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Physical review accelerators and beams 24(8), 080702 (2021). doi:10.1103/PhysRevAccelBeams.24.080702, Echo-enabled harmonic generation free-electron lasers (EEHG FELs)are promising candidates to produce fully coherent soft x-ray pulses by virtue of efficient high harmonic frequency up-conversion from UV lasers.The ultimate spectral limit of EEHG, however, remains unclear, because of the broadening and distortions induced in the output spectrum by residual broadband energy modulations in the electron beam. We present a mathematical description of the impact of incoherent(broadband) energy modulations on the bunching spectrum produced by the microbunching instability through both the accelerator and the EEHG line. The model is in agreementwith a systematic experimental characterization of the FERMI EEHGFEL in the photon energy range $130-210$ eV. We find that amplification of electron beam energy distortions primarily in the EEHG dispersive sections explains an observed reductionof the FEL spectral brightness that is proportional to the EEHGharmonic number. Local maxima of the FEL spectral brightness and of the spectralstability are found for a suitable balance of the dispersive sections'strength and the first seed laser pulse energy. Such characterizationprovides a benchmark for user experiments and future EEHG implementations designed to reach shorter wavelengths., Published by American Physical Society, College Park, MD

The advent of extreme ultraviolet (EUV) and soft x-ray free electron lasers (FELs) has enabled nonlinear optical experiments at wavelengths shorter than the visible-UV range. An important class of experiments is those based on the four-wave-mixing (FWM) approach, which are often based on interactions between pulses at different wavelengths. The exploitation of multiple EUV/soft x-ray wavelengths is not straightforward, but it can significantly expand the range of applications. In this manuscript we report on an experimental approach, based on the concomitant use of a non-collinear split-delay-and-recombination unit (“mini-Timer”) and on a two-color seeded FEL emission scheme (“twin-seed mode”). We used a diamond sample for demonstrating the capability of this setup of generating and detecting a FWM signal stimulated by two-color EUV FEL pulses. This approach can be further exploited for developing experimental methods based on non-linear EUV/x-ray optics.

International audience; Extension of stable longitudinal coherence from vacuum ultraviolet to x rays is highly sought after in the free-electron laser (FEL) community, but it is often prevented by bandwidth broadening originated in the electron beam microbunching instability. We demonstrate that a proper tuning of the linear optics before the beam enters the undulator mitigates the microbunching-induced sideband instability. The experiment was conducted at the Fermi FEL operated in echo-enabled harmonic generation mode, where the spectral brightness at 7 nm wavelength was doubled. The FEL performance is compared to nonoptimized optics solutions and characterized in terms of peak intensity and spectral bandwidth shot-to-shot stability. The technique has straightforward implementation, because it uses quadrupole magnets routinely adopted for beam transport, and it applies to any FEL architecture, so paving the way to the production of high-intensity Fourier-transform limited x-ray pulses in existing and planned FEL facilities.

We measured the chiral relaxation of photoexcited Fenchone at the Carbon K-edge. Our results demonstrate that ultrafast chiral dynamics can be probed using core level spectroscopy with circularly polarized free-electron laser pulses.

We present a method for measuring a complete frequency map of laser-dressed states with femtosecond lifetimes. It is based on collecting decay products as a function of the frequency of the excitation pulse and its delay with respect to the linearly chirped laser pulse, centered at the resonant transition frequency. The method has been tested on the case of laser-coupled 2s2p (1) P-0 and 2p(2) S-1(e) autoionizing resonances in He and is applicable to other quantum systems with short-lived states. When the laser coupling effects are known, the excitation pulse properties can be extracted from the map.

