In low-energy FEL beamlines, like SXFEL-SBP at the Shanghai Synchrotron Radiation Facility and FLASH1 and FLASH2 at DESY, SASE undulators with perfectly reasonable strength may dynamically affect the optics of the Focusing-Undulator-Defocusing-Undulator (FUDU) cells, pre-matched for a given fixed set of undulator parameters, so violently that a dynamical re-adjustment of the FUDU quadrupoles becomes mandatory. Here we refine and generalize a result reported at the FEL conference 2024. Our almost-analytical result allows implementation in the control system, and is valid for fairly general symplectic coupling-free perturbing matrices. In an approximative sense it includes undulators changing along the beamline and even missing undulators in given cells.

The Shanghai High repetition rate XFEL and Extreme light facility (SHINE) is under construction and aims at generating X-rays between 0.4 and 25 keV with three FEL beamlines at repetition rates of up to 1 MHz. The soft X-ray FEL beamline, FEL-II, will be ready for commissioning in 2025. It is designed to cover the photon energy from 0.4 to 3 keV, in which the baselines of the FEL operation modes are self-amplified spontaneous emission (SASE), self-seeding, echo-enabled harmonic generation (EEHG), and polarization control. Therefore, a high repetition-rate external seed laser, large period length modulator, soft X-ray monochromator, planar undulator, and elliptically polarized undulator have been adopted in the FEL-II beamline. Several potentials such as an ultra-short pulse mode and a multi-color mode are also foreseeable without significant equipment changes in the follow-up operation. A dual-period undulator design is suggested for the echo-enabled harmonic generation (EEHG) commissioning, and it has great potential to break through the unreachable energy of the fully coherent X-ray in the future. The FEL-II beamline will deliver SASE radiation and fully coherent radiation in all the wavelengths of interest.

FLASH is the first soft X-ray FEL user facility, routinely providing brilliant photon beams for users since 2005. The second undulator branch of this facility, FLASH2, is gap-tunable, which allows for testing and using advanced lasing concepts. In particular, we developed a two-color operation mode based on the alternatingly tuned undulator segments (every other segment is tuned to the second wavelength). This scheme is advantageous in comparison with a subsequent generation of two colors in two consecutive sections of the undulator line. First, source positions of the two FEL beams are close to each other which makes it easier to focus them on a sample. Second, the amplification is more efficient in this configuration since the segments with respectively "wrong" wavelength still act as bunchers. We studied operation of this scheme in the regime of small and large separation of tunes (up to a factor of two). We developed new methods for online intensity measurements of the two colors simultaneously that require a combination of two detectors. We also demonstrated our capabilities to measure spectral and temporal properties of two pulses with different wavelengths.

Various scientific and industrial researches such as spectroscopy and advanced nano-technologies have been demanding high flux and fully coherent extreme ultraviolet (EUV) and x-ray radiation. These demands can be commendably satisfied with a MHz-level repetition-rate seeded free-electron laser (FEL). Dictated by the seed laser system, seeded FELs have faced obstacles for the realization of MHz repetition rate. Reducing the required peak power of an external coherent seed laser can effectively increase the repetition rate of a seeded FEL. This paper presents a novel technique that employs a long modulator as a carrier for laser amplification and electron modulation, which is quite different from nominal seeded FELs. Applications of the proposed technique into high-gain harmonic generation (HGHG) and echo-enabled harmonic generation (EEHG) are investigated. Simulation results demonstrate that seed laser power is reduced by about three orders of magnitude and the FEL radiation possesses consistently high coherence and power stability with respect to the nominal HGHG or EEHG. The proposed technique paves the way for the realization of fully coherent EUV and soft x-ray FELs with a repetition rate of MHz and an average power of about 100 W.

The free-electron laser FLASH at DESY and the European XFEL are operated with superconducting radio frequency cavities and supply beam to several user experiments. The switching time between experiments is limited to dozens of microseconds. This contribution will show a regulation with a frequency shifted superconducting cavity to manipulate and change the accelerating properties of electron bunches with 250 kHz.The main challenge of the concept presented in this contribution can be summarized in this statement: finding a way to modulate the energy of individual bunches in a single-source multiple-cavity scheme for a potential CW upgrade of the EuXFEL.

