Multi-bend Achromat Lattice Research Articles

Emittance optimization under magnet strength limitation for a multi-bend achromat lattice

Diffraction-limited storage rings (DLSRs) based on multi-bend achromat (MBA) lattices are being developed towards much lower emittances. For instance, for the future development, MAX IV designed a 19BA lattice to replace the present 7BA lattice, achieving an emittance of 16 pm·rad. While this 19BA lattice, with a significantly increased number of unit cells, requires extremely strong quadrupoles and sextupoles, which will result in very small vacuum chambers and can thus significantly increase beam coupling impedance and potentially enhance beam instabilities. This issue raises a question of how we can reduce magnet strengths while achieving the emittance goal. In this paper, based on a simplified model where an MBA lattice is considered to consist of a number of identical unit cells, emittance optimization is numerically studied under magnet strength limitation. The studied results show that for a given arc length and emittance goal, choosing an appropriate number of unit cells with relatively large horizontal cell tunes can significantly reduce magnet strengths. As a practical example, an 11BA lattice with relatively large unit cell tunes is designed and compared with a 17BA lattice with smaller unit cell tunes. The two lattices have roughly the same emittance with the same energy, ring circumference and number of periods, while the magnets of the 11BA lattice are significantly weaker.

Off-energy operation for the Extremely Brilliant Source at the European Synchrotron Radiation Facility

The European Synchrotron Radiation Facility Extremely Brilliant Source (ESRF-EBS) is the first fourth generation 6 GeV storage ring (SR) light source making use of the hybrid multibend achromat lattice, reaching a natural horizontal emittance of 140 pm rad. Further, reducing the horizontal emittance would provide a more brilliant and a higher quality photon source for the EBS users. One way of achieving this is to operate the SR off-energy. The first approach reduces the electron beam energy by −1%, which gives a 121 pm rad natural horizontal emittance. To fulfill operation requirements, the full ring had to be rematched, including both the quadrupoles and the sextupoles in the linear optics correction. The off-energy settings are then tested in the SR in terms of lifetime, injection efficiency, and operability. Published by the American Physical Society 2024

Study of chromaticity correction methods for a hybrid multi-bend-achromat lattice

The hybrid multi-bend-achromat (MBA) lattice is developed for the demand of higher luminosity at both collider and synchrotron light source. For a hybrid MBA lattice, its negative chromaticities must be corrected with sextupoles, which lead to nonlinearities, thus limiting the dynamic aperture (DA) and momentum aperture (MA). To get efficient injection and long beam lifetime, these nonlinearities must be carefully handled, while it is always difficult to optimize the nonlinearities with limited knobs for the fixed linear lattice. Therefore, conducting chromaticity correction is of importance in linear lattice design that can achieve better nonlinear dynamics. In this paper, three chromaticity correction methods are compared using multi-objective genetic algorithm (MOGA). A hybrid MBA of 2 GeV, as an example, is designed with a natural emittance of 4.4 nm•rad.

Design and comparison of hybrid multi-bend achromat lattices for HALF storage ring

Design and comparison of hybrid multi-bend achromat lattices for HALF storage ring

Demonstration of machine learning-enhanced multi-objective optimization of ultrahigh-brightness lattices for 4th-generation synchrotron light sources

Fourth-generation storage rings enabled by multi-bend achromat lattices are being inaugurated worldwide and many more are planned for the next decade. These sources deliver stable ultra-high brightness radiation with unmatched levels of transverse coherence by virtue of their highly advanced magnetic lattices. Optimization of these challenging and strongly nonlinear lattices with many degrees of freedom bounded by extensive sets of constraints and multiple often conflicting optimization goals is highly demanding and requires application of the most advanced numerical tools available to the community. While multi-objective genetic algorithms have been very successful in supporting these optimization efforts, the algorithms suffer from a fundamental limitation of their stochastic nature: an exceedingly vast number of candidate lattices, most of which eventually are rejected, has to be fully evaluated. This comes at immense computational cost and thus drives excessive runtime despite use of large supercomputing clusters. We therefore propose to employ deep learning techniques and iterative retraining of neural networks to massively accelerate such lattice evaluation, thereby allowing lattice optimization to rely on far fewer a priori assumptions, open up to larger search ranges, and include right from the start and in parallel multiple error distributions to find truly global optima, all while completing a full optimization campaign in weeks rather than months. In this paper we present the neural network designs, the deep learning approach, iterative retraining procedures, and demonstrate how these machine learning techniques can be incorporated into existing state-of-the-art optimization workflows with only minimal changes applied to the optimization pipeline itself and none at all to the employed tracking codes.