This paper is an addendum to reference (Brynes et al 2018 New J. Phys. 20 073035), in which we studied the transverse emittance growth due to coherent synchrotron radiation (CSR) in the bunch compressor of a free-electron laser. Analytic results based on the theory of CSR were compared with results from experiment and simulation. Recent results have been published (Stupakov 2019 arXiv:1901.10745) which correct the theoretical emittance growth, predicting a smaller increase than that which was expected based on previous results. When comparing these new calculations with the emittance growth that was measured experimentally, and with 3D simulations, we find an improved agreement when the bunch compression approaches its maximum value.

The generation of attosecond pulse trains at free-electron lasers opens new opportunities in ultrafast science, as it gives access, for the first time, to reproducible, programmable, extreme ultraviolet (XUV) waveforms with high intensity. In this work, we present a detailed analysis of the theoretical model underlying the temporal characterization of the attosecond pulse trains recently generated at the free-electron laser FERMI. In particular, the validity of the approximations used for the correlated analysis of the photoelectron spectra generated in the two-color photoionization experiments are thoroughly discussed. The ranges of validity of the assumptions, in connection with the main experimental parameters, are derived.

Synopsis We have observed the autoionization of the laser-coupled 2s2p 1 Po and 2p 2 1 Se resonances in helium. The ions were collected while varying the frequency and delay of the extreme-ultraviolet (EUV) excitation pulse with respect to the linearly chirped visible (VIS) laser pulse. From the measured frequency-delay map the Autler-Townes splitting, the EUV-VIS cross-correlation and the linear chirp parameter were extracted.

We demonstrate that emission of coherent transition radiation by a ∼1 GeV energy-electron beam passing through an Al foil is enhanced in intensity and extended in frequency spectral range, by the energy correlation established along the beam by coherent synchrotron radiation wakefield, in the presence of a proper electron optics in the beam delivery system. Analytical and numerical models, based on experimental electron beam parameters collected at the FERMI free electron laser (FEL), predict transition radiation with two intensity peaks at ∼0.3 THz and ∼1.5 THz, and extending up to 8.5 THz with intensity above 20 dB w.r.t. the main peak. Up to 80-µJ pulse energy integrated over the full bandwidth is expected at the source, and in agreement with experimental pulse energy measurements. By virtue of its implementation in an FEL beam dump line, this work promises dissemination of user-oriented multi-THz beamlines parasitic and self-synchronized to EUV and x-ray FELs.

International audience; We demonstrate experimentally the control of the polarization (ellipticity and polarization axis) of femtosecond high-order harmonics. The method relies on a two-color (omega - 2 omega) configuration, where both omega and 2 omega generating fields have linear polarizations with a variable crossing angle. We correlate our measurements with the conservation rules of energy and linear momentum accounting for harmonic generation in a two-color field. We evidence that the generation process, and especially the number of omega and 2 omega photons absorbed for generating a given harmonic, strongly depends on the crossing angle. Finally, relying on a simple formalism, we derive analytical formulae for calculating both polarization axis and ellipticity of the separate harmonics. The model corroborates our results and represents a base for future investigations.

Free-electron lasers (FELs) are promising devices for generating light with laser-like properties in the extreme ultraviolet and X-ray spectral regions. Recently, FELs based on the self-amplified spontaneous emission (SASE) mechanism have allowed major breakthroughs in diffraction and spectroscopy applications, despite the relatively large shot-to-shot intensity and photon-energy fluctuations and the limited longitudinal coherence inherent in the SASE mechanism. Here, we report results on the initial performance of the FERMI seeded FEL, based on the high-gain harmonic generation configuration, in which an external laser is used to initiate the emission process. Emission from the FERMI FEL-1 source occurs in the form of pulses carrying energy of several tens of microjoules per pulse and tunable throughout the 65 to 20 nm wavelength range, with unprecedented shot-to-shot wavelength stability, low-intensity fluctuations, close to transform-limited bandwidth, transverse and longitudinal coherence and full control of polarization.

