Design and optimization of diffraction-limited storage ring lattices based on many-objective evolutionary algorithms

Multi-objective evolutionary algorithms(MOEAs) are typically used to optimize two or three objectives in the accelerator field and perform well. However, the performance of these algorithms may severely deteriorate when the optimization objectives for an accelerator are equal to or greater than four. Recently, many-objective evolutionary algorithms(MaOEAs)that can solve problems with four or more optimization objectives have received extensive attention. In this study, two diffraction-limited storage ring(DLSR) lattices of the Extremely Brilliant Source(ESRF-EBS) type with different energies were designed and optimized using three MaOEAs and a widely used MOEA. The initial population was found to have a significant impact on the performance of the algorithms and was carefully studied. The performances of the four algorithms were compared, and the results demonstrated that the grid-based evolutionary algorithm(GrEA) had the best performance.Ma OEAs were applied in many-objective optimization of DLSR lattices for the first time, and lattices with natural emittances of 116 and 23 pm·rad were obtained at energies of 2 and 6 GeV, respectively, both with reasonable dynamic aperture and local momentum aperture(LMA). This work provides a valuable reference for future many-objective optimization of DLSRs.

Absolute dielectronic recombination rate coefficients of highly charged ions at the storage ring CSRm and CSRe

Dielectronic recombination(DR)is one of the dominant electron-ion recombination mechanisms for most highly charged ions(HCIs)in cosmic plasmas,and thus,it determines the charge state distribution and ionization balance therein.To reliably interpret spectra from cosmic sources and model the astrophysical plasmas,precise DR rate coefficients are required to build up an accurate understanding of the ionization balance of the sources.The main cooler storage ring(CSRm)and the experimental cooler storage ring(CSRe)at the Heavy-Ion Research Facility in Lanzhou(HIRFL)are both equipped with electron cooling devices,which provide an excellent experimental platform for electron-ion collision studies for HCIs.Here,the status of the DR experiments at the HIRFL-CSR is outlined,and the DR measurements with Na-like Kr25^(+)ions at the CSRm and CSRe are taken as examples.In addition,the plasma recombination rate coefficients for Ar12^(+),14^(+),Ca14^(+),16^(+),17^(+),Ni19^(+),and Kr25^(+)ions obtained at the HIRFL-CSR are provided.All the data presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j00113.00092.

Intra-beam scattering and beam lifetime in a candidate lattice of the soft X-ray diffraction-limited storage ring for the upgraded SSRF

New-generation synchrotron light sources are being designed and operated worldwide to provide brighter radiation by reducing the beam emittance to X-ray diffraction limits.Intra-beam scattering(IBS)and Touschek scattering in such facilities are significant and require attention because of their ultra-low emittance.Therefore,cure strategies need to be carefully studied to obtain highquality photon beams.For the Shanghai Synchrotron Radiation Facility Upgrade(SSRF-U),a candidate lattice of the storage ring,reaching the soft X-ray diffraction limit,was designed and presented for the first time in this study.The emittance growth and beam lifetime in the SSRF-U storage ring were studied using particle simulations for a series of different machine configurations.The gains with RF frequencies of 100 MHz and 500 MHz were compared.Along with a better filling pattern,a more suitable RF frequency was adopted in the SSRF-U.The variations in the equilibrium beam emittance with beam coupling and bunch-lengthening were identified using simulations.Optimal beam coupling and required bunch-lengthening for the SSRF-U storage ring were thus determined.The fitness of the beam energy in the SSRF-U was subsequently assessed using the obtained parameters.Additionally,the Touschek scattering and beam lifetime were calculated,and an acceptable total beam lifetime was obtained.

Using a pre-kicker to ensure safe extractions from the HEPS storage ring

The High Energy Photon Source(HEPS)is a 6 GeV diffraction-limited storage ring light source under construction.The swap-out injection is adopted with the depleted bunch recycled via high-energy accumulation in the booster.The extremely high beam energy density of the bunches with an ultra-low emittance(about 30 pm horizontally and 3 pm vertically)and high bunch charges(from 1.33 to 14.4 nC)extracted from the storage ring could cause hazardous damage to the extraction Lambertson magnet in case of extraction kicker failure.To this end,we proposed the use of a pre-kicker to spoil the bunches prior to extraction,significantly reducing the maximum beam energy density down to within a safe region while still maintaining highly efficient extractions.The main parameters of the pre-kicker are simulated and discussed.