14th International Conference on Synchrotron Radiation Instrumentation (SRI 2021), 28 March to 1 April 2022

The International Conference on Synchrotron Radiation Instrumentation (SRI) is a unique and significant international forum held every three years in the community of synchrotron radiation (SR) and free electron lasers (FEL). It is the prime forum for fostering connections between cutting-edge synchrotron radiation instrumentation, science, and the requirements of the user community. The SRI 2021 had originally been scheduled to take place in Hamburg in summer 2021. Due to the COVID-19 pandemic, it was postponed to 2022 and held as an online event.More than 1160 international participants from 25 countries met virtually at the SRI 2021. In nearly 290 talks and 450 posters, latest results were presented. Although it was an online-only conference, lively discussions took place in the nearly 40 parallel sessions, and the eight poster sessions were also very well attended.The main topics of the SRI conference were: new SR and FEL facilities, update plans of these facilities, and recent developments in various instrumentation areas like beamline design, X-ray optics, sample environments, detectors and spectrometers, data acquisition, and data analysis techniques or automation. These innovations contributed to new results for a wide range of experimental techniques and scientific applications such as X-ray scattering and spectroscopy, bio- and scanning imaging, structural biology crystallography, coherent techniques, or in-situ/operando methods. A dedicated session concerned industrial applications of synchrotron radiation.The field of synchrotron radiation instrumentation is currently seeing very active development due to various factors. Firstly, the number of SR sources world-wide is increasing significantly, with new sources in particular in Europe and in Asia. Secondly, a new generation of storage rings with new multi-bend achromat lattices are being implemented at a growing number of existing facilities. These facilities offer a significant increase of brilliance and coherence and thereby lead to new and improved applications of synchrotron radiation, in particular in the areas of imaging and high spatial resolution. Thirdly, the increase of soft and hard X-ray FEL sources worldwide and the maturation of their experimental techniques and scientific applications is the background for a strongly increasing number of developments for ultrafast time-resolved investigations of dynamic behaviour of materials and reactions. Most of the keynote speakers and many invited and contributed talks or posters at the conference showed new results directly related to these three major developments.Lists of International Advisory Committee (listed by facility), Scientific Programme Committee (listed by facility), Local Organising Committee (listed by facility) are available in this PDF.

X-ray Diffraction Imaging of Deformations in Thin Films and Nano-Objects.

The quantification and localization of elastic strains and defects in crystals are necessary to control and predict the functioning of materials. The X-ray imaging of strains has made very impressive progress in recent years. On the one hand, progress in optical elements for focusing X-rays now makes it possible to carry out X-ray diffraction mapping with a resolution in the 50–100 nm range, while lensless imaging techniques reach a typical resolution of 5–10 nm. This continuous evolution is also a consequence of the development of new two-dimensional detectors with hybrid pixels whose dynamics, reading speed and low noise level have revolutionized measurement strategies. In addition, a new accelerator ring concept (HMBA network: hybrid multi-bend achromat lattice) is allowing a very significant increase (a factor of 100) in the brilliance and coherent flux of synchrotron radiation facilities, thanks to the reduction in the horizontal size of the source. This review is intended as a progress report in a rapidly evolving field. The next ten years should allow the emergence of three-dimensional imaging methods of strains that are fast enough to follow, in situ, the evolution of a material under stress or during a transition. Handling massive amounts of data will not be the least of the challenges.

Storage rings in Korea as synchrotron radiation source

Remarkable progress has been made in photon beam brightness from storage rings. From the early 90’s, third-generation storage rings (3GSRs) have been put into operation and have provided very bright photon beams using insertion devices. Fourth-generation storage rings (4GSRs) that exploit the multi-bend achromat lattice concept may be able to surpass the brightness and coherence that have been attained using present third-generation storage rings. Recently, a 4GSR project was officially approved to meet the increasing demand from the growing user community in Korea. This paper describes progress in the development of storage rings in Korea, including the status and the plans for PLS-II, and the results on the conceptual design for Korea-4GSR.

Design of double-bend and multibend achromat lattices with large dynamic aperture and approximate invariants

A numerical method to design nonlinear double- and multi-bend achromat (DBA and MBA) lattices with approximate invariants of motion is investigated. The search for such nonlinear lattices is motivated by Fermilab's Integrable Optics Test Accelerator (IOTA), whose design is based on an integrable Hamiltonian system with two invariants of motion. While it may not be possible to design an achromatic lattice for a dedicated synchrotron light source storage ring with one or more exact invariants of motion, it is possible to tune the sextupoles and octupoles in existing DBA and MBA lattices to produce approximate invariants. In our procedure, the lattice is tuned while minimizing the turn-by-turn fluctuations of the Courant-Snyder actions $J_x$ and $J_y$ at several distinct amplitudes, while simultaneously minimizing diffusion of the on-energy betatron tunes. The resulting lattices share some important features with integrable ones, such as a large dynamic aperture, trajectories confined to invariant tori, robustness to resonances and errors, and a large amplitude-dependent tune-spread. Compared to the nominal NSLS-II lattice, the single- and multi-bunch instability thresholds are increased and the bunch-by-bunch feedback gain can be reduced.