The hitherto unexplored two-photon doubly excited states [Ne∗(2p-13s)]2 were experimentally identified using the seeded, fully coherent, intense extreme ultraviolet free-electron laser FERMI. These states undergo ultrafast interatomic Coulombic decay (ICD), which predominantly produces singly ionized dimers. In order to obtain the rate of ICD, the resulting yield of Ne2+ ions was recorded as a function of delay between the extreme ultraviolet pump and UV probe laser pulses. The extracted lifetimes of the long-lived doubly excited states, 390(-130/+450) fs, and of the short-lived ones, less than 150 fs, are in good agreement with ab initio quantum mechanical calculations.

The hitherto unexplored two-photon doubly excited states [Ne^{*}(2p^{-1}3s)]_{2} were experimentally identified using the seeded, fully coherent, intense extreme ultraviolet free-electron laser FERMI. These states undergo ultrafast interatomic Coulombic decay (ICD), which predominantly produces singly ionized dimers. In order to obtain the rate of ICD, the resulting yield of Ne_{2}^{+} ions was recorded as a function of delay between the extreme ultraviolet pump and UV probe laser pulses. The extracted lifetimes of the long-lived doubly excited states, 390(-130/+450) fs, and of the short-lived ones, less than 150 fs, are in good agreement with ab initio quantum mechanical calculations.

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.

According to standard thermodynamics, the efficiency of a cyclic machine is strictly lower than one. Such a result is a straightforward consequence of the second principle of thermodynamics. Recent advances in the study of the thermodynamics of long-range interacting system report however on a rather intricate zoology of peculiar behaviors, which are occasionally in contrast with customarily accepted scenarios, dueling with intuition and common sense. In this paper, a thermodynamical cycle is assembled for an ideal device working with non-Boltzmanian long-range fluid and operating in contact with two thermal reservoirs. Assuming the microcanonical or canonical temperature to be the correct thermodynamic temperature, we obtain a paradoxical conclusion: the system is in fact analytically shown to violate the second principle of thermodynamics. This phenomenon ultimately relates to the existence of regions in the canonical ensemble where the energy decreases with the average kinetic temperature. We argue that the validity of the second principle of thermodynamics can be possibly regained, by revisiting the definition of canonical ensemble, as well as the Fourier law of heat transport, and consequently relaxing the constraint on the maximal efficiency as imposed by the Carnot theorem.

Using harmonic emission from circularly polarized undulator is a procedure that is normally employed on synchrotron beamlines in order to extend the covered spectral range. A similar capability is likewise beneficial for next generation free-electron lasers. In this paper, we perform a first quantitative experimental analysis of the angular distribution of free-electron laser harmonic emission from helical undulators. Experimental results are compared to those obtained by means of a theoretical model based on the paraxial solution of Maxwell’s equations. PACS numbers

In a free-electron laser set up as a single-pass amplifier, the evolution of the optical beam in the weak-field regime is ruled by the so-called Integral Equation. We derive this equation by a different analytical technique with respect to the one employed in earlier works. Our approach proves to be mathematically simpler and more physically transparent with respect to the original one.

FERMI@elettra is a fourth-generation light source user facility under construction at the Elettra Laboratory in Trieste, Italy. The high-quality 1.2 GeV electron beam drives two-seeded Free Electron Lasers (FELs) in the wavelength range 100−10 nm. Wavelength tunability, variable polarization and higher electron beam energies to reach even shorter output wavelengths are also in the machine delivery plan. This paper describes the physics processes that have been modelled to simulate FERMI@elettra and the computer codes used to optimize the machine design. The paper focuses on several design challenges and how these translate into modelling and simulation challenges.

Taking advantage of the storage ring free electron laser beamline at Elettra, we have implemented an experimental setup for the generation of sub-picosecond (ps) coherent optical pulses in the VUV range. The setup is based on the frequency up-conversion of a high-power external signal (provided by a Ti:Sapphire laser) and makes use of a relativistic electron bunch as resonating medium. The produced VUV pulses have peak power in MW range, variable polarization, high shot to shot stability and control of the timing parameters at the ps level. In this paper, we present the first characterization of the temporal and spectral features of the emitted light. The radiation can be exploited for new experiments in the fields of dynamical phenomena, non-linear physics, magnetism and biology.

