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.

Since 2016, the two free-electron laser (FEL) lines FLASH1 and FLASH2 have been run simultaneously for users at DESY in Hamburg. With the installation of variable gap undulators in the new FLASH2 FEL line, many new possibilities have opened up in terms of photon parameters for experiments. What has been tested so far is post-saturation tapering, reverse tapering, harmonic lasing, harmonic lasing self-seeding and two-color lasing. At the moment, we are working on concepts to enhance the capabilities of the FLASH facility even further. A major part of the upgrade plans, known as FLASH2020, will involve the exchange of the fixed gap undulators in FLASH1 and the implementation of a new flexible undulator scheme aimed at providing coherent radiation for multi-color experiments over a broad wavelength range. The recent achievements in FLASH2 and the current status of plans for the further development of the facility are presented.

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.

X-ray pump/X-ray probe applications are made possible at X-ray Free Electron Laser (XFEL) facilities by generating two X-ray pulses with different wavelengths and controllable temporal delay. In order to enable this capability at the European XFEL, an upgrade project to equip the soft X-ray SASE3 beamline with a magnetic chicane is underway. In the present paper we describe the status of the project, its scientific focus and expected performance, including start-to-end simulations of the photon beam transport up to the sample, as well as recent experimental results demonstrating two-color lasing at photon energies of 805 eV + 835 eV and 910 eV + 950 eV. Additionally, we discuss methods to analyze the spectral properties and the intensity of the generated radiation to provide on-line diagnostics for future user experiments.

Harmonic lasing is a possible mode of operation of X-ray FEL user facilities that allows us to provide brilliant beams of higher energy photons for user experiments. Another useful application of harmonic lasing is the so-called harmonic lasing self-seeded free electron laser (HLSS FEL) that allows the improvement of spectral brightness of these facilities. In the past, harmonic lasing has been demonstrated in the FEL oscillators in infrared and visible wavelength ranges, but not in high-gain FELs and not at short wavelengths. In this paper we report on the first evidence of the harmonic lasing and the first operation of the HLSS FEL at the soft X-ray FEL user facility FLASH in the wavelength range between 4.5 nm and 15 nm. Spectral brightness was improved in comparison with self-amplified spontaneous emission (SASE) FEL by a factor of six in the exponential gain regime. A better performance of HLSS FEL with respect to SASE FEL in the post-saturation regime with a tapered undulator was observed as well. The first demonstration of harmonic lasing in a high-gain FEL and at short wavelengths paves the way for a variety of applications of this new operation mode in X-ray FELs.

We report on a resonant magnetic scattering experiment using soft x-ray pulses generated from a free-electron laser (FEL). The free-electron laser was operated at a fundamental wavelength of 7.97 nm and radiation at the fifth harmonic originating from self-amplified stimulated emission at 1.59 nm with an average energy of 4 nJ per pulse was detected. We demonstrate the feasibility of resonant magnetic scattering at FEL sources by using a Co/Pd multilayer as prototype sample that was illuminated with 20-fs-long soft x-ray pulses tuned to the $\text{Co}{L}_3$ absorption edge at 778.1 eV (1.59 nm).