A compact electron storage ring for lithographical applications

The physical design for a novel low-energy compact-storage-ring-based extreme ultraviolet(EUV)light source was systemically studied.The design process considers the linear and nonlinear beam optics,including transverse matching and the optimization of the dynamic aperture,momentum aperture,and beam lifetime.With a total circumference of 36.7 m and a beam energy of 400 MeV,the storage ring can operate with an average beam current of up to 1 A.With the undulator as the radiator,this facility has the potential to emit EUV radia-tion at 13.5 nm with an average power exceeding 10 W within the bandwidth.In addition,the collective instabili-ties of the lattice at high beam current were analyzed;it was found that the typical instabilities which may occur in an electron storage ring can be reasonably controlled in our design.With the advantages of variable beam energy and current,this design exhibits great promise as a new can-didate for various EUV lithographical applications requir-ing tunable radiation power.

Optimization of dynamic aperture by using non-dominated sorting genetic algorithm-Ⅱ in a diffraction-limited storage ring with solenoids for generating round beam

Purpose Round beam,i.e.,with equal horizontal and vertical emittance,is preferable than a horizontally flat one for some beamline applications in Diffraction-limited storage rings(DLSRs),for the purposes of reducing the number of photons getting discarded and better phase space match between photon and electron beam.Conventional methods of obtaining round beam inescapably results in a reduction of dynamic aperture(DA).In order to recover the DA as much as possible for improving the injection efficiency,the DA optimization by using Non-dominated sorting genetic algorithm-Ⅱ(NSGA-Ⅱ)to generate round beam,particularly to one of the designed lattice of the High Energy Photon Source(HEPS)storage ring,are presented.Method According to the general unconstrained model of NSGA-Ⅱ,we modified the standard model by using parallel computing to optimize round beam lattices with errors,especially for a strong coupling,such as solenoid scheme.Results and conclusion The results of numerical tracking verify the correction of the theory framework of solenoids with fringe fields and demonstrates the feasibility on the HEPS storage ring with errors to operate in round beam mode after optimizing DA.

Vibration Control Research for the 3rd Generation Synchrotron Light Source Storage Ring Mechanical Components

The 3rd generation synchrotron light source requires high level of electron beam orbit stability.Shanghai Synchrotron Radiation Facility (SSRF) is a 3rd generation light source under construction;its orbit stability requirement is up to micro or sub-micro range.The storage ring mechanical components vibration caused by the ground motion would influence the orbit stability.The ground motion of SSRF is severe.It is essential to control the vibration of the mechanical components.Vibration damping is an effective method to control the vibration.The author designed a vibration damping structure for the SSRF mechanical components.The test results show that it can effectively control the mechanical vibration.

Radiation Dose Monitoring and Analysis for the Construction of the Upgraded Beijing Electron-Positron Collider(BEPCⅡ) During Its Storage Ring Operation

In this paper,the average dose level is introduced in an environment and area when BEPCⅡis debugged. The typical dose graphs are offered when the electronic storage ring is debugged and works in the synchrotron radiation mode.At the same time,some suggestions about radiation protection are presented.All the data indicate that the main and local part shielding satisfy the need and attain the design target.

Modification and optimization of the storage ring lattice of the High Energy Photon Source

Purpose For the High Energy Photon Source(HEPS),a green-field fourth-generation storage ring light source,the prelimi-nary design report(PDR)was completed in 2018,when the accelerator physics design had been basically finished.During the subsequent hardware and engineering design of the HEPS storage ring based on the PDR design,a few problems and challenges emerged,calling for modifications of the lattice.Method In this paper,we will introduce the background and reasons for the modifications and present the linear optics and simulation results for the nonlinear performance of the modified lattice of the HEPS storage ring.Result and conclusion The modified lattice satisfies the requirements from hardware and engineering design.