The generation of highly coherent radiation in a high repetition rate free electron laser driven by a superconducting linear accelerator has become a topic of growing interest. External seeding schemes like high-gain harmonic generation (HGHG) and echo-enabled harmonic generation are proven to be able to generate coherent radiation in the extreme ultraviolet and x-ray range. However, the repetition rate of current laser systems with sufficient power to modulate the electron beam is limited to the kilohertz range. Recently, to achieve seeding at a high repetition rate, an optical resonator scheme has been introduced to recirculate the radiation in the modulator to seed the electron bunches. In this paper, two harmonic optical klystron resonator configurations either starting with a seed laser or starting from shot noise are studied. With the harmonic optical klystron as the seeding source, the efficiency of harmonic radiation generation at a comparatively high harmonic can be significantly enhanced when compared with a standard single-stage HGHG. Simulation results show that highly coherent, stable, and high repetition rate pulses in the water window range could be generated by the proposed seeding schemes. Some practical considerations including beam energy chirp effects and the power density effects on mirrors are discussed.

Current FEL development efforts aim at improving the control of coherence at high repetition rate while keeping the wavelength tunability. Seeding schemes, like HGHG and EEHG, allow for the generation of fully coherent FEL pulses, but the powerful external seed laser required limits the repetition rate that can be achieved. In turn, this impacts the average brightness and the amount of statistics that experiments can do. In order to solve this issue, here we take a unique approach and discuss the use of one or more optical cavities to seed the electron bunches accelerated in a superconducting linac to modulate their energy. Like standard seeding schemes, the cavity is followed by a dispersive section, which manipulates the longitudinal phase space of the electron bunches, inducing longitudinal density modulations with high harmonic content that undergo the FEL process in an amplifier placed downstream. We will discuss technical requirements for implementing these setups and their operation range based on numerical simulations.

The free-electron laser (FEL) community is interested in taking full advantage of the high-repetition-rates of FELs run by superconducting machines while maintaining the spectral properties achieved with external seeding techniques. Since the feasibility of seed lasers operating at a repetition-rate of MHz and with sufficient energy in a useful wavelength range, such as the ultraviolet (UV) range is challenging, a seeded oscillator-amplifier scheme is proposed instead for generation of fully coherent and high-repetition-rate radiation. The process is triggered by an external seed laser while an optical feedback system feeds the radiation back to the entrance of the modulator where it overlaps with the next electron bunch. Downstream from the feedback system, the electron bunches are then used for harmonic generation. We discuss the optimization of dedicated simulations and we investigate the stability of this scheme with numerical simulations. As a result, we address the control of the reflectivity of the resonator as a key parameter to achieve a stable HGHG seeded radiation. Finally, we show the impact of the power fluctuations in the oscillator on the bunching amplitude with analytical and simulated results. The output FEL radiation wavelengths considered are 4.167 nm and 60 nm.

For more than a decade free-electron lasers (FELs) have been in operation, providing scientists from many disciplines with the benefits of ultrashort, nearly transversely coherent radiation pulses with wavelengths down to the \AA{}ngstrom range. If no further techniques are applied, the FEL will only amplify radiation from the stochastic distributed electron density in the electron bunch. Contemporary developments aim at producing stable and single-mode radiation by preparing an electron bunch with favorable longitudinal electron density distributions using magnets and conventional laser pulses (seed), hence the name ``seeding.'' In recent years, short wavelength FELs at high electron beam energies and high repetition rates were proposed and built. At those repetition rates, an external seed with sufficient power to manipulate the electron beam cannot be provided by present state-of-the-art laser systems, thus no external seeding scheme could be applied yet. In this paper, we present ways to seed FELs to generate short wavelength radiation at high repetition rates, making use of tested electron beam manipulation schemes. For our parameter study, we used the parameters of FLASH, the free-electron laser in Hamburg. First simulations are presented, showing the feasibility of the method proposed.