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.

The optical klystron enhancement to a self-amplified spontaneous emission (SASE) free electron laser (FEL) has been deeply studied in theory and in simulations. In this FEL scheme, a relativistic electron beam passes through two undulators, separated by a dispersive section. The latter converts the electron-beam energy modulation produced in the first undulator in density modulation, thus enhancing the free-electron laser gain. We report the first experiment that has been carried out at the FERMI facility in Trieste, of enhancement to a SASE FEL by using the optical klystron scheme. XUV photons have been produced with an intensity several orders of magnitude larger than in pure SASE mode. The impact of the uncorrelated energy spread of the electron beam on the optical klystron SASE performance has been also investigated.

FERMI is the first user facility based upon an externally seeded free-electron laser (FEL) that delivers a coherent and tunable UV radiation (down to 4 nm at the fundamental) in a number of different configurations. A microbunching instability (MBI) developing in the bunch compressors and in the rest of the linac can degrade the quality of the high brightness electron beam sufficiently to reduce the FEL output intensity and spectral brightness. A laser heater installed in the low energy (100 MeV) part of the FERMI accelerator increases the local energy spread to provide Landau damping against this instability. In this paper we summarize the main results obtained with the FERMI laser heater since it commissioning in 2012. We present the measurement of the reduction of the incoherent energy spread at the linac exit induced by the heating of the electron beam at the beginning of the linac. We also discuss the positive effects of such heating upon the emission of coherent optical transition radiation and the FEL performances both in terms of intensity and spectrum. Moreover, we report about results that have been used to experimentally demonstrate that for transversely uniform heating the local energy spread augmentation is characterized by a non-Gaussian distribution that can be preserved up to the FEL undulator entrance with a significant impact on the performance of high-gain harmonic generation (HGHG) FELs, especially at soft x-ray wavelengths.

Polarization control is a key feature of light generated by short-wavelength free-electron lasers. In this work, we report the first experimental characterization of the polarization properties of an extreme ultraviolet high gain free-electron laser operated with crossed polarized undulators. We investigate the average degree of polarization and the shot-to-shot stability and we analyze aspects such as existing possibilities for controlling and switching the polarization state of the emitted light. The results are in agreement with predictions based on Gaussian beams propagation.

Thin film magnetization reversal without applying external fields is an attractive perspective for applications in sensors and devices. One way to accomplish it is by fine-tuning the microstructure of a magnetic substrate via temperature control, as in the case of a thin Fe layer deposited on a $\mathrm{MnAs}/\mathrm{GaAs}(001)$ template. This work reports a time-resolved resonant scattering study exploring the magnetic and structural properties of the $\mathrm{Fe}/\mathrm{MnAs}$ system, using a 100 fs optical laser pulse to trigger local temperature variations and a 100 fs x-ray free-electron laser pulse to probe the induced magnetic and structural dynamics. The experiment provides direct evidence that a single optical laser pulse can reverse the Fe magnetization locally. It reveals that the time scale of the magnetization reversal is slower than that of the MnAs structural transformations triggered by the optical pulse, which take place after a few picoseconds already.

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.

We discuss the analogies between two classical models of the single-pass free electron laser dynamics and of the beam-wave plasma instability. Moreover, a formal bridge between the two areas of investigation is established. This connection is here exploited to derive a reduced Hamiltonian formulation for the saturated regime of the free electron laser.

In this paper, a deep characterization is provided of the longitudinal dynamics of a storage-ring free-electron laser. Closed analytical expressions are derived for the main statistical parameters of the system (i.e. beam energy spread, intensity, centroid position and rms value of the laser distribution) as a function of the light-electron beam detuning at each pass inside the interaction region. Moreover, the transition between the stable “cw” regime and the unstable pulsed behaviour is shown to be a Hopf bifurcation. Finally, a feedback procedure is introduced which suppresses the bifurcation and significantly improves the system stability.