Optimizing the lattice design of a diffraction-limited storage ring with a rational combination of particle swarm and genetic algorithms

In the lattice design of a diffraction-limited storage ring（DLSR） consisting of compact multi-bend achromats（MBAs）, it is challenging to simultaneously achieve an ultralow emittance and a satisfactory nonlinear performance, due to extremely large nonlinearities and limited tuning ranges of the element parameters. Nevertheless, in this paper we show that the potential of a DLSR design can be explored with a successive and iterative implementation of the multi-objective particle swarm optimization（MOPSO） and multi-objective genetic algorithm（MOGA）. For the High Energy Photon Source, a planned kilometer-scale DLSR, optimizations indicate that it is feasible to attain a natural emittance of about 50 pm·rad, and simultaneously realize a sufficient ring acceptance for on-axis longitudinal injection, by using a hybrid MBA lattice. In particular, this study demonstrates that a rational combination of the MOPSO and MOGA is more effective than either of them alone, in approaching the true global optima of an explorative multi-objective problem with many optimizing variables and local optima.

Towards the ultimate storage ring: The lattice design for Beijing Advanced Photon Source

A storage ring-based light source, Beijing Advanced Photon Source （BAPS）, is proposed to store a 5 GeV low-emittance electron beam and to provide high-brilliance coherent radiation. In this paper, we report our efforts of pushing down the emittance of BAPS to approach the so-called ultimate storage ring, while fixing the circumference to about 1200 m. To help deal with the challenge of beam dynamics associated with the intrinsic, very strong nonlinearities in an ultralow-emittance ring, a linear optics design and nonlinear optimization, such combination of several progressive technologies is used in the as a modified theoretical minimum emittance cell with small- aperture magnets, quasi-3rd-order achromat, theoretical analyzer based on Lie Algebra and Hamiltonian analysis, multi-objective genetic algorithm and frequency map analysis. These technologies enable us to obtain satisfactory beam dynamics in one lattice design with natural emittance of 75 pro.

Lattice optimization for the HLS-Ⅱ storage ring

The upgrade project of the Hefei Light Source （HLS）, named HLS-Ⅱ, is under way, whose storage ring will be reconstructed. The HLS-Ⅱ storage ring has lower emittance and more straight sections available for insertion devices compared with the present HLS storage ring. The scan method is applied to the linear lattice optimization for the HLS-Ⅱ storage ring to get thorough information about the lattice. To reduce the computation amount, several scans with different grid spacing values are conducted. And, the calculation of the chromatic sextupole strength for the achromatic mode is included in the scan, which is useful for nonlinear lattice optimization. To better analyze the obtained solutions in the scan, the lattice properties and the variables of quadrupole strengths are statistically analyzed. And, the process of selecting solutions is described in detail, including the choice of the working point, the settings for the emittance and optical functions, and the restriction of maximum magnet strength. Two obtained lattices, one for the achromatic mode and the other for the non-achromatic mode, are presented, including their optical functions and optimized dynamic apertures.

Physics issues in diffraction limited storage ring design

Diffraction limited electron storage ring is considered a promising candidate for future light sources,whose main characteristics are higher brilliance,better transverse coherence and better stability.The challenge of diffraction limited storage ring design is how to achieve the ultra low beam emittance with acceptable nonlinear performance.Effective linear and nonlinear parameter optimization methods based on Artificial Intelligence were developed for the storage ring physical design.As an example of application,partial physical design of HALS(Hefei Advanced Light Source),which is a diffraction limited VUV and soft X-ray light source,was introduced.Severe emittance growth due to the Intra Beam Scattering effect,which is the main obstacle to achieve ultra low emittance,was estimated quantitatively and possible cures were discussed.It is inspiring that better performance of diffraction limited storage ring can be achieved in principle with careful parameter optimization.

A design strategy of achievable linear optics for a complex storage ring lattice

A design strategy is discussed in this paper,and it provides much convenience for effectively exploring achievable linear optics and globally investigating the flexibility of a complex lattice with super-periodicity.A matching method of fractional steps,which means separately finding the standard cell setting and the matching cell setting,is adopted to simplify the complexity of the linear beam optics design in the complex lattice.The multi-objective genetic algorithm is used to find most of all the stable linear optics,and reach a target solution after multi-generational propagation,both in the standard cell and the matching cell.A fitting algorithm with gradient information is used to restore the periodicity and symmetry of the lattice,and finely adjust the linear optics for further optimization.This design strategy is applied in the Shanghai Synchrotron Radiation Facility（SSRF） storage ring,and the results are presented.

