Transverse Gradient Undulator Research Articles

Shaping Micro-Bunched Electron Beams for Compact X-ray Free-Electron Lasers with Transverse Gradient Undulators

Laser-modulator-based micro-bunching of electron beams has been applied to many novel operating modes of X-ray free-electron lasers from harmonic generation to attosecond pulse production. Recently, it was also identified as a key enabling technology for the production of a compact XFEL driven by a relatively low-energy beam. In traditional laser modulator schemes with low-energy and high-current bunches, collective effects limit the possible working points that can be employed, and thus it is difficult to achieve optimal XFEL performance. We propose to utilize transverse longitudinal coupling in a transverse gradient undulator (TGU) to shape micro-bunched electron beams so as to optimize their performance in a compact X-ray free-electron laser. We show that a TGU added to a conventional laser modulator stage enables much more flexibility in the design, allowing one to generate longer micro-bunches less subject to slippage effects and even lower the slice emittance of the micro-bunches. We present a theoretical analysis of laser-based micro-bunching with an added TGU, simulation of compression with collective effects in such systems, and finally XFEL simulations demonstrating the gains in peak power enabled by the TGU. Although we focus on the application to compact XFELs, what we propose is a general phase space manipulation that may find utility in other applications as well.

Transverse gradient undulator in a storage ring x-ray free electron laser oscillator

Modern electron storage rings produce bright x rays via spontaneous synchrotron emission, which is useful for a variety of scientific applications. The x-ray free-electron laser oscillator (XFELO) has the potential to amplify this output, both in terms of peak power and photon coherence. However, even current fourth generation storage rings (4GSRs) lack the requisite electron beam brightness to drive the XFELO due to its electron energy spread. The transverse gradient undulator (TGU) can overcome this issue, thus providing a practical means to couple the 4GSR to the XFELO. In this study, we first examine the theoretical basis of the TGU interaction by deriving the 3D TGU gain formula in the low gain approximation. Then, we perform an optimization study of the gain formula in order to determine optimal beam and machine parameters. Finally, we construct a hypothetical storage ring TGU-XFELO based on near-optimal parameters and report on its projected performance using multistage numerical simulation. We also discuss potential implementation challenges associated with the ring-FEL coupling.

Efficiency enhancement of free-electron laser oscillator by kicking the electron beam orbit in a transverse gradient undulator

The conversion efficiency of a conventional free-electron laser (FEL) is on the level of Pierce parameter, which means that only a small portion of electron beam energy is converted into the electric field. Undulator tapering is a common way to enhance the FEL efficiency, however, it has limited effect when applying in the FEL oscillator. Inspired by the fast kicker developed in the high-repetition-rate FELs and storage rings, in this paper we propose to kick the electron beam orbit transversely in a transverse gradient undulator (TGU) after the FEL is saturated in oscillator. The electron beam will experience a different undulator strength after the beam orbit is deflected to the off-axis position. It can be regarded as a dynamic tapering method within the macrobunch while the dynamic detuning on the undulator strength with the normal tapering method is almost impossible in oscillator. Though the TGU will reduce the initial small-signal gain, the FEL efficiency still can be greatly enhanced. Numerical simulations demonstrated that the maximum FEL power can be enhanced to more than 3 times of the normal FEL oscillator.

Erratum: Radiation emitted by transverse-gradient undulators [Phys. Rev. Accel. Beams 19 , 090704 (2016)

Received 28 August 2020DOI:https://doi.org/10.1103/PhysRevAccelBeams.23.099901Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasSingle-particle dynamicsPhysical SystemsPlasma acceleration & new acceleration techniquesSynchrotron radiation & free-electron lasersAccelerators & Beams