Proper diagnostics of intense free-electron laser (FEL) X-ray pulses is indisputably important for experimental data analysis as well as for the protection of beamline optical elements. New challenges for beam diagnostic methods are introduced by modern FEL facilities capable of delivering powerful pulses at megahertz (MHz) repetition rates. In this paper, we report the first characterization of a defocused MHz 13.5-nm beam generated by the free-electron laser in Hamburg (FLASH) using the method of multi-pulse desorption imprints in poly(methyl methacrylate)(PMMA). The beam fluence profile is reconstructed in a novel and highly accurate way that takes into account the nonlinear response of material removal to total dose delivered by multiple pulses. The algorithm is applied to experimental data of single-shot ablation imprints and multi-shot desorption imprints at both low (10 Hz) and high (1 MHz) repetition rates. Reconstructed response functions show a great agreement with the theoretical desorption response function model.

The THz-field-driven streak camera has proven to be a powerful diagnostic-technique that enables the shot-to-shot characterization of the duration and the arrival time jitter of free electron laser (FEL) pulses. Here we investigate the performance of three computational approaches capable to determine the duration of FEL pulses with complex temporal structures from single-shot measurements of up to three simultaneously recorded spectra. We use numerically simulated FEL pulses in order to validate the accuracy of the pulse length retrieval in average as well as in a single-shot mode. We discuss requirements for the THz field strength in order to achieve reliable results and compare our numerical study with the analysis of experimental data that were obtained at the FEL in Hamburg - FLASH.

Longitudinal space-charge effects can act as a driver for short wavelength radiation production in a longitudinal space-charge amplifier (LSCA) *. A single cascade of an LSCA was tested using the hardware of the sFLASH experiment installed at the FEL user facility FLASH (at DESY, Hamburg). Scans of the longitudinal dispersion of the chicane were performed with the tightly focused electron beam for different compression settings, while recording the intensity of the emission from a few-period undulator. We present experimental results and estimates on electron beam properties.

Echo-enabled harmonic generation (EEHG) is a promising technique for seeded free electron lasers (FELs) not only to go down to wavelengths of 4 nm but also to simplify the schemes that are currently used to achieve a similar wavelength range (double cascade HGHG). Thus a study optimizing the EEHG performance in the wavelength range from 60 to 4nm has been performed. The more critical working point, at 4 nm, is here analyzed in terms of seed laser stability for two different seed laser frequencies: visible and UV.

In recent years, there is interest of the Free-Electron Laser (FEL) community in external-seeding techniques such as the Echo-Enabled Harmonic Generation (EEHG) and the HighGain Harmonic Generation (HGHG). With these techniques, pulses of an improved temporal coherence are generated, but at the same time, they are limited by the repetition rates that seed lasers can currently offer with the required pulse energies. A big challenge is to combine the advantages of seeding schemes with high repetition rates. For this purpose, we study a combination of an oscillator-amplifier. The modulator in the oscillator is used at a long wavelength to modulate the electron beam and an amplifier is operated to extract the FEL radiation of the desired harmonic. This way we can use a seed laser of 10 Hz in a burst mode and a resonator to feedback the radiation at repetition rates of superconducting accelerators instead of using an external seed at these high-repetition rates. In this contribution, we present simulation results of a seeded oscillator-amplifier FEL in an HGHG scheme.

The spectral and temporal properties of Free-Electron Lasers (FEL) operating on the basis of self-amplified spontaneous emission (SASE) suffer from the stochastic behavior of the start-up process that fluctuates on a bunch-to-bunch basis. Several so-called ”seeding”-techniques using external radiation fields to overcome this limitation have been proposed and demonstrated. The external seed is usually generated by high-power laser systems, which are not yet available with a sufficient laser pulse energy at the high repetition rates of superconducting FEL facilities. In this contribution we discuss several seeding schemes that lower the requirements for the used laser systems, enabling seeded operation at high repetition rates by the means of a resonatoramplifier setup.

