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The undulator is a key luminous component of the Shanghai high repetition rate x-ray free electron laser and extreme light facility, and the motion control system is an important part of the undulator. The main task of the motion control system is to complete the high precision adjustment of the gap and taper between the upper magnetic pole girder and lower magnetic pole girder, so as to adjust the wavelength of the radiation light. According to the development requirements of the motion control system for the U26 undulator, which is a conventional permanent magnet, this paper proposes a new motion control system with double position feedback closed-loop control, including programmable logic controller (PLC) closed-loop control based on position feedback by a linear absolute encoder (LAE) and driver closed-loop control based on position feedback by a rotary absolute encoder (RAE) of a servo motor. Multiple motion tests of the U26 undulator have shown that the repeatability accuracy of the gap is ±50 nm and the gap drive can reach 0.1 µm step size, the error of which is about ±20 nm according to the feedback of the LAE. The conclusion can be drawn that the motion step size and repeatability accuracy of the motion control system for the U26 undulator are improved by one order of magnitude on the basis of meeting all technical requirements. At the same time, motor torque protection, motor temperature protection, and redundant position protection with RAE can further improve the reliability and safety of the motion control system for the U26 undulator.

The Shanghai high-repetition-rate XFEL and extreme light facility (SHINE) plans to install several elliptically polarizing undulators (EPUs) as afterburners behind the planar undulator section to obtain nearly saturated circularly polarized free-electron laser (FEL) radiation. Therefore, the SHINE R&D project needs to develop a 4-m-long EPU with an effective magnetic field of 1.5 T, a period of 68 mm, and a minimum gap of 3 mm. A magnetic force compensation EPU prototype has recently been built and tested at the Shanghai Synchrotron Radiation Facility (SSRF) based on the addition of permanent magnets. This prototype can realize magnetic compensation under various polarization modes in all working gaps, thereby reducing the deformation of the girders and maintaining sufficient rigidity of the mechanical structure. A girder deformation monitoring system was established to obtain real force compensation feedback. The final magnetic field measurement results meet the physical requirements, and the proposed scheme can be used as an alternative to the EPU with a high magnetic field and large magnetic force.

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.

The X-ray free-electron laser oscillator (XFELO) has received significant attention due to its ability to produce fully coherent, high-brightness, and highly stable X-ray beams. Despite these advantages, the operation of the XFELO can be impeded by the surrounding environment. Specifically, vibrations of the optical components within the cavity can lead to poor alignment, which can diminish the interaction between the light and electrons in the undulator. Consequently, the quality of the output X-rays may be compromised. This study aims to investigate the impact of mirror vibrations on the output laser at various vibration frequencies. Firstly, we develop three single-frequency vibration models at 10 Hz, 0.01 MHz, and 1.1 MHz to investigate the changes in energy, spectral width, beam size, and beam divergence angle of the output laser. Secondly, we build a more complex multi-frequency vibration model based on the single-frequency one to simulate the realistic vibration of the mirror. Finally, we utilize the multi-frequency vibration model to investigate the tolerance limits of the output laser to vibration amplitude at different vibration frequencies of the mirror. The results show that the tolerance of the amplitude near the low and middle frequencies has less effect on the output power, which is approximately 250 nrad or more. However, in certain particular instances, particularly in the vicinity of the resonant frequency, there will be deviations from the tolerance limit. These deviations can result in values that are excessively high or excessively low. The study could prove useful in the future installation of XFELOs.

Shanghai Soft X-ray Free-Electron Laser (SXFEL) is the first X-ray free-electron laser facility in China. The initial commissioning of the beamline was carried out in May 2021. Herein, we present a status report and the first experimental results obtained during the early commissioning of Kirkpatrick-Baez (KB) mirrors for the Coherent Scattering and Imaging (CSI) endstation, including three types of diagnostics. A bright X-ray focal spot of less than 3 μm was achieved by using edge-scan and silicon ablation imprint measurements. In order to confirm the spot size, the attenuated beam and full beam are used respectively for the two measurement methods.

