Spontaneous Undulator Radiation Research Articles

Off-axis spectrum and small signal gain of dual harmonic planar undulator

The spectral properties of the spontaneous undulator radiation generated from the dual harmonic planar undulator configuration are analyzed. The effect of changing the observation point away from the axis on radiation is demonstrated. The expressions for off-axis undulator radiation and off-axis small signal gain are derived using the generalized Bessel function. The emission of radiation at odd and even harmonics and the effect of the additional harmonic field on the intensity and small signal gain are analyzed. The present work can also be used for the diagnostic study of errors in the undulator field and the detector setting for FEL measurements.

On the physics of generation of even and odd harmonics in the undulators of free electron lasers

We theoretically explore the physics of even and odd harmonics generation and radiation in undulators of single pass free electron lasers (FELs). Planar undulators are studied as a most common design. The results are obtained analytically and some of them also numerically. In the analytical form the contributions of various factors to the harmonic generation are distinguished and their effect is analyzed. The results are verified with numerical simulations and compared with reported experimental data; the data for best documented FELs in terms of harmonic generation, LEUTL and LCLS, is analyzed. The reasons for even harmonic generation are identified; we show that they differ for the spontaneous undulator radiation and for the stimulated FEL radiation. Comparative analysis is performed with various theoretical models for the FEL harmonic powers. The advantages and possibilities of amplification and radiation the second FEL harmonic in the LCLS-II FEL with variable deflection parameter is demonstrated for the harmonic lasing self-seed (HLSS) FEL design. The possibility to suppress the radiated second harmonic in a FEL by a guiding field of a weak second harmonic of the main undulator field with negative phase is shown. This can be used to reduce the reflected signal of the second harmonic generation (SHG) when the nonlinear harmonic response of the mater is investigated.

Analysis of the spectral properties of free electron lasers in X-RAY and other bands

Analytical formalism for the description of free electron laser (FEL) spectrum is proposed with account for the electron beam size, divergences, beam energy spread, the off-axis deflection and the periodic harmonic and non-periodic constant magnetic field components in undulators. The exact analytical expressions for the spontaneous undulator radiation (UR) are obtained in terms of generalized Bessel and Airy functions, which describe the spectrum line shape and intensities. The obtained analytical formulae distinguish the effects of each installation and beam parameter on the FEL harmonic radiation. The enhanced phenomenological model is employed for the FEL modeling; it describes the harmonic powers evolution along the undulators and gradual saturation around the saturation length with account for the saturated powers oscillations. With this model, we study the generation of FEL harmonics, including even, in several instances of FEL experiments at LCLS, LEUTL and PAL-XFEL. We analytically demonstrate the even harmonics reasons in the LCLS and LEUTL FEL experiments. The spectrum line split due to the beam size is demonstrated analytically and compared with experimentally measured spectral characteristics. The PAL-XFEL experiment is analyzed and compared with the LCLS experiment; the possibility of high harmonic radiation in it is explored. The modeling results fully agree with the measured values in the studied FELs. The analytical formalism shows physical background for each harmonic in every FEL. It allows the analysis of the radiation and beam alignment in projected, built and working FELs and it can help minimizing losses and correcting magnetic fields as well as projecting experiments with FELs.

Spontaneous and Stimulated Undulator Radiation in Symmetric and Asymmetric Multi-Periodic Magnetic Fields

In this work, the radiation from electrons in multi-periodic undulator fields with symmetric and asymmetric harmonics was analyzed using generalized Bessel functions formalism. The asymmetric, symmetric, and anti-symmetric periodic magnetic fields with harmonics were studied in order to get the enhanced radiation of the high harmonics of undulator radiation (UR). The effect on the spontaneous and stimulated UR was explored. The exact integral forms for the Bessel coefficients were obtained for undulators with general symmetric and asymmetric field harmonics. Spectral properties of the radiation from several configurations of the undulator fields with harmonics were compared with each other. The resulting spontaneous UR spectrum and harmonic intensities were obtained analytically in the form of integrals and compared with the respective results that were obtained numerically with SPECTRA program. The dimensionless scaling parameter of a free electron laser (FEL)—the Pierce parameter (ρ)—was computed and compared for the different considered undulators. We studied the differences in the behavior of the high-gain single pass FEL harmonics and the spontaneous UR harmonics in the same undulators. The undulators with variable deflection parameter (k) were considered. The effect of the k parameter (deflection parameter for a common planar undulator) on the spontaneous UR and on the high-gain FEL radiation was explored. In this context, an experiment with variable strength undulators at FLASH 2 FEL was analyzed; the shorter saturated length in high harmonic self-seeding (HHSS) regime vs. self-amplified spontaneous emission (SASE) is explained.