Physics issues of the diffraction-limited storage ring light source

<p indent=0mm>The synchrotron radiation light source based on electron storage ring is the most widely used high-performance X-ray source in the field of basic scientific research in the 20th century, and has undergone three generations of development. One important direction of the new generation light source, i.e., the fourth generation light source, is the so-called diffraction-limited storage ring (DLSR) light source. DLSR, with ultra-high average brightness, high repetition frequency, multi-user, high stability, complementary to the free electron laser (FEL), has a great development in recent decades. By adopting lattice design based on compact multi-bend achromats (MBAs), DLSR allows to achieve one or two orders of magnitude lower emittance approaching the diffraction limit of X-rays, and much higher brightness and coherence than available in the third generation light source, while inheriting the high brightness, multi-user and high stability advantages of existing ring light sources. In this paper, the progress made in the last few decades in physics design and optimization of the DLSR, especially on the ultralow-emittance lattice and injection schemes, will be overviewed. To achieve an ultralow emittance, lattice structures of standard MBA and hybrid MBA, and novel magnets of high-gradient quadrupole, antibend, longitudinal gradient dipole and complex bend, have been proposed. To obtain optimized beam dynamics in a DLSR, theoretical and numerical methods have been developed to date. Due to the fact that the nonlinearities are extremely high in a DLSR and the nonlinear dynamics is greatly coupled with the linear optics, the most effective and most commonly used way is global and stochastic optimization of the ring performance evaluated by numerical tracking. To deal with the challenges of injecting to a DLSR with small dynamic acceptance, different injection schemes, such as, pulsed multipole injection, on-axis swap-out injection and on-axis longitudinal injection, have been proposed. Collective effects, especially the intra beam scattering and the Touschek effects, become significant as emittance decreases, requiring methods of bunch lengthening and transverse feedback to ensure the stability of the particle motion at a high beam current. Besides, a few developing topics in DLSR physics will be discussed. Machine learning, the method of transferring disorder data into useful information, is an important branch of artificial intelligence, and has been used in accelerator control system and beam commissioning. This method would be very useful and helpful in the design and optimization, initial commissioning and daily operation of a DLSR. A rational combination of machine learning and multi-objective optimization algorithm, like multi-objective genetic algorithm and multi-objective particle swarm algorithm, can effectively improve the optimization performance, and has been successfully applied in nonlinear optimization of light sources. In addition, improving the performance of synchrotron radiation by combining the beam physics of DLSR and the principle of FEL is one developing research topic which might be able to provide base for further development of the DLSR. Combined with bypass and transverse gradient undulator, high gain FEL could be achieved in the storage ring. Besides, double ring light source, divided into two loops, the inner ring is DLSR, and the other is FEL with more long straight sections, was proposed to improve the utilization rate of the beams.

Laser-slicing at a low-emittance storage ring.

Laser-slicing at a diffraction-limited storage ring light source in the soft X-ray region is investigated with theoretical and numerical modelling. It turns out that the slicing efficiency is favoured by the ultra-low beam emittance, and that slicing can be implemented without interference to the standard multi-bunch operation. Spatial and spectral separation of the sub-picosecond radiation pulse from a hundreds of picosecond-long background is achieved by virtue of 1:1 imaging of the radiation source. The spectral separation is enhanced when the radiator is a transverse gradient undulator. The proposed configuration applied to the Elettra 2.0 six-bend achromatic lattice envisages total slicing efficiency as high as 10-7, one order of magnitude larger than the demonstrated state-of-the-art, at the expense of pulse durations as long as 0.4 ps FWHM and average laser power as high as ∼40 W.

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.

Study of a free-electron laser driven by a laser-plasma accelerated beam at Peking University

The percent level energy spread and large divergence of laser-plasma beam are the main challenges of realizing compact short-wavelength free-electron lasers based on laser-plasma accelerators. These issues can be solved with proposed transverse gradient undulator method or bunch decompression method along with proper transport design. We present a study of using an expected 500 MeV laser-plasma beam with 0.3 mm⋅mrad normalized emittance and 0.3 mrad divergence at Peking University to drive compact free-electron laser at 30 nm. We employ the bunch decompression method with a chromatic matching beamline as well as the transverse gradient undulator method with assumed matched beam. Simulation shows that 700 MW power, 9.7 fs pulse duration and 0.85% relative bandwidth FEL output can be obtained using chromatic matched bunch decompression method. FEL with similar performance can be obtained using the transverse gradient undulator scheme.

Generation of coherent two-color pulses at two adjacent harmonics in a seeded free-electron laser

The growing requirements of pump-probe techniques and nonlinear optics experiments greatly promote the studies of two-color free-electron lasers (FELs). We propose a new method to generate coherent two-color pulses in a high-gain harmonic generation (HGHG) FEL. In this scheme, an initial tilted electron beam is sent though the modulator and dispersive section of an HGHG FEL to generate the bunching at harmonics of the seed laser. Then a transverse gradient undulator (TGU) is adopted as the radiator and in such radiator, only two separated fractions of the tilted beam will resonate at two adjacent harmonics of the seed laser and are enabled to emit the coherent two-color pulses simultaneously. The time separation between the two pulses are on the order of hundreds of femtoseconds, and can be precisely controlled by varying the tilted amplitude of the electron beam and/or the transverse gradient of the TGU radiator. Numerical simulations confirm the validity and feasibility of this scheme in the EUV waveband.

