Planar Undulator Research Articles

Optimization of SASE operation for an X-ray free-electron laser Using multiple objective evolutionary algorithms

Performance of Self Amplifed Spontaneous Emission (SASE) operation for an X-ray Free-Electron Laser (FEL), is optimized by Multiple Objective Evolutionary Algorithms (MOEA). Different types of hybrid planar undulators are considered to achieve 0.5 Å ≤ λ FEL ≤ 1.5 Å wavelength range. This demand is regarded as a continuous optimization problem, and hence, an evolutionary algorithm is designed to find optimal FEL performance parameters. An encoding scheme comprising of undulator period (λ u ) and undulator gap (g) is adopted here to find optimal values for saturation power (P sat ) and λ FEL subject to several physical constraints on λ u and g such as the ratio of g/λ u and L sat . It is shown that MOEA gives optimal solutions for estimation of L sat with plausible P sat values.

Generation of Coherent X-ray Harmonic Radiation in a Single-Pass Free-Electron Laser with Phase Shift of Electrons Relative to Photons

Evolution of bunching and harmonic power is theoretically studied for a single-pass free-electron laser (FEL) in which electrons are periodically phase-shifted relative to photons in intervals between undulators with harmonics of magnetic field. Analytical calculations are used to reveal the configuration of magnetic field of an asymmetric elliptical and planar undulators that make it possible to suppress the fundamental and amplify several higher harmonics. The evolution of power and bunching is analyzed using a phenomenological model of FEL that describes violation of bunching between the undulator stages and a relatively high sensitivity of electron–photon interaction at wavelengths of higher harmonics to energy spread, size, deflection of the beam from the axis, etc. Expressions for the Bessel coefficients of the planar and elliptical undulators with field harmonics are analytically studied. Such undulators can be used in phase-shifted FELs for an increase in the power of higher (X-ray) harmonics by a factor of up to 100 in comparison with conventional FELs.

Analytical account for the off-axis effects and undulator field harmonics in FELs

We give analytical description of the spontaneous and stimulated free electron laser (FEL) harmonic generation in multiperiodic fields, accounting for the off-axis effects and field harmonics in undulators. Exact analytical expressions for the Bessel coefficients involve generalized forms of Bessel- and Airy-type functions and describe also the effect of the non-periodic magnetic components in various elliptic and planar undulators with field harmonics. They allow clear identification of proper contributions in the UR harmonic intensities and polarizations. Advanced phenomenological model of the FELs harmonic powers provides analytical description of relevant effects in FEL harmonic radiation, verified with FEL experiments. The analysis of the off-axis effects for the odd and even harmonic generation is performed for LEUTL and LCLS FEL experiments. The modelled harmonic powers perfectly fit the experimentally measured data. High levels of the 2nd harmonic are explained by the wide beam in LEUTL experiment and by the off-axis beam deviation in LCLS experiment.

Analysis of the Influence of Nonperiodic Magnetic Fields and Off-Axis Effects on the Radiation of X-Ray FEL and Other FELs

Undulator radiation (UR) in an undulator with field harmonics in two orthogonal planes is theoretically studied taking nonperiodic magnetic components and off-axis effects into account. New analytical expressions for the UR spectrum and UR intensity are written explicitly in terms of the generalized Bessel function and Airy function. In limiting cases, they describe the radiation of a two-frequency planar undulator, a helical undulator, and an elliptical undulator. The influence of the finite size of the electron beam, the emittance, electron beam deflection from the axis, the spread of the electron energy, and the influence of the constant components of the magnetic field are taken into account analytically. The expressions make it possible to distinguish the contributions of each field component and characteristics of the beam and undulator to the generation of UR harmonics. The phenomenological FEL model is used to study the evolution of harmonic power in the FEL experiments of LCLS and LEUTL. The influence of the beam parameters and undulator parameters on the harmonic generation is analyzed. The theoretical results of the power and radiation spectrum of the FEL are in agreement with experiments. It is shown that the second harmonic in the X-ray FEL of LCLS can be due to the beam deflection from the axis by $${\sim}12$$ $$\mu$$ m, and the second harmonic in the UV-A FEL of LEUTL is due to wide ( $${\sim}0.2$$ mm) beams of electrons and photons.