Control of undulator radiation using a Laser Plasma Acceleration Source

Spontaneous undulator radiation emission, after the COXINEL line using a Laser Plasma acceleration (LPA) source, has been observed. The line enables to manipulate the electron beam phase space such as emittance, dispersion and energy spread along a 10 m long transport. The large divergence is handled at a very early stage to mitigate the chromatic emittance, using high gradient permanent magnet based quadrupoles mounted on translation tables. The operating energy is between 161-180 MeV focused in a 2-m long cryo-ready undulator with a period of 18 mm emitting light in the Ultra-Violet range. The spectral flux is characterized using a spectrometer. The wavelength is tuned by either changing the electron beam energy or by adjusting the undulator gap. The radiation pattern signature is illustrated alongside its dependence on the energy spread that is modified by introducing a slit in a magnetic chicane where a small relative bandwidth of 5% has been achieved.

Water-Window X-Ray Pulses from a Laser-Plasma Driven Undulator

Femtosecond (fs) x-ray pulses are a key tool to study the structure and dynamics of matter on its natural length and time scale. To complement radio-frequency accelerator-based large-scale facilities, novel laser-based mechanisms hold promise for compact laboratory-scale x-ray sources. Laser-plasma driven undulator radiation in particular offers high peak-brightness, optically synchronized few-fs pulses reaching into the few-nanometer (nm) regime. To date, however, few experiments have successfully demonstrated plasma-driven undulator radiation. Those that have, typically operated at single and comparably long wavelengths. Here we demonstrate plasma-driven undulator radiation with octave-spanning tuneability at discrete wavelengths reaching from 13 nm to 4 nm. Studying spontaneous undulator radiation is an important step towards a plasma-driven free-electron laser. Our specific setup creates a photon pulse, which closely resembles the plasma electron bunch length and charge profile and thus might enable novel methods to characterize the longitudinal electron phase space.

Observation of a THz-sub-THz spontaneous coherent undulator radiation driven by a low energy electron beam from a thermionic RF electron gun

We report observations of an intense, multi-band, sub-THz and THz radiation extracted from a ∼2-3 MeV electron beam with a flat transverse profile propagating in an oversized rectangular waveguide placed into a 3.25 mm gap of a planar undulator having 1.3 cm period and ∼20 cm length. Radiation outcoupling is accomplished using a horn antenna and a miniature permanent in-vacuum magnet separating the mm-sub-mm-waves and electron beam. A table-top experiment utilizes a radio frequency thermionic electron gun delivering a thousand momentum-chirped microbunches per macropulse and an alpha-magnet producing microbunches of a sub-mm length. Total radiated energy of a sub-millijoule per a microsecond radio frequency macropulse is demonstrated with flux more than ten micro-Joules per centimeter squared. With 1 THz filter the energy measured is about 1 microjoule and flux of a few micro-Joules per centimeter squared.

Electron Beam Brightness and Undulator Radiation Brilliance for a Laser Plasma Acceleration Based Free Electron Laser

We report here on spontaneous undulator radiation and free electron laser calculations after a 10-m long transport line (COXINEL) using a Laser Plasma acceleration (LPA) source. The line enables the manipulation of the properties of the produced electron beams (energy spread, divergence, dispersion) in view of light source applications. The electron beam brightness and undulator radiation brilliance are addressed by an analytical approach enabling us to point out the influence of chromatic effects in the COXINEL case.