Progress on experiments towards LWFA-driven transverse gradient undulator-based FELs

Free Electron Lasers (FEL) are commonly regarded as the potential key application of laser wakefield accelerators (LWFA). It has been found that electron bunches exiting from state-of-the-art LWFAs exhibit a normalized 6-dimensional beam brightness comparable to those in conventional linear accelerators. Effectively exploiting this beneficial beam property for LWFA-based FELs is challenging due to the extreme initial conditions particularly in terms of beam divergence and energy spread. Several different approaches for capturing, reshaping and matching LWFA beams to suited undulators, such as bunch decompression or transverse-gradient undulator schemes, are currently being explored. In this article the transverse gradient undulator concept will be discussed with a focus on recent experimental achievements.

Reversible beam heater for suppression of microbunching instability by transverse gradient undulators

The microbunching instability driven by beam collective effects in a linear accelerator of a free-electron laser (FEL) facility significantly degrades the electron beam quality and FEL performance. A conventional method to suppress this instability is to introduce an additional uncorrelated energy spread by laser-electron interaction, which has been successfully operated in the Linac Coherent Light Source and Fermi@Elettra, etc. Some other ideas are recently proposed to suppress the instability without increasing energy spread, which could benefit the seeded FEL schemes. In this paper, we propose a reversible electron beam heater using two transverse gradient undulators to suppress the microbunching instability. This scheme introduces both an energy spread increase and a transverse-to-longitudinal phase space coupling, which suppress the microbunching instabilities driven by both longitudinal space charge and coherent synchrotron radiation before and within the system. Finally the induced energy spread increase and emittance growth are reversed. Theoretical analysis and numerical simulations are presented to verify the feasibility of the scheme and indicate the capability to improve the seeded FEL radiation performance.

Phase-merging enhanced harmonic generation free-electron laser with a normal modulator.

A phase-merging enhanced harmonic generation free-electron laser (FEL) was proposed to increase the harmonic conversion efficiency of seeded FELs and promote the radiation wavelength towards the X-ray spectral region. However, this requires a specially designed transverse gradient undulator (TGU) as the modulator to couple the transverse and longitudinal phase space of the electron beam. In this paper, the generation of the phase-merging effect is explored using the natural field gradient of a normal planar undulator. In this method, a vertical dispersion on the electron beam is introduced and then the dispersed beam travels through a normal modulator in a vertical off-axis orbit where the vertical field gradient is selected properly in terms of the vertical dispersion strength and modulation amplitude. The phase-merging effect will be generated after passing through the dispersive chicane. Theoretical analysis and numerical simulations for a seeded soft X-ray FEL based on parameters of the Shanghai Soft X-ray FEL project are presented. Compared with a TGU modulator, using the natural gradient of a normal planar modulator has the distinct advantage that the gradient can be conveniently tuned in quite a large range by adjusting the beam orbit offset.

Transverse gradient in Apple-type undulators.

Apple-type undulators are globally recognized as the most flexible devices for the production of variable polarized light in the soft X-ray regime, both at synchrotron and free-electron laser facilities. Recently, the implementation of transverse gradient undulators has been proposed to enhance the performance of new generation light sources. In this paper it is demonstrated that Apple undulators do not only generate linear and elliptical polarized light but also variable transverse gradient under certain conditions. A general theoretical framework is introduced to evaluate the K-value and its transverse gradient for an Apple undulator, and formulas for all regular operational modes and different Apple types (including the most recent Delta type and Apple X) are calculated and critically discussed.

Normal planar undulators doubling as transverse gradient undulators

The transverse gradient undulator (TGU) has important application in the short-wavelength high-gain free electron lasers (FELs) driven by laser-plasma accelerators. However, the usual transversely tapered TGUs need special design and manufacture, and the transverse gradient cannot be tuned arbitrarily. In this paper we explore a new and simple method of using the natural transverse gradient of a normal planar undulator to compensate the beam energy spread effect. In this method, a vertical dispersion on the electron beam is introduced, then the dispersed beam passes through a normal undulator with a vertical off-axis orbit where the vertical field gradient is selected properly related to the dispersion strength and the beam energy spread. Theoretical analysis and numerical simulations for self-amplified spontaneous emission FELs based on laser plasma accelerators are presented, and indicate that this method can greatly reduce the effect of the beam energy spread, leading to a similar enhancement on FEL performance as the usual transversely tapered TGU, but with the advantages of economy, tunable transverse gradient and no demand of extra field for correcting the orbit deflection induced by the field gradient.Received 21 December 2016DOI:https://doi.org/10.1103/PhysRevAccelBeams.20.020707Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Physical SystemsSynchrotron radiation & free-electron lasersAccelerators & Beams