The magnet design for the HLS storage ring upgrade project

In order to improve the performance of the Hefei Light Source （HLS）,in particular to get higher brilliance synchrotron radiation and increase the number of straight section insertion devices,an upgrade project called HLSII will be launched soon.The storage ring lattice,which has a double bend achromatic structure with four periods,comprises eight dipoles,32 quadrupoles and 32 combined function sextupoles.The design and analysis of the magnets are shown in this paper,along with the optimization of the multipurpose combined function magnet,which consists of three magnets：skew quadrupole,horizontal dipole and vertical dipole,with the main sextupole magnet.This type of magnet is the first one that has been designed and used in China.The mechanical design and fabrication procedures for the magnets are also presented.

Tune optimization of the third generation light source storage ring based on Frequency Map Analysis

Tune optimization is necessary to optimize the nonlinearity of the third generation light source storage ring. In this paper we summarize the common strategies for choosing a tune and discuss tune op- timization. Frequency Map Analysis （FMA） is applied as a tune scanning tool to reveal information about nonlinear resonances and guide the tune optimization. The Shanghai Synchrotron Radiation Facility （SSRF） storage ring is taken as a test lattice, and the optimum solutions are presented in this paper. Moreover, the third order regular structural resonances excited by sextupoles are particularly investigated, and it is found that these resonances distort the tune shifts with amplitude and show a stop-band like the linear structural resonances.

Low emittance lattice for the storage ring of the Turkish Light Source Facility TURKAY

The TAC （Turkish Accelerator Center） project aims to build an accelerator center in Turkey. The first stage of the project is to construct an Infra-Red Free Electron Laser （IR-FEL） facility. The second stage is to build a synchrotron radiation facility named TURKAY, which is a third generation synchrotron radiation light source that aims to achieve a high brilliance photon beam from a low emittance electron beam at 3 GeV. The electron beam parameters are highly dependent on the magnetic lattice of the storage ring. In this paper a low emittance storage ring for TURKAY is proposed and the beam dynamic properties of the magnetic lattice are investigated.

Nonlinear optimization of the modern synchrotron radiation storage ring based on frequency map analysis

In this paper, we present a rule to improve the nonlinear solution with frequency map analysis （FMA）, and without frequently revisiting the optimization algorithm. Two aspects of FMA are emphasized. The first one is the tune shift with amplitude, which can be used to improve the solution of harmonic sextupoles, and thus obtain a large dynamic aperture. The second one is the tune diffusion rate, which can be used to select a quiet tune. Application of these ideas is carried out in the storage ring of the Shanghai Synchrotron Radiation Facility （SSRF）, and the detailed processes, as well as better solutions, are presented in this paper. Discussions about the nonlinear behaviors of off-momentum particles are also presented.

Linear optics calibration and nonlinear optimization during the commissioning of the SSRF storage ring

Phase I commissioning of the SSRF storage ring on 3.0 GeV beam energy was started at the end of December 2007. A lot of encouraging results have been obtained so far. In this paper, calibrations of the linear optics during the commissioning are discussed, and some measured results about the nonlinearity given. Calibration procedure emphasizes correcting quadrupole magnetic coefficients with the Linear Optics from Closed Orbit (LOCO) technique. After fitting the closed orbit response matrix, the linear optics of the four test modes is substantially corrected, and the measured physical parameters agree well with the designed ones.

Improved nonlinear optimization in the storage ring of the modern synchrotron radiation light source

In the storage ring of the third generation light sources, nonlinear optimization is an indispensable course in order to obtain ample dynamic acceptances and to reach high injection efficiency and long beam lifetime, especially in a low emittance lattice. An improved optimization algorithm based on the single resonance approach, which takes relative weight and initial Harmonic Sextupole Integral Strength （HSIS） as search variables, is discussed in this paper. Applications of the improved method in several test lattices are presented. Detailed analysis of the storage ring of the Shanghai Synchrotron Radiation Facility （SSRF） is particularly emphasized. Furthermore, cancellation of the driving terms is investigated to reveal the physical mechanism of the harmonic sextupole compensation. Sensitivity to the weight and the initial HSIS as well as dependence of the optimum solution on the convergent factor is analyzed.