Interferometry for full temporal reconstruction of laser-plasma accelerator-based seeded free electron lasers

The spectacular development of Laser-Plasma Accelerators (LPA) appears very promising for a free electron laser application. The handling of the inherent properties of those LPA beams already allowed controlled production of LPA–based spontaneous undulator radiation. Stepping further, we here unveil that the forthcoming LPA–based seeded FELs will present distinctive spatio-spectral distributions. Relying on numerical simulations and simple analytical models, we show how those interferometric patterns can be exploited to retrieve, in single-shot, the spectro-temporal content and source point properties of the FEL pulses.

An X-ray gas monitor for free-electron lasers.

A novel X-ray gas monitor (XGM) has been developed which allows the measurement of absolute photon pulse energy and photon beam position at all existing and upcoming free-electron lasers (FELs) over a broad spectral range covering vacuum ultraviolet (VUV), extreme ultraviolet (EUV) and soft and hard X-rays. The XGM covers a wide dynamic range from spontaneous undulator radiation to FEL radiation and provides a temporal resolution of better than 200 ns. The XGM consists of two X-ray gas-monitor detectors (XGMDs) and two huge-aperture open electron multipliers (HAMPs). The HAMP enhances the detection efficiency of the XGM for low-intensity radiation down to 105 photons per pulse and for FEL radiation in the hard X-ray spectral range, while the XGMD operates in higher-intensity regimes. The relative standard uncertainty for measurements of the absolute photon pulse energy is well below 10%, and down to 1% for measurements of relative pulse-to-pulse intensity on pulses with more than 1010 photons per pulse. The accuracy of beam-position monitoring in the vertical and horizontal directions is of the order of 10 µm.

Lux – A laser–plasma driven undulator beamline

The Lux beamline is a novel type of laser–plasma accelerator. Building on the joint expertise of the University of Hamburg and Desy the beamline was carefully designed to combine state-of-the-art expertise in laser–plasma acceleration with the latest advances in accelerator technology and beam diagnostics. Lux introduces a paradigm change moving from single-shot demonstration experiments towards available, stable and controllable accelerator operation. Here, we discuss the general design concepts of Lux and present first critical milestones that have recently been achieved, including the generation of electron beams at the repetition rate of up to 5 Hz with energies above 600 MeV and the generation of spontaneous undulator radiation at a wavelength well below 9 nm.

Helical undulator based on partial redistribution of uniform magnetic field

A new type of helical undulator based on redistribution of magnetic field of a solenoid by ferromagnetic helix has been proposed and studied both in theory and experiment. Such undulators are very simple and efficient for promising sources of coherent spontaneous THz undulator radiation from dense electron bunches formed in laser-driven photo-injectors.

High-harmonic x-ray undulator radiation for nanoscale-wavelength free-electron lasers

We explore the undulator radiation (UR) from relativistic electrons in two-frequency undulators intended for use in x-ray free-electron lasers (FELs). We use an exact analytical account for the major sources of spectral line broadening of the spontaneous UR to describe the UR spectrum, intensity and emission line shape. We also show possible partial compensation of the off-axis divergence by ad hoc imposed weak transverse constant magnetic components. The harmonic radiation of the two-frequency undulator is studied. High-harmonics amplification in the two-frequency undulator is underlined for possible use in x-ray FELs and the generation of powerful x-ray radiation is demonstrated. The evolution of high harmonic power is studied with the help of the developed phenomenological self-amplified spontaneous emission FEL model. The performance of a high-gain harmonic generation FEL with a two-frequency undulator–prebuncher is explored. Harmonic multiplication cascades are introduced in FELs to obtain nanometer x-ray FEL radiation in reduced size FELs at ~30 m with seed from commercially available excimer laser and ~0.5 GeV electrons.