FLASH is the first soft X-ray FEL user facility, routinely providing brilliant photon beams for users since 2005. The second undulator branch of this facility, FLASH2, is gap-tunable which allows to test and use advanced lasing con-cepts. In particular, we tested recently a two-color mode of operation based on the alternation of tunes of the undulator segments (every other segment is tuned to the second wavelength). This scheme is advantageous in comparison with a subsequent generation of two colors in two consec-utive sections of the undulator line. First, source positions of the two FEL beams are close to each other which makes it easier to handle them. Second, the amplification is more efficient in this configuration since the segments with re-spectively ”wrong” wavelength still act as bunchers. We developed methods for online intensity measurements of the two colors simultaneously that require a combination of two detectors. We present some examples of such measurements in the XUV and soft X-ray regimes.

Free-electron lasers (FELs) based on the self-amplified spontaneous emission (SASE) principle generate photon pulses with typically poor longitudinal coherence. FEL seeding techniques greatly improve longitudinal coherence by initiating FEL amplification in a controlled way using coherent light pulses. The sFLASH experiment installed at the FEL user facility FLASH at DESY in Hamburg is dedicated to the study of external seeding techniques. In this paper, the layout of the sFLASH seeding experiment is presented and an overview of recent developments is given.

The THz beamline at FLASH, DESY, provides both tunable (1-300 THz) narrow-bandwidth (∼10%) and broad-bandwidth intense (up to 150 uJ) THz pulses delivered in 1 MHz bursts and naturally synchronized with free-electron laser X-ray pulses. Combination of these pulses, along with the auxiliary NIR and VIS ultrashort lasers, supports a plethora of dynamic investigations in physics, material science and biology. The unique features of the FLASH THz pulses and the accelerator source, however, bring along a set of challenges in the diagnostics of their key parameters: pulse energy, spectral, temporal and spatial profiles. Here, these challenges are discussed and the pulse diagnostic tools developed at FLASH are presented. In particular, a radiometric power measurement is presented that enables the derivation of the average pulse energy within a pulse burst across the spectral range, jitter-corrected electro-optical sampling for the full spectro-temporal pulse characterization, spatial beam profiling along the beam transport line and at the sample, and a lamellar grating based Fourier transform infrared spectrometer for the on-line assessment of the average THz pulse spectra. Corresponding measurement results provide a comprehensive insight into the THz beamline capabilities.

Deutsches Elektronen-Synchrotron (DESY), Notkestrasse 85, D-22607 Hamburg, Germany, Institute of Physics Belgrade, Pregrevica 118, 11080 Belgrade, Serbia, Vinca Institute of Nuclear Sciences, Belgrade, Serbia, Center for Free-Electron Laser Science, Deutsches Elektronen-Synchrotron (DESY), Notkestrasse 85, D-22607 Hamburg, Germany, Department of Physics, S. P. Pune University, Pune, India, SLAC National Accelerator Laboratory, Menlo Park, California, USA, Elettra – Sincrotrone Trieste SCpA, 34149 Basovizza, Trieste, Italy, Helmholtz-Zentrum DresdenRossendorf (HZDR), Bautzner Landstraße 400, 01328 Dresden, Germany, European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany, German Aerospace Center (DLR), Institute of Optical Sensor Systems, Rutherfordstraße 2, 12489 Berlin, Germany, and Institute of Optics and Atomic Physics, Technical University of Berlin, Strasse des 17 Juni 135, 10623 Berlin, Germany. *Correspondence e-mail: nikola.stojanovic@desy.de

Wavefront-propagation simulations have been performed to complete the design of a monochromator beamline for FLASH2, the variable-gap undulator line at the soft X-ray free-electron laser in Hamburg (FLASH). Prior to propagation through the beamline optical elements, the parameters of the photon source were generated using the GENESIS code which includes the free-electron laser experimental data. Threshold tolerances for the misalignment of mirror angles are calculated and, since diffraction effects were included in the simulations, the minimum quality with respect to the slope errors required for the optics is determined.