Undulator and free-electron laser radiation with field harmonics and off-axis effects taken into account analytically

We present an analytic description of the generation of undulator radiation (UR) harmonics in a generalized elliptic undulator with field harmonics. The obtained analytic expressions for generalized Bessel and Airy functions describe the UR spectral lines and radiation intensity in the general and particular cases of two-frequency planar and helical undulators and also for other elliptic and planar undulators. We analytically describe the effect of finite electron beam size, beam emittance, off-axis deflection of electrons, electron energy spread, and beam-bending permanent magnetic components. The obtained analytic expressions distinguish the contributions made by each field component and by the beam and undulator parameters to the generation of radiation harmonics. Using an analytic model of single-pass free-electron lasers (FELs), we analyze the power evolution of harmonics in the LCLS, LEUTL, and SACLA FEL experiments. We discuss the effect that the beam and undulator parameters have on the generation of harmonics. It is shown that the strong second harmonics of radiation observed in experiments are caused by the detected beam deviation from the axis by 15μm over one gain length of 1.5 m in the X-ray LCLS FEL and by the large beam cross section of ∼ 200;μm in the LEUTL FEL. The results of modeling are fully consistent with experiments, which confirms the validity of the presented theoretical description of FEL power and radiation spectral density.

Planar wiggler as a tool for generating hard twisted photons

Simple formulas for the probability of radiation of twisted photons by scalar and Dirac particles with quantum recoil taken into account are derived. We show that the quantum recoil does not spoil the selection rule for the forward radiation of twisted photons in the planar undulator: m+n is an even number, where n is the harmonic number and m is the projection of the total angular momentum of the radiated twisted photon. The explicit formulas for the radiation probability of twisted photons produced in the planar wiggler are obtained with account for the quantum recoil. The radiation of twisted photons by GeV electrons in the planar wiggler and in the crystalline undulator is investigated.

Thermal Analysis of a Superconducting Undulator Cryostat for the APS Upgrade

The Advanced Photon Source Upgrade includes four 4.8-m-long superconducting undulator (SCU) cryostats, each containing two planar undulator NbTi magnets up to 1.9 m long. The cooling is provided by six cryocoolers arranged in three thermal circuits. The magnets are indirectly cooled with LHe penetrating through channels in the magnet cores. This 4 K circuit, which also includes a LHe tank, is cooled by five 4 K cryocooler 2nd stages. A beam vacuum, which is thermally isolated from the magnets, is cooled by one 10 K cryocooler 2nd stage. A thermal shield and warm parts of current leads are cooled by the 1st stages of all six cryocoolers. This paper presents an ANSYS-based thermal analysis of the new SCU cryostat including all thermal circuits. The benchmarked thermal conductance between the cryocooler cold heads and the LHe tank are used in the calculations as well as the measured cryocooler load lines. The model predicts temperatures in the system, total 4 K heat loads, and excess cooling power for various operational modes of the undulator.

A New Superconducting Undulator Cryostat for the APS Upgrade

The Advanced Photon Source (APS) is in the midst of a major facility upgrade including both a new electron storage ring (SR) and many new insertion devices (IDs) providing x-ray photon beams to a new suite of experimental end stations. Included among the new IDs are four 4.8-meter superconducting undulator (SCU) cryostats, each containing two 1.8-meter planar undulator magnets operating at 4.2 K in either a phase shifted or canted configuration. We describe a new, compact cryocooler-based cryostat design which supports the magnets and associated subsystems and also fits the space constraints of the SR ID straight sections. The design is an evolution of earlier single-magnet 2-meter cryostats, retaining some subsystem commonality while incorporating lessons learned and several features unique to the challenge of supporting two independently operable undulator magnets in a single device.

Probability of radiation of twisted photons by cold relativistic particle bunches