Background: Small bowel adenocarcinoma (SBA) is a rare gastrointestinal tumor with high malignancy. The aim of this study was to comprehensively evaluate the distant metastasis pattern and establish nomograms predicting survival for SBA.Methods: From 2010 to 2015, patients diagnosed with SBA were identified based on the Surveillance, Epidemiology, and End Results (SEER) database. Kaplan–Meier survival analysis was applied to compare survival differences between metastasis patterns. Then, univariate and multivariate cox analyses were applied to screened out independent prognostic factors of cancer-specific survival (CSS) and overall survival (OS), and identify the risk factors for metastasis of SBA. To assess the discrimination and calibration of nomograms, the concordance index (C-index), calibration curves, receiver-operating characteristic curve (ROC), and decision curve analysis (DCA) were calculated.Results: Kaplan–Meier curves revealed that metastasis patterns were significantly correlated with CSS (p < 0.001) and OS (p < 0.001). Then, the metastasis pattern was showed to be an independent prognostic factor of OS and CSS in patients with SBA, as well as age, grade, T stage, N stage, surgery, retrieval of regional lymph nodes, and chemotherapy. Combining these factors, we constructed prognostic nomograms, which suggested that the metastasis pattern made the greatest contribution to the survival of patients with SBA. Nomograms for OS and CSS had a C-index of 0.787 and 0.793, respectively. Calibration curves showed an excellent agreement between probability and actual observation in the training and validation cohort. Decision curve analysis also exhibited its clinical value with an improved net benefit. In addition, the models we constructed had better prognostic accuracy and clinical utility than traditional TNM staging based on C-index and ROC. Further, Cox regression analysis showed that old age, poor differentiation, N2, and not receiving chemotherapy were the risk factors for prognosis in patients with metastatic SBA.Conclusion: As an independent prognostic factor, the metastasis pattern exhibited the greatest predictive effect on OS and CSS for patients with SBA. Adjuvant chemotherapy had a positive effect on the survival of patients with SBA. Nomograms for predicting 3-and 5-year OS and CSS of patients with SBA were constructed, which could identify patients with higher risk and might be superior in predicting the survival of patients with SBA than TNM staging.

Linear accelerator-based free-electron lasers (FELs) are the leading source of fully coherent X-rays with ultra-high peak powers and ultra-short pulse lengths. Current X-ray FEL facilities have proved their worth as useful tools for diverse scientific applications. In this paper, we present an overview of the features and future prospects of X-ray FELs, including the working principles and properties of X-ray FELs, the operational status of different FEL facilities worldwide, the applications supported by such facilities, and the current developments and outlook for X-ray FEL-based research.

The Shanghai soft X-ray Free-Electron Laser facility (SXFEL), which is the first X-ray FEL facility in China, is being constructed in two phases: the test facility (SXFEL-TF) and the user facility (SXFEL-UF). The test facility was initiated in 2006 and funded in 2014. The commissioning of the test facility was finished in 2020. The user facility was funded in 2016 to upgrade the accelerator energy and build two undulator lines with five experimental end-stations. The output photon energy of the user facility will cover the whole water window range. This paper presents an overview of the SXFEL facility, including considerations of the upgrade, layout and design, construction status, commissioning progress and future plans.

External seeded free-electron lasers (FELs) hold promising prospects for producing intense coherent radiation at high harmonics of a conventional laser. The practical harmonic up-conversion efficiencies of current seeding techniques are limited by various three-dimensional effects on the electron beam. In this paper, a novel method is proposed to extend the wavelength coverage of a seeded FEL by combining the reverse taper undulator with the echo-enabled harmonic generation. The proposed technique can significantly enhance the bunching at ultra-high harmonics and preserve the electron beam qualities from degradation by deleterious effects. Theoretical analysis and numerical simulation are performed, and the results demonstrate that stable, intense, nearly fully coherent FEL pulses with photon energy up to 1 keV can be generated. The proposed technique may open up new opportunities to obtain laser-like pulses at sub-nanometer wavelength.

