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The free electron laser (FEL) amplifier is implemented in x-ray FEL facilities to generate short wavelength radiation. The problem of an efficiency increase of an FEL amplifier is now of great practical importance. The technique of undulator tapering in the postsaturation regime is used at the existing x-ray FELs LCLS, SACLA and FERMI, and is planned for use at FLASH, European XFEL, Swiss FEL, and PAL XFEL. There are also discussions on the future of high peak and average power FELs for scientific and industrial applications. In this paper we perform a detailed analysis of the tapering strategies for high power seeded FEL amplifiers. Analysis of the radiation properties from the modulated electron beam and application of similarity techniques allows us to derive the universal law of the undulator tapering.

One of the most challenging tasks for extreme ultraviolet, soft and hard x-ray free-electron laser photon diagnostics is the precise determination of the photon pulse duration, which is typically in the sub 100 fs range. Nine different methods, able to determine such ultrashort photon pulse durations, were compared experimentally at FLASH, the self-amplified spontaneous emission free-electron laser at DESY in Hamburg, in order to identify advantages and disadvantages of different methods. Radiation pulses at a wavelength of 13.5 and 24.0 nm together with the corresponding electron bunch duration were measured by indirect methods like analyzing spectral correlations, statistical fluctuations, and energy modulations of the electron bunch and also by direct methods like autocorrelation techniques, terahertz streaking, or reflectivity changes of solid state samples. In this paper, we present a comprehensive overview of the various techniques and a comparison of the individual experimental results. The information gained is of utmost importance for the future development of reliable pulse duration monitors indispensable for successful experiments with ultrashort extreme ultraviolet pulses.

Baseline design of a typical x-ray free electron laser (FEL) undulator assumes a planar configuration which results in a linear polarization of the FEL radiation. However, many experiments at x-ray FEL user facilities would profit from using a circularly polarized radiation. As a cheap upgrade, one can consider an installation of a short helical (or cross-planar) afterburner, but then one should have an efficient method to suppress the powerful linearly polarized background from the main undulator. In this paper we propose a new method for such a suppression: an application of the reverse taper in the main undulator. We discover that in a certain range of the taper strength, the density modulation (bunching) at saturation is practically the same as in the case of a nontapered undulator while the power of linearly polarized radiation is suppressed by orders of magnitude. Then strongly modulated electron beam radiates at full power in the afterburner. Considering the SASE3 undulator of the European XFEL as a practical example, we demonstrate that soft x-ray radiation pulses with peak power in excess of 100 GW and an ultimately high degree of circular polarization can be produced. The proposed method is rather universal, i.e., it can be used at SASE FELs and seeded (self-seeded) FELs, with any wavelength of interest, in a wide range of electron beam parameters, and with any repetition rate. It can be used at different x-ray FEL facilities, in particular at Linac Coherent Light Source after installation of the helical afterburner in the near future.

Harmonic lasing in a free electron laser with a planar undulator (under the condition that the fundamental frequency is suppressed) might be a cheap and efficient way of extension of wavelength ranges of existing and planned x-ray free electron laser (FEL) facilities. Contrary to nonlinear harmonic generation, harmonic lasing can provide much more intense, stable, and narrow-band FEL beam which is easier to handle due to the suppressed fundamental frequency. In this paper we perform a parametrization of the solution of the eigenvalue equation for lasing at odd harmonics, and present an explicit expression for FEL gain length, taking into account all essential effects. We propose and discuss methods for suppression of the fundamental harmonic. We also suggest a combined use of harmonic lasing and lasing at the retuned fundamental wavelength in order to reduce bandwidth and to increase brilliance of x-ray beam at saturation. Considering 3rd harmonic lasing as a practical example, we come to the conclusion that it is much more robust than usually thought, and can be widely used in the existing or planned x-ray FEL (XFEL) facilities. In particular, Linac Coherent Light Source (LCLS) after a minor modification can lase to saturation at the 3rd harmonic up to the photon energy of 25–30 keV providing multigigawatt power level and narrow bandwidth. As for the European XFEL, harmonic lasing would allow one to extend operating range (ultimately up to 100 keV), to reduce FEL bandwidth and to increase brilliance, to enable two-color operation for pump-probe experiments, and to provide more flexible operation at different electron energies. Similar improvements can be realized in other x-ray FEL facilities with gap-tunable undulators like FLASH II, SACLA, LCLS II, etc. Harmonic lasing can be an attractive option for compact x-ray FELs (driven by electron beams with a relatively low energy), allowing the use of the standard undulator technology instead of small-gap in-vacuum devices. Finally, in this paper we discover that in a part of the parameter space, corresponding to the operating range of soft x-ray beam lines of x-ray FEL facilities (like SASE3 beam line of the European XFEL), harmonics can grow faster than the fundamental wavelength. This feature can be used in some experiments, but might also be an unwanted phenomenon, and we discuss possible measures to diminish it.

The successful operation of x-ray free-electron lasers (FELs), like the Linac Coherent Light Source or the Free-Electron Laser in Hamburg (FLASH), makes unprecedented research on matter at atomic length and ultrafast time scales possible. However, in order to take advantage of these unique light sources and to meet the strict requirements of many experiments in photon science, FEL photon pulse durations need to be known and tunable. This can be achieved by controlling the FEL driving electron beams, and high-resolution longitudinal electron beam diagnostics can be utilized to provide constraints on the expected FEL photon pulse durations. In this paper, we present comparative measurements of soft x-ray pulse durations and electron bunch lengths at FLASH. The soft x-ray pulse durations were measured by FEL radiation pulse energy statistics and compared to electron bunch lengths determined by frequency-domain spectroscopy of coherent transition radiation in the terahertz range and time-domain longitudinal phase space measurements. The experimental results, theoretical considerations, and simulations show that high-resolution longitudinal electron beam diagnostics provide reasonable constraints on the expected FEL photon pulse durations. In addition, we demonstrated the generation of soft x-ray pulses with durations below 50 fs (FWHM) after the implementation of the new uniform electron bunch compression scheme used at FLASH.