Coherent spontaneous THz undulator radiation from dense electron bunches formed in laser-driven photo-injectors

Coherent spontaneous THz undulator radiation from dense electron bunches formed in laser-driven photo-injectors

Energy enhancement and spectrum narrowing in terahertz electron sources due to negative mass instability

Simulations of coherent spontaneous undulator radiation in a waveguide demonstrate that the use of negative mass instability (NMI) for retaining longitudinal sizes of dense electron bunches, which are formed in laser-driven photoinjectors, allows one to increase power capabilities of a terahertz radiation source by many times. The NMI is realized in an undulator with combined helical and over-resonance uniform longitudinal magnetic fields due to nonisochronous longitudinal oscillations of electrons, whose frequencies increase/decrease with increasing/decreasing particle energy. In such conditions, an effective longitudinal size of the bunches can be preserved at long distance even at an extremely high electron density. Correspondingly, an energy extraction efficiency of more than 20% is revealed at a narrow frequency radiation spectrum, suggesting realization of a compact and powerful THz source.

Feasibility of a ring FEL at low emittance storage rings

A scheme for generating coherent radiation at latest generation low emittance storage rings such as PETRA III at DESY (Balewski et al., 2004 [1]) is proposed. The scheme is based on focusing and subsequent defocusing of the electron beam in the longitudinal phase space at the undulator location. The expected performance characteristics are estimated for radiation in the wavelength range of 500–1500eV. It is shown that the average brightness is increased by several orders of magnitude compared to spontaneous undulator radiation, which can open new perspectives for photon-hungry soft X-ray spectroscopy techniques.

Undulator Radiation of Dense Plane Electron Bunches

A simple and general self-consistent theory of coherent spontaneous undulator radiation from electron bunches has been developed. The approach is based on the model of a moving and radiating plane layer filled with oscillating relativistic electrons (gas of radiating and interacting 1-D particles). Using simple expressions for the field of a charged plane makes it easy to consider both Coulomb and radiation interaction of the electrons in bunches with arbitrary particle trajectories, energy chirp, and velocity and density distributions. The application of the developed theory for estimations of a compact radiation source in the terahertz frequency range has demonstrated the possibility of efficiency enhancement and narrowing of the radiation spectrum by means of using bunches with decreasing electron density.

Absolute pulse energy measurements of soft x-rays at the Linac Coherent Light Source.

This paper reports novel measurements of x-ray optical radiation on an absolute scale from the intense and ultra-short radiation generated in the soft x-ray regime of a free electron laser. We give a brief description of the detection principle for radiation measurements which was specifically adapted for this photon energy range. We present data characterizing the soft x-ray instrument at the Linac Coherent Light Source (LCLS) with respect to the radiant power output and transmission by using an absolute detector temporarily placed at the downstream end of the instrument. This provides an estimation of the reflectivity of all x-ray optical elements in the beamline and provides the absolute photon number per bandwidth per pulse. This parameter is important for many experiments that need to understand the trade-offs between high energy resolution and high flux, such as experiments focused on studying materials via resonant processes. Furthermore, the results are compared with the LCLS diagnostic gas detectors to test the limits of linearity, and observations are reported on radiation contamination from spontaneous undulator radiation and higher harmonic content.

Competition between coherent emission and broadband spontaneous emission in the quantum free electron laser

We extend previous analyses of spontaneous emission in a quantum free electron laser (QFEL) and competition between spontaneous and coherent QFEL emission to include a broad distribution of photon frequencies and momenta appropriate for spontaneous undulator radiation. We show that although the predictions of monochromatic and broadband models predict different electron momentum distributions for the quantum regime due to spontaneous emission alone after many photon emissions, the inclusion of broadband spontaneous emission has a negligible effect on the competition between spontaneous and coherent emission in the QFEL. Numerical results from both models are well described by the same condition for the threshold/critical value of spontaneous emission rate.

Momentum spread in a relativistic electron beam in an undulator

The motion of the relativistic electron beam in the spatially periodic magnetic field of an undulator has been considered taking into account the effect of the incoherent field of the spontaneous undulator radiation on the motion of the electrons. An expression for the rms momentum of the electrons has been obtained. It has been shown that the momentum spread in the ultrarelativistic electron beam increases in the spontaneous incoherent emission mode. Conditions for the self-amplification of the spontaneous undulator radiation in ultrashort-wavelength free-electron lasers have been discussed.