Compact beam transport system for free-electron lasers driven by a laser plasma accelerator

Utilizing laser-driven plasma accelerators (LPAs) as a high-quality electron beam source is a promising approach to significantly downsize the x-ray free-electron laser (XFEL) facility. A multi-GeV LPA beam can be generated in several-centimeter acceleration distance, with a high peak current and a low transverse emittance, which will considerably benefit a compact FEL design. However, the large initial angular divergence and energy spread make it challenging to transport the beam and realize FEL radiation. In this paper, a novel design of beam transport system is proposed to maintain the superior features of the LPA beam and a transverse gradient undulator (TGU) is also adopted as an effective energy spread compensator to generate high-brilliance FEL radiation. Theoretical analysis and numerical simulations are presented based on a demonstration experiment with an electron energy of 380 MeV and a radiation wavelength of 30 nm.

Transverse to longitudinal phase space coupling in an electron beam for suppression of microbunching instability

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.

Radiation emitted by transverse-gradient undulators

Conventional undulators are used in synchrotron light sources to produce radiation with a narrow relative spectral width as compared to bending magnets or wigglers. The spectral width of the radiation produced by conventional undulators is determined by the number of undulator periods and by the energy spread and emittance of the electron beam. In more compact electron sources like for instance laser plasma accelerators the energy spread becomes the dominating factor. Due to this effect these electron sources cannot in general be used for high-gain free electron lasers (FELs). In order to overcome this limitation, modified undulator schemes, so-called transverse gradient undulators (TGUs), were proposed and a first superconducting TGU was built at Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany. In this paper simulations of the expected synchrotron radiation spectral distribution are presented. An experimental test with that device is under preparation at the laser wakefield accelerator at the JETI laser at the University of Jena, Germany.

Generation of ultra-large-bandwidth X-ray free-electron-laser pulses with a transverse-gradient undulator.

A new and simple method to generate X-ray free-electron-laser radiation with unprecedented spectral bandwidth above the 10% level is presented. The broad bandwidth is achieved by sending a transversely tilted beam through a transverse-gradient undulator. The extent of the bandwidth can easily be controlled by variation of the beam tilt or the undulator gradient. Numerical simulations confirm the validity and feasibility of this method.

Operating synchrotron light sources with a high gain free electron laser

Since the 1980s synchrotron light sources have been considered as drivers of a high repetition rate (RR), high gain free electron laser (FEL) inserted in a by-pass line or in the ring itself. As of today, the high peak current required by the laser is not deemed to be compatible with the standard multi-bunch filling pattern of synchrotrons, and in particular with the operation of insertion device (ID) beamlines. We show that this problem can be overcome by virtue of magnetic bunch length compression in a ring section, and that, after lasing, the beam returns to equilibrium conditions without beam quality disruption. Bunch length compression brings a double advantage: the high peak current stimulates a high gain FEL emission, while the large energy spread makes the beam less sensitive to the FEL heating and to the microwave instability in the ring. The beam’s large energy spread at the undulator is matched to the FEL energy bandwidth through a transverse gradient undulator. Feasibility of lasing at 25 nm is shown for the Elettra synchrotron light source at 1 GeV, and scaling to shorter wavelengths as a function of momentum compaction, beam energy and transverse emittance in higher energy, larger rings is discussed. For the Elettra case study, a low (100 Hz) and a high (463 kHz) FEL RR are considered, corresponding to an average FEL output power at the level of ∼1 W (∼1013 photons per pulse) and ∼300 W (∼1011 photons per pulse), respectively. We also find that, as a by-product of compression, the ∼5 W Renieri’s limit on the average FEL power can be overcome. Our conclusion is that existing and planned synchrotron light sources may be made compatible with this new hybrid IDs-plus-FEL operational mode, with little impact on the standard beamlines functionality.

Transverse Gradient Undulators and FEL operating with large energy spread

Undulators exhibiting a gradient of the field in the transverse direction have been proposed to mitigate the effects of the gain dilution in Free Electron Laser devices operating with large energy spread. The actual use of the device depends on the realization of a field distribution with quasi-vanishing quadrupolar terms in the tapering directions. We analyze the effect of a Transverse Gradient Undulator on the FEL operation and critically review the possibility of an appropriate field implementation.