtained for moderate intracavity power. Analysis shows that the configuration ensured a stable output power of the amplifier section.

We discuss non-conventional undulator configurations for SASE FEL devices aimed at enhancing the emission on higher harmonics, reducing the saturation length and operating in less sensitive conditions for the electron beam qualities.

The Super-ACO storage ring Free Electron Laser (FEL) has been operated using an alternative operating point characterized by a non-zero dispersion function in the undulator straight section, linking the transverse motion of the electrons to the energy spread, and by a low momentum compaction factor. The longitudinal to transverse coupled electron beam motion induces a modified dynamics of the Super-ACO FEL. The FEL characteristics, such as the FEL power, pulse duration and spectral width are presented and analyzed in terms of storage ring FEL dynamics.

The status of the art of the VUV-X-ray FEL sources, the limit of the relevant technologies and the future perspectives are analysed. Possible strategies aimed at developing the design of a road map toward very short wavelengths, very high brilliance and very short pulses are discussed. Within such a framework we report and comment on the proposed devices.