X-ray free electron laser oscillators (XFELOs) are future light sources that produce fully coherent hard x-ray pulses. Based on the low-gain principle, the XFELO traps x-ray pulses in an optical cavity composed of multiple Bragg-reflecting mirrors that have high reflectivity in a bandwidth of about ten meV. The crystal mirrors exposed to intense x-ray beams in the optical cavity are subject to thermal deformations that would shift and distort the Bragg reflectivity curve. Therefore, the stability of the XFELO operation depends on the ability of the mirrors to maintain the Bragg reflection under such thermal load. A new approach was used to analyze the thermal load of the mirrors. The approach utilizes a dedicated Bragg reflection physical process in geant4 to obtain precise absorption information of the XFELO pulses in the crystal. Following transient thermal behavior, including single pulse and multiple pulse inputs, was analyzed by finite element analysis software based on the energy absorption information extracted from the geant4 simulation. It is shown that, for a typical XFELO pulse depositing about ten microjoules energy the over a spot of tens of micrometers in radius, the thermal relaxation time across the thickness is on tens of nanoseconds scale. In this situation, a simplified heat-load model is then developed to integrate the heat load in the XFELO. With the simplified model, the potential impact of the thermal load on the XFELO operation is estimated. When a large amount of heat remains in the crystal, the pulse energy drops significantly and has large oscillations due to negative feedback of the temperature change on the pulse energy.

High-intensity, fully coherent x-ray pulse with a tunable polarization over a wide spectral range is of great importance to many experiments. In this paper, we propose a tapered crossed-polarized undulator configuration for an x-ray free electron laser oscillator (XFELO) to produce arbitrarily polarized x-ray pulses in the hard x-ray region. A numerical example utilizing the parameters of the Shanghai High-Repetition-Rate XFEL and Extreme Light Facility (SHINE) is presented to demonstrate the generation of polarization controllable, fully coherent hard x-ray pulses with 99.9% polarization degree and 20 kHz polarization switching rate. The analysis presents that this scheme holds the possibility to be used in an energy tunable XFELO built from multiple Bragg mirrors.

The parallel operation of multiple undulator lines with a wide spectral range is an important way to increase the usability of x-ray free electron laser (XFEL) facilities, especially for machines with high-repetition rate. In this paper, a delay system based on four double bend achromats is proposed to delay electron beams, thereby changing the arrival time of those delayed electron beams in the accelerating structure behind the system. Combined with kickers, the delay system can be used to generate bunch-to-bunch energy changed electron beams in a continuous wave XFEL facility. Start-to-end simulations based on the parameters of the Shanghai high-repetition-rate XFEL and extreme light facility are performed to demonstrate that the delay system can flexibly control electron beam energy from 1.48 to 8.74 GeV at the end of the linac.

The echo-enabled harmonic generation (EEHG) scheme holds promising prospects for efficiently generating intense coherent radiation at very high harmonics of a conventional ultraviolet seed laser. We report the lasing of the EEHG free-electron laser (FEL) at an extreme ultraviolet (EUV) wavelength with a seeded FEL facility, the Shanghai soft x-ray FEL. For the first time, we have benchmarked the basic theory of EEHG by measuring the bunching factor distributions over one octave down to the EUV region. Our results demonstrated the key advantages of the EEHG FEL, i.e., generation of very high harmonics with a small laser-induced energy spread and insensitivity to beam imperfections, and marks a great step towards fully coherent x rays with the EEHG scheme.

X-ray free-electron lasers (XFELs) are cutting-edge scientific instruments for a wide range of disciplines. Conventionally, the narrow bandwidth is pursued in an XFEL. However, in recent years, the large-bandwidth XFEL operation schemes are proposed for x-ray spectroscopy and x-ray crystallography, in which overcompression is a promising scheme to produce broad-bandwidth XFEL pulses through increasing the electron beam energy chirp. In this paper, combining with the beam yaw correction to overcome the transverse slice misalignment caused by the coherent synchrotron radiation, finding out the overcompression working point of the linac is treated as a many-objective (having four or more objectives) optimization problem, thus the nondominated sorting genetic algorithm III (NSGA-III) is applied to the beam dynamic optimization for the first time. Start-to-end simulations demonstrate a full bandwidth of 4.79% for Shanghai soft x-ray free-electron laser user facility. Furthermore, the NSGA-III is found to be very efficient by providing a set of reference points with preferences. This paves the way for applying this algorithm to online optimization of a real machine.