A new injector is one of the necessary upgrades to be made in the existing ELETTRA linac to improve its performance to the level required for FEL operation. To this end, the design of an RF photo-injector is in progress at ELETTRA. Several types of RF guns are currently under consideration. The drive laser system, beam optics, diagnostics, and other relevant issues are also being addressed.

Different methods can be used to concentrate the power generated by a storage-ring free-electron laser into a series of giant pulses. One of these techniques, Q-switching, is based on a periodically induced detuning between the electron bunches circulating into the ring and the light pulse stored in the optical cavity. Such a method has been recently implemented at ELETTRA. This new regime significantly improves the peak power and the reproducibility of laser signal making the source more reliable. A full characterization of such an operation mode is presented in this paper.

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.

A new optics providing an emittance close to the minimum theoretical value has been proposed for the Super-ACO storage ring with a reduced value of the momentum compaction factor and non-zero dispersive function in the Free-Electron Laser (FEL) section. It has been adapted to the FEL operation mode, with two RF cavities at 100 and 500 MHz. The obtained results concerning this new optics and the FEL oscillation are presented.

This paper is devoted to a theoretical analysis of the dynamical properties of a Storage Ring Free Electron Laser in the presence of an imperfect synchronism between the electron bunch and the laser pulse at each pass inside the optical cavity. The resulting “cw” and pulsed regimes are investigated in detail for the case of the Super-ACO Free Electron Laser. Numerical results are shown to be in good agreement with experimental data.

Aim of this paper is to give a general overview of different theoretical approaches to the physics of a Storage Ring Free Electron Laser. Predictions obtained using the main numerical codes developed world-wide will be compared with experimental results.

FERMI, based at Elettra (Trieste, Italy) is the first free electron laser (FEL) facility operated for user experiments in seeded mode. Another unique property of FERMI, among other FEL sources, is to allow control of the polarization state of the radiation. Polarization dependence in the study of the interaction of coherent, high field, short-pulse ionizing radiation with matter, is a new frontier with potential in a wide range of research areas. The first measurement of the polarization-state of VUV light from a single-pass FEL was performed at FERMI FEL-1 operated in the 52 nm-26 nm range. Three different experimental techniques were used. The experiments were carried out at the end-station of two different beamlines to assess the impact of transport optics and provide polarization data for the end user. In this paper we summarize the results obtained from different setups. The results are consistent with each other and allow a general discussion about the viability of permanent diagnostics aimed at monitoring the polarization of FEL pulses.

We present the main features of CITIUS, a new light source for ultrafast science, generating tunable, intense, femtosecond pulses in the spectral range from IR to XUV. The XUV pulses (about 105-108 photons/pulse in the range 14-80 eV) are produced by laser-induced high-order harmonic generation in gas. This radiation is monochromatized by a time-preserving monochromator, allowing also to work with high-resolution andwidth selection. The tunable IR-UV pulses (1012--1015 photons/pulse in the range 0.4-5.6 eV) are generated by an optical parametric amplifier, which is driven by a fraction of the same laser pulse that enerates high order harmonics. The IR-UV and XUV pulses follow dierent optical paths and are eventually recombined on the ample for pump-probe experiments. The new light source will become the fulcrum of a new center located at the University of Nova Gorica, active in a wide range of scientific fields, including materials science, catalysis, biochemistry and magnetism. We also present the results of two pump-probe experiments: with the first one, we fully characterized the temporal duration of harmonic pulses in the time-preserving configuration; with the second one, we demonstrated the possibility of using CITIUS for selective investigation of the ultra-fast dynamics of dierent elements in a magnetic compound.