The probability to detect a twisted photon produced by a cold relativistic particle bunch of charged particles is derived. The radiation of twisted photons by such particle bunches in stationary electromagnetic fields and in propagating electromagnetic waves is investigated. Several general properties of both incoherent and coherent contributions to the radiation probability of twisted photons are established. It is shown that the incoherent radiation by bunches of particles traversing normally an isotropic dispersive medium (the edge, transition, and Vavilov–Cherenkov radiations) and by bunches moving in a helical undulator does not depend on the azimuthal distribution of particles in the bunch and is the same as for round bunches. As for planar undulators, the incoherent radiation by particle bunches is the same as for the bunches symmetric under reflection with respect to the axis of a twisted photon detector. At high energies of detected twisted photons, this property is universal and holds for the forward incoherent radiation by any cold relativistic particle bunch. The coherent radiation of twisted photons by such particle bunches obeys the property that we call the addition rule. This rule provides a simple means to describe the properties of coherent radiation of twisted photons. Furthermore, the strong addition rule is established for the coherent radiation by sufficiently long helical bunches. The use of this rule allows one to elaborate superradiant pure sources of twisted photons. The coherent radiation by helical bunches is considered for the edge, transition, and Vavilov–Cherenkov processes and for particles moving in undulators and plane laser waves with circular polarization. In these cases, the sum rules are deduced for the total probability to detect a twisted photon and for the projection of the total angular momentum per photon. The explicit expressions for both incoherent and coherent interference factors are derived for several simple bunch profiles.

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.

Генерация когерентного рентгеновского излучения гармоник в однопроходном лазере на свободных электронах со сдвигом фаз электронов относительно фотонов

Theoretical study of the radiated FEL power and bunching is conducted in single-pass free electron laser (FEL) with repetitive shift of the photon pulse with respect to the electron bunch in between the sections of the undulator with field harmonics. Using the analytical calculations, the asymmetric elliptic and planar undulator fields are identified for the undulators to be able to reduce the fundamental tone and enhance the harmonic radiation. This effect is amplified by the phase shift kπ/n, k=2,4,6… of the electrons and photons between the undulator sections. This allows n-th FEL harmonic reach its peak power beyond the fundamental saturation FEL length. It is not possible to achieve in a common FEL due to fast increase of the energy spread, induced by the fundamental tone along FEL and its early saturation. The phenomenological model of the FEL is used for the analysis of the bunching coefficients and harmonic powers evolution in the FEL. The model describes the debunching between the undulator sections, where the phase shift is imposed, and accounts for the higher sensitivity to losses of the electron-photon interaction at high harmonic wavelengths. The losses are due to the beam energy spread and emittance, deviation off the axis, diffraction etc. Explicit expressions for the Bessel coefficients of the planar and elliptic undulators with field harmonics are obtained and analyzed. The combination of the undulator field harmonics is identified, which reduces the fundamental tone and enhances the 3rd and 5th UR harmonics as compared with the radiation from a planar undulator. We propose the use of these undulators in a FEL with the electron-photon phase shift, which increases high harmonic powers in X-ray band by ~100 times with respect to common FELs.

A hard X-ray self-amplified spontaneous emission free-electron laser optimizationusing evolutionary algorithms for dedicated user applications

Accelerator-based fourth-generation light sources are utilized in a wide range of interdisciplinary applications such as nanotechnology, materials science, biosciences, and medicine. A hard X-ray free-electron laser (FEL), as a state-of-the-art light source, was optimized using evolutionary algorithms for dedicated user applications such as X-ray Raman scattering (XRS), resonant inelastic X-ray scattering (RIXS), and X-ray emission spectroscopies (XES). Optimal parameter sets were obtained for an in-vacuum planar undulator driven by an 8 GeV electron beam. Performance parameters of self-amplified spontaneous emission (SASE) operation (i.e. optimized SASE performance parameters through evolutionary algorithms) were found to be consistent with operating X-ray FEL facilities around the world. It is shown that FEL characteristics for specific user experiments can be optimized by finding several evolutionary algorithm solutions within the range of 5 keV to 10 keV.

Design of an X-ray undulator: optimization considerations for SASE operation

Accelerator-based fourth-generation light sources, namely, free-electron lasers (FELs), offer unique radiation characteristics, such as tunable, coherent, high-power, ultra-short pulses. They rely on novel technology with challenging parameters, from which the practicability is currently being proved by world-class facilities like the European XFEL, LCLS, FLASH, and SACLA. When contriving such superior light characteristics, “state-of-the-art” linear accelerator (linac) and undulator technologies come into prominence. In this respect, design and simulation studies for a planar X-ray undulator are considered to optimize the FEL generation process by self-amplified spontaneous emission (SASE). Three main performance parameters for SASE operation (i.e., 1D gain length, saturation power, and saturation length) are compared and discussed by means of numerical calculations and simulation results. It is shown that hard X-ray FEL pulses (down to sub-angstroms) are generable via in-vacuum hybrid undulators driven by an 8 GeV electron linac.