We propose a scheme that can generate attosecond x-ray pulses through an angular dispersion enhanced self-amplified spontaneous emission (ESASE) free electron laser (FEL). In this scheme, an angular dispersion section is implemented into a conventional ESASE set-up, together with a few cycle laser pulse to manipulate the electron beam effectively. During the procedure, the transverse-longitudinal phase space coupling is introduced into the electron beam in addition to the energy modulation and momentum compaction processes. As a result, the peak current of the electron beam will be strengthened significantly within a narrow width of the electron bunch, which can be used to generate ultrashort FEL pulses. Comparing to a conventional ESASE scheme, the proposed scheme can reduce the required modulation laser power by at least one order of magnitude. The signal-to-noise ratio of the final FEL radiation pulses can also be improved. In addition, we discuss the possibility of using this scheme to generate two-pulse two-color x-ray FEL with tunable central wavelengths and time delays for a conceivable x-ray pump/x-ray probe experiment.

In order to effectively improve the output quality of x-ray free electron laser (XFEL), we theoretically propose an XFEL scheme seeded by atomic inner-shell laser. Atomic inner-shell lasers based on neutral atoms and pumped by XFEL have been experimentally demonstrated [Rohringer et al., Nature (London) 481, 488 (2012)NATUAS0028-083610.1038/nature10721, Yoneda et al., Nature (London) 524, 446 (2015)NATUAS0028-083610.1038/nature14894], which produced sub-femtosecond X-ray pulses with increased temporal coherence. It shows that, by using the inner-shell laser as a seed to modulate the electron bunch, very stable and almost fully-coherent short-wavelength XFEL pulses can be generated. The proposed scheme holds promising prospects in x-ray wavelengths, and even shorter.

X-ray free-electron laser oscillator (XFELO) is expected to be a cutting-edge tool for fully coherent x-ray laser generation, and undulator taper technique is well-known for considerably increasing the efficiency of free-electron lasers (FELs). In order to combine the advantages of these two schemes, FEL amplifier seeded by XFELO is proposed by simply using a chirped electron beam. With the right choice of the beam parameters, the bunch tail is within the gain bandwidth of XFELO, and lase to saturation, which will be served as a seeding for further amplification. Meanwhile, the bunch head which is outside the gain bandwidth of XFELO, is preserved and used in the following FEL amplifier. It is found that the natural “double-horn” beam current, as well as residual energy chirp from chicane compressor, are quite suitable for the new scheme. Inheriting the advantages from XFELO seeding and undulator tapering, it is feasible to generate nearly terawatt level, fully coherent x-ray pulses with unprecedented shot-to-shot stability, which might open up new scientific opportunities in various research fields.

The low-gain free-electron laser (FEL) oscillators are cutting-edge tools to produce fully coherent radiation in the spectral region from terahertz to vacuum ultraviolet, and potentially in hard x ray. In this paper, it is proposed to utilize an FEL oscillator with multistage undulators to enable gain cascading in a single pass, making it possible to achieve shorter single pulse lengths, higher peak power, and even higher pulse energy than the normal FEL oscillator. Theoretical analysis and numerical simulations in the infrared and hard x-ray regions show that our proposal is effective.

A simplified one-dimensional theoretical model for free-electron laser oscillator (FELO) calculation which reserves the main physics is proposed. Instead of using traditional macroparticles sampling method, the theoretical model takes advantage of low gain theory to calculate the optical power single-pass gain in the undulator analytically, and some reasonable approximations are made to simplify the calculation of power growth in the cavity. The theoretical analysis of single-pass gain, power growth, time-dependent laser profile evolution and cavity desynchronism are accomplished more efficiently. We present the results of infrared wavelength FELO and X-ray FELO with the new model. The results are validated by simulation with GENESIS and OPC.

Deriving single or few cycle terahertz (THz) pulse by an intense femtosecond laser through cascaded optical rectification is a crucial technique in cutting-edge time-resolved spectroscopy to characterize micro-scale structures and ultrafast dynamics. Due to the broadband nature of the ultrafast driving laser, the chromatic effect limits the THz conversion efficiency in optical rectification crystals, especially for those implementing the pulse-front tilt scheme, e.g. lithium niobate (LN) crystal, has been prevalently used in the past decade. In this research we developed a brand new type of LN crystal utilizing Brewster coupling, and conducted systematically experimental and simulative investigation for the chromatic effect and multi-dimensionally entangled parameters in THz generation, predicting that an extreme conversion efficiency of ∼10% would be potentially achievable at the THz absorption coefficient of ∼0.5 cm ^−1 . Moreover, we first discovered that the chirp of the driving laser plays a decisive role in the pulse-front tilt scheme, and the THz generation efficiency could be enhanced tremendously by applying an appropriate chirp.

