STUDIES OF COHERENT FREE-ELECTRON LASERS DRIVEN BY COMPACT LINACS OR BY PLASMA WAKEFIELD ACCELERATORS

Free-Electron Lasers (FELs) constitute the last generation of synchrotron light sources: they are conventionally driven by a radio-frequency linear electron accelerator (LINAC), where the electron beam is accelerated to relativistic energies, followed by a chain of undulator magnets, which force the electron beam to oscillate and emit radiation. High brightness, tunable and transversely coherent radiation pulses with unique properties are finally delivered to the downstream experimental stations for a wide range of applications in the fields of physics, biology, medicine and chemistry. External seeding techniques aimed at improving the intrinsically poor temporal coherence and shot-to-shot stability of a FEL starting from shot noise have been proposed and experimentally demonstrated. State-of-the-art fully coherent FELs make use of an external coherent signal, which is basically a high-power laser system seeding and imprinting its coherence properties on the electrons at the undulator entrance, and exploit seeded schemes based on frequency up-conversion to increase the low frequency of the seed laser and generate fully coherent radiation at shorter wavelengths. Independently of the specific seeded scheme, the output FEL radiation properties, such as wavelength and repetition rate, strongly depend on those of the seed laser. In particular, the repetition rate capability of conventional high-power lasers is limited to few kHz at maximum, which is incompatible with the MHz-class ones of a superconducting LINAC, while their wavelength limits the minimum output wavelength that can be achieved with reasonable harmonic up-conversions: the study of alternative seeding sources and FEL configurations overcoming this limitation, thus exploiting the potentials of superconducting LINACs, is the new frontier of FEL science. Such research line has synergies with another ambitious and innovative frontier of accelerator science, the study and development of plasma-based accelerators as well as advancements towards their application in light sources, whose ultimate goal is to make advanced radiation sources available to a wide range of users with the realisation of compact user facilities that could be built in small-scale laboratories. \par This thesis deals with theoretical and numerical studies of novel schemes for a fully coherent FEL driven by a compact LINAC at high repetition rate or by a plasma-wakefield accelerator. Coherent and high repetition rate FEL pulses would enable high resolution experiments and more data collection in shorter experimental times respectively, greatly improving the ongoing science at FELs by supporting new experiments. In this scenario and in the framework of the MariX and BriXSinO projects in Milan, Italy, I investigated the FEL oscillator (FELO) configuration in different spectral regions from the THz down to the X-rays by means of a simulation code, written in Fortran, which iterates the required simulation steps for its study. \\ Based on the acquired knowledge of the FELO scheme, producing high-power coherent pulses suitable for FEL seeding, this thesis proposes two novel FEL oscillator-amplifier setups capable of generating high repetition rate and coherent radiation at short wavelengths in the tender X-ray range ($0.3-0.5$ nm). In these two schemes, the seed pulses are provided by an Extreme-Ultra-Violet (EUV) FELO equipped with Molibdenum/Silicium multilayer mirrors and frequency up-conversion based on the electron beam phase space manipulation is performed. The first proposed scheme, seeded by the EUV FELO, similarly to a fresh bunch High-Gain Harmonic Generation (HGHG) FEL scheme, is a three-stage harmonic FEL cascade made of different undulator sections, where the seed modulates the electron bunches inducing non-linear phase space motions and the emission of higher harmonics in the following undulators. FEL emission in the final radiator up to the 35th harmonics of the FELO wavelength has been predicted by simulations, with the generaton of $10^9-10^{10}$ coherent photons per shot in the tender X-ray range at 0.5 MHz. The same EUV FELO has been considered for seeding an Echo-Enhanced Harmonic Generation (EEHG) FEL cascade: the generation of intense ($10^8-10^{10}$ photons per shot), ultra-short (down to 1 fs) and coherent FEL pulses up to the 50th harmonics of the seed has been simulated, demonstrating a higher versatility, tunability and efficiency. %has been proposed in literature for overcoming the limits posed by the incoherent energy spread and to reach higher harmonic orders: the seed is split in two pulses seeding the electron beam in two different modulators followed by two dispersive sections for harmonic bunching generation and a final radiator stage. %Another option for the MariX X-ray FEL is a FELO based on an X-ray cavity as direct source of coherent X-rays. The design study of