We report results of a free-electron laser operating with the high gain harmonic generation configuration in the wavelength rage from 60 to 20 nm. With the recent experiments done at the FERMI free-electron laser facility in Trieste we demonstrated the capability of the used method to produce highly coherent pulses allowing to improve the performances of FELs in the EUV spectral range overcoming some of the limitations that are typical of systems based on the self amplified spontaneous emission (SASE). Taking advantage of the seeding scheme adopted for FERMI high photon energy stability and a very high longitudinal and transverse coherence have been measured. The operation of the FERMI FEL facility will allow improving the use of the FEL light for those experiments that require a small spectral bandwidth or a precise control of the photon energy.

Systematic studies on the Free Electron Laser (FEL) line and micropulse have been performed on the Super-ACO storage ring FEL with a monochromator and a double-sweep streak camera under various conditions of operation (detuning, “CW” and Q-switched mode). From these data, it appears that the FEL is usually operated very close to the Fourier limit.

Les lasers a electrons libres (LEL) sur anneau de stockage sont des sources coherentes, accordables et intenses qui peuvent couvrir le domaine UV, comme celui de Super-ACO qui permet d'atteindre 300 nm avec des puissances et des niveaux de stabilite tres satisfaisants. Ces performances ont permis d'initier un programme d'applications base notamment sur des experiences pompe/sonde resolues en temps realisees en combinant le LEL avec le Rayonnement Synchrotron, emis par differentes lignes de lumiere, et naturellement synchronise. Le champ d'application s'etend de la physique des surfaces, aux sciences des materiaux et a la photo-biologie en solution.

Control of the electron-beam longitudinal-phase-space distribution is of crucial importance in a number of accelerator applications, such as linac-driven free-electron lasers, colliders and energy recovery linacs. Some longitudinal-phase-space features produced by nonlinear electron beam self- fields, such as a quadratic energy chirp introduced by geometric longitudinal wakefields in radio-frequency (rf) accelerator structures, cannot be compensated by ordinary tuning of the linac rf phases nor corrected by a single high harmonic accelerating cavity. In this Letter we report an experimental demonstration of the removal of the quadratic energy chirp by properly shaping the electron beam current at the photoinjector. Specifically, a longitudinal ramp in the current distribution at the cathode linearizes the longitudinal wakefields in the downstream linac, resulting in a flat electron current and energy distribution. We present longitudinal-phase-space measurements in this novel configuration compared to those typically obtained without longitudinal current shaping at the FERMI linac.

We present here the state of the art of Storage Ring Free Electron Lasers under operation in Europe. Free electrons Lasers (FELs) are coherent, high power and tuneable radiation sources, obtained by the interaction of an optical wave with a bunch of ultrarelavistic electrons wiggling in a periodical permanent magnetic structure. The developments and the results obtained recently in the UV domain by the FELs operating in Europe on Synchrotron Facilities, Super ACO and ELETTRA, offer new opportunities for using these sources in several scientific domains, and foresee uniques performances for the proposed FEL on the third generation french Synchrotron SOLEIL.

Frequency pulling is a well-known phenomenon in standard laser physics, leading to a shift of the laser frequency when the cavity and maximum gain frequencies are detuned. In this letter we present the first experimental demonstration of frequency pulling in single-pass free-electron lasers. Measurements are performed using the single-pass free-electron laser installed on the Elettra storage ring.

After less than two years of commissioning the FERMI@Elettra free electron laser is now entering into the operation phase and is providing light to the first user experiments. To reach the final ambitious goals of providing high power coherent pulses with fundamental wavelengths down to 4 nm, the system will need further studies and additional commissioning time in 2011 when fine tuning of the major systems such as the electron gun and the main accelerator will take place. Nevertheless, FERMI is already able to provide light with unique characteristics allowing Users to perform experiments not possible with other facilities. Based on a 1.5 GeV electron linear accelerator, FERMI@Elettra has two seeded FEL lines that cover the whole spectral range from 100 nm down to 4 nm with fully coherent pulses. The use of the high gain harmonic generation scheme initiated by a tunable laser in the UV allows FERMI to produce light characterized by both transverse and full temporal coherence. The use of specially designed undulators allows full control of the FEL polarization and can be continuously varied from linear to circular in any orientation or ellipticity. Here we will report about the first results and the future plans for FERMI@Elettra.