A longitudinal space charge amplifier (LSCA), operating in soft x-ray regime, was recently proposed. Such an amplifier consists of a few amplification cascades (focusing channel and chicane) and a short radiator undulator in the end. The broadband nature of LSCA supports generation of few-cycle pulses as well as wavelength compression. In this paper we consider an application of these properties of LSCA for generation of attosecond x-ray pulses. It is shown that a compact and cheap addition to the soft x-ray free-electron laser facility FLASH would allow one to generate 60 attosecond (FWHM) long x-ray pulses with the peak power at the 100 MW level and a contrast above 98%.

Longitudinal space charge (LSC) driven microbunching instability in electron beam formation systems of x-ray free-electron lasers (FELs) is a recently discovered effect hampering beam instrumentation and FEL operation. The instability was observed in different facilities in infrared and visible wavelength ranges. In this paper we propose to use such an instability for generation of vacuum ultraviolet (VUV) and x-ray radiation. A typical longitudinal space charge amplifier (LSCA) consists of few amplification cascades (drift space plus chicane) with a short undulator behind the last cascade. If the amplifier starts up from the shot noise, the amplified density modulation has a wide band, on the order of unity. The bandwidth of the radiation within the central cone is given by an inverse number of undulator periods. A wavelength compression could be an attractive option for LSCA since the process is broadband, and a high compression stability is not required. LSCA can be used as a cheap addition to the existing or planned short-wavelength FELs. In particular, it can produce the second color for a pump-probe experiment. It is also possible to generate attosecond pulses in the VUV and x-ray regimes. Some user experiments can profit from a relatively large bandwidth of the radiation, and this is easy to obtain in the LSCA scheme. Finally, since the amplification mechanism is broadband and robust, LSCA can be an interesting alternative to the self-amplified spontaneous emission free-electron laser (SASE FEL) in the case of using laser-plasma accelerators as drivers of light sources.

We propose a new scheme for two-color operation of an x-ray self-amplified spontaneous emission free electron laser (SASE FEL). The scheme is based on an intrinsic feature of such a device: chaotic modulations of electron beam energy and energy spread on the scale of FEL coherence length are converted into large density modulations on the same scale with the help of a dispersion section, installed behind the x-ray undulator. Powerful radiation is then generated with the help of a dedicated radiator (like an undulator that selects a narrow spectral line), or one can simply use, for instance, broadband edge radiation. A typical radiation wavelength can be as short as a FEL coherence length, and can be redshifted by increasing the dispersion section strength. In practice it means the wavelength ranges from vacuum ultraviolet to infrared. The long-wavelength radiation pulse is naturally synchronized with the x-ray pulse and can be either directly used in pump-probe experiments or cross correlated with a high-power pulse from a conventional laser system. In this way experimenters overcome jitter problems and can perform pump-probe experiments with femtosecond resolution. Additional possibilities like on-line monitoring of x-ray pulse duration (making “optical replica” of an x-ray pulse) are also discussed in the paper. The proposed scheme is very simple, cheap, and robust, and therefore can be easily realized in facilities like FLASH, European XFEL, LCLS, and SCSS.

Influence of a linear energy chirp in the electron beam on a self-amplified spontaneous emission (SASE) Free Electron Laser (FEL) operation is studied analytically and numerically using a 1D model. Analytical results are based on the theoretical background developed by Krinsky and Huang [Phys. Rev. ST Accel. Beams 6, 050702 (2003)PRABFM1098-4402]. Explicit expressions for Green’s functions and for output power of a SASE FEL are obtained for the high-gain linear regime in the limits of small and large energy chirp parameters. Saturation length and power versus energy chirp parameter are calculated numerically. It is shown that the effect of linear energy chirp on FEL gain is equivalent to the linear undulator tapering (or linear energy variation along the undulator). A consequence of this fact is a possibility to perfectly compensate FEL gain degradation, caused by the energy chirp, by means of the undulator tapering independently of the value of the energy chirp parameter. An application of this effect for generation of attosecond pulses from a hard x-ray FEL is proposed. Strong energy modulation within a short slice of an electron bunch is produced by a few-cycle optical laser pulse in a short undulator, placed in front of the main undulator. Gain degradation within this slice is compensated by an appropriate undulator taper while the rest of the bunch suffers from this taper and does not lase. Three-dimensional simulations predict that short (200 attoseconds) high-power (up to 100 GW) pulses can be produced in Angstrom wavelength range with a high degree of contrast. A possibility to reduce pulse duration to sub-100 attosecond scale is discussed.

Recent theoretical and experimental studies have shown that the self-amplified spontaneous emission free-electron laser (SASE FEL) with a planar undulator holds a potential for generation of relatively strong coherent radiation at the third harmonic of the fundamental frequency. Here we present a detailed study of the nonlinear harmonic generation in the SASE FEL obtained with a time-dependent FEL simulation code. Using similarity techniques we present universal dependencies for temporal, spectral, and statistical properties of the odd harmonics of the radiation from SASE FEL. In particular, we derived universal formulas for radiation power of the odd harmonics at saturation. It was also found that coherence time at saturation falls inversely proportional to the harmonic number, and relative spectrum bandwidth remains constant with the harmonic number.