Characteristics of Photon Beam and Preservation of Coherence in Fourth-Generation Light Sources

Fourth-generation storage rings (4GSRs) that exploit the multi-bend achromat lattice concept may be able to surpass the brightness and coherence that are attained using the present third-generation storage rings. This paper presents the characteristics of photon beams and an analysis of their coherence properties in Korea-4GSR to represent 4GSRs.

Design of Double- and Multi-Bend Achromat Lattices with Large Dynamic Aperture and Approximate Invariants

A numerical method to design nonlinear double- and multi-bend achromat (DBA and MBA) lattices with approximate invariants of motion is investigated. The search for such nonlinear lattices is motivated by Fermilab's Integrable Optics Test Accelerator (IOTA), whose design is based on an integrable Hamiltonian system with two invariants of motion. While it may not be possible to design an achromatic lattice for a dedicated synchrotron light source storage ring with one or more exact invariants of motion, it is possible to tune the sextupoles and octupoles in existing DBA and MBA lattices to produce approximate invariants. In our procedure, the lattice is tuned while minimizing the turn-by-turn fluctuations of the Courant-Snyder actions $J_x$ and $J_y$ at several distinct amplitudes, while simultaneously minimizing diffusion of the on-energy betatron tunes. The resulting lattices share some important features with integrable ones, such as a large dynamic aperture, trajectories confined to invariant tori, robustness to resonances and errors, and a large amplitude-dependent tune-spread.

Constraint handling in constrained optimization of a storage ring multi-bend-achromat lattice

In the design of multi-bend achromat (MBA) lattices for diffraction-limited storage rings (DLSRs), usually, many magnet parameters need to be adjusted, and the constraints to be satisfied can be stringent. When using an evolutionary algorithm to optimize such a complicated lattice, there can be only few or even none of lattice solutions satisfying the constraints in the early evolution stage of the algorithm, which may significantly affect the optimization result. Therefore, the techniques for constraint handling in an evolutionary algorithm will be important for better optimizing MBA lattices. In this paper, three typical constraint handling methods that are incorporated into a multi-objective particle swarm optimization algorithm are used to optimize a hybrid 7BA lattice for a 2.2 GeV DLSR. In this lattice optimization, the impacts of the population size of the algorithm and the constraint condition on the optimization result are studied for these methods, and comparisons are also made among these methods. It is shown that, in general, the penalty function method is a better constraint handling method for optimizing MBA lattices. From the optimization result obtained by the penalty function method, a lattice with a natural emittance of about 84 pm⋅rad is selected, which has large dynamic aperture and momentum aperture.

Comparison of constrained optimization methods for designing a multi-bend achromat lattice

In the design of a multi-bend achromat (MBA) lattice for a diffraction-limited storage ring, there are usually many magnet parameters to be optimized and some stringent constraints to be satisfied. For example, to cancel out nonlinear dynamics effects, the phase advances between some sections are generally required to be set to certain values in the lattice design. For better designing a MBA lattice using an evolutionary algorithm, the handling of constraints will be important, because it is very hard to satisfy the constraints for most or even all of solutions in the early generations of the algorithm. This paper will first describe some methods for handling constraints, which are then applied to designing a hybrid 7BA lattice. The comparison of these methods shows that better lattice solutions can be obtained by including constraints into objective functions.

A Novel Non-Linear Strip-Line Kicker Driven by Fast Pulser in Common Mode

The next generation storage ring-based light sources adopt multi-bend achromat lattices to achieve a low emittance. The dynamic apertures of these machines are usually less than 10 mm so that the traditional pulsed local bump injection is difficult to achieve. Off-axis injection with a pulsed multipole or a non-linear kicker could be a viable solution which requires a moderate dynamic aperture of a few mm. In this paper, a novel non-linear kicker design is presented. Unlike pulsed sextupole or nonlinear kicker magnet, the nonlinear kicker we proposed is a traveling wave kicker with 2 strip-line electrodes driven by a nanosecond-level fast pulser in common mode. The disturbance to the stored beam is minimal since the perturbation is limited to the target bunch alone.

Multi-Bend Achromat Lattice Design for the Future of TPS Upgrade

We present a TPS upgrade option with the hybrid 7BA (H7BA) lattice. We also derive a simple formula on optimal dipole angle distribution among H7BA dipoles. The agreement is satisfactory. We also report preliminary results on the dynamic aperture (DA) optimization. Possible improvement on H7BA lattice is outlined.