Properties of THz coherent undulator radiation generated from a compact accelerator source at Kyoto University

A compact accelerator-base source of THz Coherent Undulator Radiation (THz-CUR) at the Kyoto University has been developed with the purpose of providing intense quasimonochromatic and tunable THz-CUR at frequencies below 1 THz. The source is driven by a compact accelerator using a photocathode RF gun, which emits an electron beam with a fixed energy of 4.6 MeV and high bunch charge. The THz-CUR from our source can be generated when a compressed electron bunch passes through a planar undulator. In this study, we investigate the properties of this radiation, including the total radiation energy, spatial distribution, and power spectrum. With an electron beam of 160 pC bunch charge, the total radiation energy of THz-CUR at 0.16 THz was 1.2 µJ in the micropulse. The THz-CUR covering the frequency range from 0.16 THz to 0.65 THz could be produced by changing the magnetic field of the undulator at a 60 pC bunch charge. Due to the influence of the space charge forces causing the degradation of electron beam qualities, saturation of the radiation energy occurred, and the radiation power spectrum at a frequency of 0.65 THz could not be observed in the high charge condition (160 pC). The effects of bunch lengthening, energy spread, and emittance growth and the influence of the phase error on the generation of THz radiation are also discussed in this paper. This opens up the possibility of understanding the generation of THz-CUR and sheds further light on the enhancement of the radiation power.

Generating three-color pulses in high-gain harmonic-generation free-electron lasers with atilted electron bunch.

A multi-color light source is a significant tool for nonlinear optics experiments, pump-dump/repump-probe experiments and in other fields. Here, a novel method is proposed to create three-color pulses based on a high-gain harmonic-generation (HGHG) free-electron laser with a tilted electron bunch. In this method, the initial bunch tilt is created by transverse wakefields after the bunch passes through a corrugated structure with an off-axis orbit, and is further enlarged in a following drift section. Then the tilted bunch experiences the off-axis field of a quadrupole magnet to cool down the large transverse velocity induced before. After that, it enters an HGHG configuration adopting a transverse gradient undulator (TGU) as the radiator, where only three separated fractions of the tilted bunch will resonate at three adjacent harmonics of the seed wavelength and are enabled to emit three-color pulses simultaneously. In addition, the use of the natural transverse gradient of a normal planar undulator instead of the TGU radiator to emit three-color pulses is also studied in detail. Numerical simulations including the generation of the tilted bunch and the free-electron laser radiation confirm the validity and feasibility of this scheme both for the TGU radiator and the natural gradient in the extreme-ultraviolet waveband.

Thermal Analysis of a Helical Superconducting Undulator Cryostat

A novel cryocooler-cooled helical superconducting undulator (HSCU) was built and installed in the Advanced Photon Source (APS) storage ring and has been in operation since January 2018. The new cryostat for the HSCU is a major improvement of the cryogenic system used for the existing APS planar superconducting undulators. In both systems, superconducting magnets are cooled independently from the beam chamber by liquid helium (LHe) passing through a channel in the magnet/mold assembly. The original planar undulator cryostat consists of three thermal circuits: the outer shield circuit to cool both the warm part of the magnet current leads and the outer shield, the beam chamber cooling circuit to cool the beam chamber and the inner shield, and the magnet cooling circuit to cool the magnets and the LHe tank. On the other hand, the new system consists of only two thermal circuits: the thermal shield circuit to cool the beam chamber, the shield, and the warm part of the magnet leads; and the magnet cooling circuit to cool the LHe tank and the magnet/mold assembly. An finite element analysis-based thermal model of the new HSCU cryostat was developed while the cryogenic performance of the HSCU was measured in a series of standalone tests as well as after installation in the storage ring. This paper presents a thermal analysis of the new HSCU cryostat and, in particular, a comparison of calculated and measured temperatures as well as the excess cooling capacity of the new cryostat in static and dynamic (beam-induced heating) modes.

First measurements with the K-monochromator at the European XFEL.