We propose a new scheme to generate high-brightness and temporal coherent soft x-ray radiation in a seeded free-electron laser. The proposed scheme is based on the coherent harmonic generation (CHG) and superradiant principles. A CHG scheme is first used to generate a coherent signal at ultrahigh harmonics of the seed. This coherent signal is then amplified by a series of chicane-undulator modules via the fresh bunch and superradiant processes in the following radiator. Using a representative of a realistic set of parameters, three-dimensional simulations have been carried out and the simulations results demonstrated that 10 GW-level ultrashort (∼20 fs) coherent radiation pulses in the water window can be achieved by using a 1.6 GeV electron beam based on the proposed technique.

The microbunching instability developed during the beam compression process in the linear accelerator (LINAC) of a free-electron laser (FEL) facility has always been a problem that degrades the lasing performance, and even no FEL is able to be produced if the beam quality is destroyed too much by the instability. A common way to suppress the microbunching instability is to introduce extra uncorrelated energy spread by the laser heater that heats the beam through the interaction between the electron and laser beam, as what has been successfully implemented in the Linac Coherent Light Source and Fermi@Elettra. In this paper, a simple and effective scheme is proposed to suppress the microbunching instability by adding two transverse gradient undulators (TGU) before and after the magnetic bunch compressor. The additional uncorrelated energy spread and the density mixing from the transverse spread brought up by the first TGU results in significant suppression of the instability. Meanwhile, the extra slice energy spread and the transverse emittance can also be effectively recovered by the second TGU. The magnitude of the suppression can be easily controlled by varying the strength of the magnetic fields of the TGUs. Theoretical analysis and numerical simulations demonstrate the capability of the proposed technique in the LINAC of an x-ray free-electron laser facility.

The beam energy spread at the entrance of an undulator system is of paramount importance for efficient density modulation in high-gain seeded free-electron lasers (FELs). In this paper, the dependences of high harmonic bunching efficiency in high-gain harmonic generation (HGHG), echo-enabled harmonic generation (EEHG) and phase-merging enhanced harmonic generation (PEHG) schemes on the electron beam energy spread distribution are studied. Theoretical investigations and multidimensional numerical simulations are applied to the cases of uniform and saddle beam energy distributions and compared to a traditional Gaussian distribution. It shows that the uniform and saddle electron energy distributions significantly enhance the bunching performance of HGHG FELs, while they almost have no influence on EEHG and PEHG schemes. A further start-to-end simulation example demonstrated that, with the saddle distribution of sliced beam energy spread controlled by a laser heater, the 30th harmonic can be directly generated by a single-stage HGHG scheme for a soft x-ray FEL facility.

The microbunching instability in the linear accelerator (linac) of a free-electron laser facility has always been a problem that degrades the electron beam quality. In this paper, a quite simple and inexpensive technique is proposed to smooth the electron beam current profile to suppress the instability. By directly adding a short undulator with a transverse gradient field right after the injector to couple the transverse spread into the longitudinal direction, additional density mixing in the electron beam is introduced to smooth the current profile, which results in the reduction of the gain of the microbunching instability. The magnitude of the density mixing can be easily controlled by varying the strength of the undulator magnetic field. Theoretical analysis and numerical simulations demonstrate the capability of the proposed technique in the accelerator of an x-ray free-electron laser.

Independently from conventional electron beam based procedures, the photon beam based diagnostic is an alternative way for electron trajectory alignment and commissioning of numerous undulator cells in high-gain short-wavelength free-electron lasers (FELs). In this paper, using the microbunched electron beam and the undulator fine-tuning technique, a novel method based on the spatial profile analysis of coherent harmonic radiation from individual or two consecutive undulator segments, the so-called coherent photon beam based diagnostic, is proposed for undulator alignment and commissioning in seeded FELs. The preliminary experimental results at the Shanghai deep ultraviolet FEL test facility are presented. It shows that the proposed method is effective and convenient in the electron beam trajectory control, the undulator magnetic gap verification, and the phase match between two undulator segments.