Design of a hybrid ten-bend-achromat lattice for a diffraction-limited storage ring light source

Abstract The hybrid multi-bend achromat (MBA) lattice concept, proposed by ESRF EBS, has been used in some diffraction-limited storage ring (DLSR) designs due to both the lower emittance and the better nonlinear performance achieved. In this paper, to reduce the emittance for a given storage ring circumference, we extended the hybrid MBA lattice from the typical hybrid 7BA to a hybrid 10BA with three additional combined function bending magnets in the lattice center, since the emittance scales inversely with the third power of the number of bending magnets. For the hybrid 10BA lattice, two kinds of phase advances between dispersion bumps have been studied in designing a DLSR with an energy of 2.4 GeV and a circumference of 324 m. The dynamic aperture of the designed DLSR with a natural emittance of 120 ∼ 130 pm ⋅ rad is large, and the momentum aperture is also acceptable.

Magnetic cross-talk simulation between Q2 and L-bend magnets of APS-U

The Advanced Photon Source Upgrade project (APS-U) will replace the present storage ring of the Advanced Photon Source (APS) with a new storage ring based on a multi-bend achromat (MBA) lattice. Due to the increased number of magnets in each sector of the MBA lattice, the space between magnets is very limited, with the smallest separation between magnets being only 5 cm between the Q2 quadrupole in the doublet section and the adjacent M1 longitudinal gradient dipole (L-bend). Cross-talk between these magnets is of concern and is investigated in this work. Both magnets are modeled separately in Opera-3D, and then together as per their design layout in the MBA lattice. The trajectory of a 6.0 GeV electron beam through both magnets is calculated, the local field multipoles along that trajectory computed, and the integrated harmonics compared with a superposition of the fields in the individual magnets. These simulations show that the integrated quadrupole field of the Q2 magnet drops by 0.16% due to the presence of the M1, while the integrated dipole field of the M1 is practically unaffected. The effect on the higher-order multipoles at a radius of 10 mm was less than 0.01% of the integrated dipole field, and is within acceptable limits. The detailed magnetic structures of the Q2 and the M1, electron beam trajectory through these magnets, the local main and harmonic fields along the trajectory, and their integrals with and without cross-talk are reported.

Commissioning and first-year operational results ofthe MAX IV 3 GeV ring.

The MAX IV 3 GeV electron storage ring in Lund, Sweden, is the first of a new generation of light sources to make use of the multibend-achromat lattice (MBA) to achieve ultralow emitance and hence ultrahigh brightness and transverse coherence. The conceptual basis of the MAX IV 3 GeV ring project combines a robust lattice design with a number of innovative engineering choices: compact, multifunctional magnet blocks, narrow low-conductance NEG-coated copper vacuum chambers and a 100 MHz radio-frequency system with passively operated third-harmonic cavities for bunch lengthening. In this paper, commissioning and first-year operational results of the MAX IV 3 GeV ring are presented, highlighting those aspects that are believed to be most relevant for future MBA-based storage rings. The commissioning experience of the MAX IV 3 GeV ring offers in this way an opportunity for validation of concepts that are likely to be essential ingredients of future diffraction-limited light sources.

Design study of a low-emittance lattice with a five-bend achromat

The multi-bend achromat (MBA) lattice, which can provide a small horizontal emittance in the subnanometer range, shows promise for future storage-ring-based light-source facilities. We present the linear and the nonlinear properties of an optical design and the results of its optimization. The MBA lattice is designed as a five-bend achromat, and an emittance of 0.270 nm rad is achieved. The energy and the circumference of the designed ring are 3 GeV and 499.3 m, respectively. We investigated an injection system with a single-pulsed sextupole magnet in the storage ring. We describe the space allocation in the injection section and the particle dynamics of the injected beam. The investigation shows that our design exhibits a very low emittance and a sufficient dynamic aperture, and provides a suitable injection scheme for a 3-GeV light source.

ESRF-type lattice design and optimization for the High Energy Photon Source**Supported by NSFC (11475202, 11405187) and Youth Innovation Promotion Association CAS (2015009)

A new generation of storage ring-based light sources, called diffraction-limited storage rings (DLSRs), with emittance approaching the diffraction limit for multi-keV photons by means of multi-bend achromat lattices, has attracted extensive studies worldwide. Among various DLSR proposals, the hybrid multi-bend achromat concept developed at the European Synchrotron Radiation Facility (ESRF) predicts an effective way of minimizing the emittance while keeping the required chromatic sextupole strengths to an achievable level. For the High Energy Photon Source planned to be built in Beijing, an ESRF-type lattice design consisting of 48 hybrid seven-bend achromats is proposed to reach emittance as low as 60 pm·rad with a circumference of about 1296 m. Sufficient dynamic aperture, allowing vertical on-axis injection, and moderate momentum acceptance are achieved simultaneously for a promising ring performance.