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.

A multi-length bunch design for electron storage rings with odd buckets

A scheme with two superconducting RF cavities is designed to upgrade electron storage rings with odd buckets to multi-length bunches. In this paper, the Hefei Light Source（HLS） is given as an example for odd buckets. As it is designed for 45 buckets, which is a multiple of 3, simultaneous generation of three different lengths of bunches is proposed with the presently applied user optics. The final result, without low-α optics, is to fill HLS with long bunches of length 50 ps, medium bunches of 23 ps and short bunches of 6 ps. Every third bucket can be filled with short bunches, of which the current limit is up to 6.6 m A, more than 60 times the limit for low-α mode.Moreover, particle tracking simulations to examine the beam dynamics, performed by ELEGANT, and calculations of the beam instabilities are presented in this paper.

Analytical treatment of the nonlinear electron cloud effect and the combined effects with beam-beam and space charge nonlinear forces in storage rings

In this paper we treat first some nonlinear beam dynamics problems in storage rings, such as beam dynamic apertures due to magnetic multipoles, wiggles, beam-beam effects, nonlinear space charge effect, and then nonlinear electron cloud effect combined with beam-beam and space charge effects, analytically. This analytical treatment is applied to BEPC II. The corresponding analytical expressions developed in this paper are useful both in understanding the physics behind these problems and also in making practical quick hand estimations.

Bunch transverse emittance increase in electron storage rings

In this paper a theoretical framework to estimate the bunch transverse emittance growing in electron storage rings due to short range transverse wakefield of the machine is established. New equilibrium emittance equations are derived and applied to explain the experimentally obtained results in ATF damping ring. This equation will be useful for linear collider damping ring design.

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.

Beam based alignment using a neural network

Beams typically do not travel through the magnet centers because of errors in storage rings.The beam deviating from the quadrupole centers is affected by additional dipole fields due to magnetic field feed-down.Beam-based alignment(BBA)is often performed to determine a golden orbit where the beam circulates around the quadrupole center axes.For storage rings with many quadrupoles,the conventional BBA procedure is time-consuming,particularly in the commissioning phase,because of the necessary iterative process.In addition,the conventional BBA method can be affected by strong coupling and the nonlinearity of the storage ring optics.In this study,a novel method based on a neural network was proposed to determine the golden orbit in a much shorter time with reasonable accuracy.This golden orbit can be used directly for operation or adopted as a starting point for conventional BBA.The method was demonstrated in the HLS-II storage ring for the first time through simulations and online experiments.The results of the experiments showed that the golden orbit obtained using this new method was consistent with that obtained using the conventional BBA.The development of this new method and the corresponding experiments are reported in this paper.

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.

High-precision high-voltage detuning system for HIAF-SRing electron target

The development of a detuning system for the precision control of electron energy is a major challenge when electron targets are used in ion-storage rings.Thus,a high-precision,high-voltage,detuning system was developed for the electron target of a high-intensity heavy-ion accelerator facility-spectrometer ring(HIAF-SRing)to produce accurate electron-ion relative energies during experiments.The system consists of auxiliary,and high-voltage detuning power supplies.The front stage of the auxiliary power supply adopts an LCC resonant converter operating in the soft-switching state and an LC filter for a sinusoidal waveform output in the post-stage.The detuning power supply is a high-voltage pulse amplifier(HVPA)connected with a high-voltage DC(HVDC)module in series.In this paper,the design and development of the detuning system are described in detail,and the test bench is presented.The test results demonstrated that the detuning system conforms to the technical specifications of the dielectronic recombination(DR)experiment.Finally,a Fe15+DR spectrum was measured using the detuning system.The experimental data demonstrated a good experimental resolution and verified the reliability and feasibility of the design.

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.

Design study of APS-U-type hybrid-MBA lattice for mid-energy DLSR

In recent years,a new generation of storage ring-based light sources,known as diffraction-limited storage rings(DLSRs),whose emittance approaches the diffraction limit for the range of X-ray wavelengths of interest to the scientific community,has garnered significant attention worldwide.Researchers have begun to design and build DLSRs.Among various DLSR proposals,the hybrid multibend achromat(H-MBA)lattice enables sextupole strengths to be maintained at a reasonable level when minimizing the emittance;hence,it has been adopted in many DLSR designs.Based on the H-7BA lattice,the design of the Advanced Photon Source Upgrade Project(APS-U)can effectively reduce emittance by replacing six quadrupoles with anti-bends.Herein,we discuss the feasibility of designing an APS-U-type H-MBA lattice for the Southern Advanced Photon Source,a mid-energy DLSR light source with ultralow emittance that has been proposed to be built adjacent to the China Spallation Neutron Source.Both linear and nonlinear dynamics are optimized to obtain a detailed design of this type of lattice.The emittance is minimized,while a sufficiently large dynamic aperture(DA)and momentum acceptance(MA)are maintained.A design comprising 36 APS-U type H-7BAs,with an energy of 3 GeV and a circumference of 972 m,is achieved.The horizontal natural emittance is 20 pm·rad,with a horizontal DA of 5.8 mm,a vertical DA of 4.5 mm,and an MA of 4%,as well as a long longitudinal damping time of 120 ms.Subsequently,a few modifications are performed based on the APS-U-type lattice to reduce the maximum value of damping time from 120 to 44 ms while maintaining other performance parameters at the same level.

Research on tune feedback of the Hefei Light SourceⅡbased on machine learning

The theory of tune feedback correction and the principle of a feedback algorithm based on machine learning are introduced,with a focus on the application of lasso regression for tune feedback correction.Simulation verification and online feedback correction results are presented.The results show that,after applying machine learning,the feedback accuracy of the tune feedback system was higher,and the betatron tune stability was further improved.

Investigations of the dielectronic recombination of phosphorus-like tin at CSRm

The electron–ion recombination for phosphorus-like^（112） Sn^（35＋）has been measured at the main cooler storage ring of the Heavy Ion Research Facility in Lanzhou, China, employing an electron–ion merged-beams technique. The absolute total recombination rate coefficients for electron–ion collision energies from 0 e V–14 e V are presented. Theoretical calculations of recombination rate coefficients were performed using the Flexible Atomic Code to compare with the experimental results. The contributions of dielectronic recombination and trielectronic recombination on the experimental rate coefficients have been identified with the help of the theoretical calculation. The present results show that the trielectronic recombination has a substantial contribution to the measured electron–ion recombination spectrum of^（112）Sn^（35＋）. Although a reasonable agreement is found between the experimental and theoretical results the precise calculation of the electron–ion recombination rate coefficients for M-shell ions is still challengeable for the current theory.

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.

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.

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.