Hard X-ray free-electron lasers (XFELs) generate intense coherent X-ray beams by passing electrons through undulators, i.e. very long periodic magnet structures, which extend over hundreds of meters. The SASE1 and SASE2 undulator systems of the European XFEL consist of 35 segments with variable-gap planar undulators which are initially tuned to precise on-axis magnetic field strengths in a magnetic measurement laboratory to keep an important quality parameter - the K-value variation from segment to segment - below a certain limit (3 × 10-4 for 12 keV photon energy). After tunnel installation only photon-based methods can determine the K-values of undulator segments with a similar accuracy. The synchrotron radiation from a single or a few segments can be spectrally filtered by a dedicated crystal monochromator (K-monochromator) and recorded with a photodiode or with an imager that provides 2D information, tuned for high sensitivity to detect low photon densities from distant single undulator segments. This instrumentation is applied for electron orbit analysis and optimization, and adjustment of individual undulators in terms of their central magnetic axis with respect to the electron beam. Single undulator segments were analysed by scanning the monochromator crystal angle and detecting the steepest slope of a photodiode signal. Alternatively, in the imaging method, an imager recorded the radiation cone of electrons passing through the undulator segment. From the spatial distribution of the radiation, the K-parameter was determined with a sufficiently high relative accuracy.

Design and fabrication of a prototype planar undulator

The main goal of this work is to get the fabrication technology of the insertion devices. A prototype undulator with the period of 48mm and the peak magnetic field of 0.75 T has been fabricated using NdFeB-SH35 magnets based on the cooperation between ILSF and NSTRI. The total magnet length is 483 mm and the number of periods is 8. The magnetic parameters of the undulator are determined in order to reach the first and third harmonics. The photon energy should cover 260 eV to 2000 eV range. In order to control the strong attractive magnetic force between the upper and lower arrays, a special mechanical mechanism has been designed and fabricated. The source of errors in the magnetic field has been discussed. The share of each errors has been investigated in the total magnetic field and their effects on the harmonics intensity have been studied. The RMS field error has been obtained to be 0.4%; also, the first and third harmonics intensity reached to more than 80% of the ideal intensities in the presence of the real magnetic field.

Harmonic Generation in Planar Undulators in Single-Pass Free Electron Lasers

The paper presents a theoretical study of the harmonic power evolution in a single-pass free-electron laser (FEL) and a comparison with some of the experimental results. The phenomenological approach which considers the main FEL parameters (current density, the Lorentz factor, electron energy spread, and the beam geometry) provides a description of any undulator. With due regard to the real laser beam parameters, the effect from high-order harmonic radiation and the beam deviation from the undulator axis on the FEL irradiation is investigated. The Bessel coefficients are calculated for the undulator in the presence of the second periodic field. The phenomenological approach provides the free-electron laser simulation experiments at Sorgente Pulsata Auto-amplificata di Radiazione Coerente (SPARC), SPring-8 Angstrom Compact Free-Electron Laser (SACLA) and Linac Coherent Light Source (LCLS). These studies include the high-harmonic generation, a comparison of the emission power evolution with the experimentally obtained data on the harmonic generation including even and odd high-order harmonics, gain and saturation lengths and the respective power. A possible effect from the third harmonic of the planar undulator magnetic field is studied in relation to the FEL irradiation. It is shown that this effect is insignificant even at the magnetic-field harmonic amplitude equaling ~1/10 of the amplitude of the ideal magnetic field in the periodic undulator. It is found that the second-harmonic generation in FEL lasing is rather weak, that is in good agreement with the measurement results as well as the behavior of the high-order harmonics.

Analysis of harmonic generation in planar and elliptic bi-harmonic undulators and FELs

Abstract We present a phenomenological model for single-pass FEL radiation power and bunching evolution in planar and elliptic undulators with two polarizations of the emitted radiation; the models allows for the suppression of low harmonics in the spectrum. We study the harmonic generation in some planar and elliptic undulators with account for the off-axis effects and for the 3rd harmonics of the undulator magnetic field. Both spontaneous and stimulated types of radiation are studied. Spontaneous UR is studied with generalized Bessel functions formalism. The analytical FEL model, which employs these Bessel functions, is verified with FEL experiments in the range of radiation wavelengths 0.15–500 nm and confirmed by numerical simulations. The phenomenological description is based on the undulator parameters and FEL parameters, such as the electron beam current, energy, spread and emittance. The analytical formulation allows fast evaluation of the FEL performance with minimal resources. The effects of the 3rd harmonic of the undulator field and properties of the beam on the spontaneous UR and on the FEL radiation are explored. Generation of high even- and odd- harmonics due to the undulator field harmonic and finite beam size is studied. Their effects on the spontaneous and stimulated UR are compared with each other.