We show that, in the continuum limit, the dynamics of Hamiltonian systems defined on a lattice with long-range couplings is well described by the Vlasov equation. This equation can be linearized around the homogeneous state, and a dispersion relation, which depends explicitly on the Fourier modes of the lattice, can be derived. This allows one to compute the stability thresholds of the homogeneous state, which turns out to depend on the mode number. When this state is unstable, the growth rates are also functions of the mode number. Explicit calculations are performed for the $\ensuremath{\alpha}$-Hamiltonian mean field model with $0\ensuremath{\leqslant}\ensuremath{\alpha}l1$, for which the mean-field mode is always found to dominate the exponential growth. The theoretical predictions are successfully compared with numerical simulations performed on a finite lattice.

We provide a detailed discussion of out-of-equilibrium phase transitions in the Hamiltonian mean-field (HMF) model in the framework of Lynden-Bell's statistical theory of the Vlasov equation. For two-level initial conditions, the caloric curve β(E) only depends on the initial value f(0) of the distribution function. We evidence different regions in the parameter space where the nature of the phase transitions between magnetized and nonmagnetized states changes: (i) For f(0)>0.10965, the system displays a second-order phase transition; (ii) for 0.109497

The possibility of observing phenomena peculiar to long-range interactions, and more specifically in the so-called Quasi-Stationary State (QSS) regime is investigated within the framework of two devices, namely the Free-Electron Laser (FEL) and the Collective Atomic Recoil Laser (CARL). The QSS dynamics has been mostly studied using the Hamiltonian Mean-Field (HMF) toy model, demonstrating in particular the presence of first versus second order phase transitions from magnetized to unmagnetized regimes in the case of HMF. Here, we give evidence of the strong connections between the HMF model and the dynamics of the two mentioned devices, and we discuss the perspectives to observe some specific QSS features experimentally. In particular, a dynamical analog of the phase transition is present in the FEL and in the CARL in its conservative regime. Regarding the dissipative CARL, a formal link is established with the HMF model. For both FEL and CARL, calculations are performed with reference to existing experimental devices, namely the FERMI@Elettra FEL under construction at Sincrotrone Trieste (Italy) and the CARL system at LENS in Florence (Italy).

The out-of-equilibrium mean-field dynamics of a model for wave-particle interaction is investigated. Such a model can be regarded as a general formulation for all those applications where the complex interplay between particles and fields is known to be central, e.g. electrostatic instabilities in plasma physics, particle acceleration, and free-electron lasers (FELs). The latter case is here assumed as a paradigmatic example. A transition separating different macroscopic regimes is numerically identified and interpreted by making use of the so-called violent-relaxation theory. In the context of free-electron lasers, such a theory is shown to be effective in predicting the saturated regime for energies below the transition. The transition is explained as a dynamical switch between two metastable regimes, and is related to the properties of a stationary point of an entropic functional., SCOPUS: ar.j, info:eu-repo/semantics/published

We propose an efficient method to compute Lyapunov exponents and Lyapunov eigenvectors of long-range interacting many-particle systems, whose dynamics is described by the Vlasov equation. We show that an expansion of a distribution function using Hermite modes (in momentum variable) and Fourier modes (in configuration variable) converges fast if an appropriate scaling parameter is introduced and identified with the inverse of the system temperature. As a consequence, dynamics and linear stability properties of many-particle states, both in the close-to and in the far-from equilibrium regimes can be predicted using a small number of expansion coefficients. As an example of a long-range interacting system we investigate stability properties of stationary states of the Hamiltonian mean-field model.