a cavity made of four diamond crystal mirrors has been carried out in collaboration with Politecnico di Milano. Based on the simulated performances of this source, fs-scale pulses with $10^10$ coherent photons per shot at 3-3.5 keV at 1 MHz are produced. %The simulated performances of these schemes, driven by the MariX electron beam, show increased stability conditions with respect to the FEL start-up from shot noise, these studies have been published in peer-reviewed international journals and contributed to the MariX Conceptual Design Report. %In the FELO configuration, high-power coherent pulses suitable for FEL seeding are generated and amplified by the passage of successive electron bunches through an undulator embedded in an optical cavity for radiation recirculation: the pulses’ wavelength and repetition rate are only linked to the availability of suitable cavity mirrors and to the cavity and electron beam repetition rate respectively, giving the possibility to provide high-frequency and coherent seed pulses at high repetition rate. %I developed a simulation code for the FELO design and model, written in Fortran, which iterates the required simulation steps, automatically launching the 3D time-dependent FEL simulation code GENESIS 1.3 after each cavity round trip and accounting for the effects of propagation and mirrors. I have been studying the FELO configuration in different spectral regions. %During the first year of PhD and in the framework of the MariX project, I studied advanced schemes for its X-ray seeded FEL. After the injector of the MariX accelerator complex, the electron beam is accelerated up to 3.8 GeV in a compact two-way Superconducting radio-frequency Linac, which operates in continuous-wave mode at 1 MHz and is equipped with an arc compressor reinjecting the beam in the Linac. %The MariX novel and compact accelerator scheme, based on the two-pass two-way Superconducting Linac and an arc for electron beam compression and reinjection in the Linac, will be demonstrated in the MariX demonstrator, called BriXSinO, to be built at the LASA laboratory in Segrate. The electron bunches are generated using a DC gun driven by an Yitterbium laser, at a maximum repetition rate of about 93 MHz. After compression, the electrons are boosted by three Superconducting cavities and then injected into the two-pass two-way Linac, where the beam passes twice with alternate verse. The last element of the device is the arc, which allows the beam to come back to the two-way main Linac and hosts an Inverse Compton Source and a THz FEL. %In this framework, I contributed with the study of the BriXSinO FEL source; named TeRra and operating in the short-THz frequency range (6-30 THz): thanks to the properties of the electron beam and due to space constraints, a FELO scheme with a two-mirror near concentric cavity hosting two short undulator modules with different periods has been chosen for the THz FEL. Source performances in both one and two-color operation, producing up to 1 kW of average power, were simulated. In this short-frequency emission range, the design study mainly focused on the definition of optimal stable oscillator parameters and working points. %Such study contributed to the BriXSinO Technical Design Report and has been recently published. \par The second topic of this thesis is the ongoing collaboration with the SPARC\\ \_LAB laboratory of INFN in Frascati in the framework of the EuPRAXIA project: objects of this collaboration are the demonstration of FEL lasing with a compact beam-driven plasma-wakefield accelerator at SPARC, whose plasma module is made of a cm-scale, 3D-printed capillary, and the design study of the EuPRAXIA FEL beamlines. \\ I contributed to the analysis of the experimental data obtained in two experiments at SPARC and the connected simulation of the FEL process. Single-spike FEL amplification at about 827 nm from shot noise with up to tens-nJ energy, characterized by high shot-to-shot energy fluctuations, has been measured and observed from both the experiment and simulations. A second experiment with the same FEL, driven by the plasma-accelerated electron beam and seeded by a portion of the same laser used for the electron photo-emission, has shown increased energy levels and stability conditions. %The result has been recently published in Nature and is promising for the future implementation of the EuPRAXIA@SPARC\_LAB FEL. This cumulative thesis finally presents the still ongoing design study of the second beamline of the EuPRAXIA@SPARC\_LAB project, a compact and seeded low-energy beamline in the standard HGHG configuration, which can be driven by either the plasma accelerator or the EuPRAXIA X-band LINAC. Simulations of its performances in the whole spectral range of operation and in the two electron beam modes are compared, showing the production of fully coherent single-spike pulses in the Vacuum-UV range from 50 to 180 nm starting from a long wavelength state-of-the-art laser pulse.