In this paper, a simple technique is proposed to induce strong density modulation into the electron beam with small energy modulation. By using the combination of a transversely dispersed electron beam and a wave-front tilted seed laser, three-dimensional manipulation of the electron beam phase space can be utilized to significantly enhance the microbunching of seeded free-electron laser schemes, which will improve the performance and extend the short-wavelength range of a single-stage seeded free-electron laser. Theoretical analysis and numerical simulations demonstrate the capability of the proposed technique in a soft x-ray free-electron laser.

Polarization switching of light sources is required over a wide spectral range to investigate the symmetry of matter. In this paper, we report the first experimental demonstration of the crossed-planar undulators technique at a seeded free-electron laser, which holds great promise for the full control and fast switching of the polarization of short-wavelength radiation. In the experiment, the polarization state of the coherent radiation at the second harmonic of the seed laser is switched successfully. The experimental results confirm the theory and pave the way for applying the crossed-planar undulators technique for seeded x-ray free-electron lasers.

Together with one of its variants, the recently proposed phase-merging enhanced harmonic generation (PEHG) free-electron laser (FEL) is systematically studied in this paper. Different from a standard high-gain harmonic generation scheme, a transverse gradient undulator is employed to introduce a phase-merging effect into the transversely dispersed electron beam in PEHG. The analytical theory of the phase-merging effect and the physical mechanism behind the phenomenon are presented. Using a representative set of beam parameters, intensive start-to-end simulations for soft x-ray FEL generation are given to illustrate the performance of PEHG. Moreover, some practical issues that may affect the performance of PEHG are also discussed.

Free-electron lasers (FELs) seeded with external lasers hold great promise for generating high power radiation with nearly transform-limited bandwidth in the soft x-ray region. However, it has been pointed out that the initial seed laser phase error will be amplified by the frequency up-conversion process, which may degrade the quality of the output radiation produced by a harmonic generation scheme. In this paper, theoretical and simulation studies on frequency chirp amplification in seeded FEL schemes with slippage effect taken into account are presented. It is found that the seed laser imperfection experienced by the electron beam can be significantly smoothed by the slippage effect in the modulator when the slippage length is comparable to the seed laser pulse length. This smoothing effect allows one to preserve the excellent temporal coherence of seeded FELs in the presence of large frequency chirp in the seed laser. Our studies show that the tolerance on frequency chirp in the seed laser for generating nearly transform-limited soft x-ray pulses in seeded FELs is much looser than previously thought and fully coherent radiation at nanometer wavelength may be reached with current technologies.

We propose a simple method to significantly enhance the temporal coherence and spectral brightness of a self-amplified spontaneous emission (SASE) free-electron laser (FEL). In this purified SASE (pSASE) FEL, a few undulator sections (called slippage-boosted sections) resonant at a subharmonic of the FEL radiation are used in the middle stage of the exponential growth regime to amplify the radiation while simultaneously reducing the FEL bandwidth. In this slippage-boosted section, the average longitudinal velocity of electrons is reduced, which effectively increases the FEL slippage length that allows the radiation fields initially far apart to create a phase relation, leading to n times increase in FEL cooperation length, where n is the ratio of the resonant wavelength of the slippage-boosted section to that of the original FEL radiation. The purified radiation, as a seed with improved temporal coherence, is further amplified to saturation in the undulator sections tuned to the FEL wavelength. Using the linac coherent light source II (LCLS-II) parameters as an example, we show that with the proposed configuration the temporal coherence and spectral brightness of a SASE FEL can be significantly enhanced. This scheme may be applied to many SASE FEL light sources to enhance the FEL performance.

The local energy spread of electron beam is a very important parameter for high-gain free-electron lasers (FELs), especially the seeded FELs. Highly accurate measurement of the extremely small local energy spread is rather challenging. In this paper, a simple method to accurately measure the average local energy spread based on the coherent harmonic generation is proposed. A one-dimensional analytical estimation is given to show the principle of this method, and three-dimensional simulation codes have been used to verify the theory. This method has been demonstrated on the Shanghai deep ultraviolet FEL, and the results show that the average local energy spread is about only 1.2 keV at the exit of the 136 MeV linac, which agrees well with the numerical simulations.