Storage Ring Lattice Research Articles

Linear and nonlinear optimization for the HALF storage ring lattice

Hefei Advanced Light Facility (HALF) is a VUV and soft X-ray diffraction-limited storage ring, which uses a modified hybrid multi-bend achromat (HMBA) lattice. In a HMBA lattice, many nonlinear effects are cancelled by the -I transformation between sextupoles. But for amplitude-dependent tune shifts (ADTS) and high-order chromaticities, generally they cannot be controlled well, which will limit the dynamic aperture and momentum aperture. To further improve the performance of the HALF lattice, linear parameters and nonlinear dynamics are optimized in this paper. First, linear lattice, ADTS and second-order chromaticity are simultaneously optimized with magnet strengths varied in large ranges to better explore good solutions. In this optimization, lattice solutions with both low emittances and relatively good nonlinear dynamics are efficiently obtained. Then, starting from the good solution region generated above, direct optimization of dynamic aperture and Touschek lifetime based on particle tracking is performed. After this second optimization, the lattices with larger DAs and longer lifetimes are obtained for HALF. This method can also be used for optimizing other HMBA lattices.

Evaluation of beam coupling impedance by generating a dedicated database in an ultra-low emittance storage ring

The evaluation and accurate understanding of the cause of collective effects and the related instabilities using corrective measures, which may limit the achievable current per bunch, is significant for a prosperous design of charged particle accelerators. We describe in detail two dominant collective effects, i.e. space-charge and wakefield effects for a multi-bend achromat (MBA) storage ring lattice under design. We have developed a detailed impedance model, which is used to study the beam dynamics, including the wakefield effects. The beam coupling impedances due to the wakefields were calculated to construct a coupling impedance database, with the wakefields of each vacuum component being maintained in a standard format. The Self-Describing Data Sets (SDDS) toolkit was used to calculate the wake potentials for all coupling impedance contributing vacuum components, to be used for an ultra-low emittance lattice design. The ELEGANT code was utilized for the particle tracking in an element-by-element procedure along the lattice. A bunch with the Gaussian distribution was assumed to calculate the model for a distributed resistive-wall impedance and the impedance generated by geometrical discontinuities for the various accelerator elements. Moreover, we evaluated the potential-well distortion effect due to longitudinal phase space motion for a system of electron bunches. The collective effects in multi-particle systems have been evaluated for the estimation of the beam instability with more accurate results, defined by their sources in the designed lattice and describing their effects on beam instabilities with remarkable consequences like energy loss and betatron tune shift.

Approximate entropy analysis for nonlinear beam dynamics

In this paper, we applied an approximate entropy (ApEn) analysis to nonlinear beam dynamics. Due to the presence of strong nonlinear magnets, the degree of chaos in beam motion gradually increases proportionally with its amplitude. Such chaos can be quantitatively characterized with ApEn of beam turn-by-turn readings. ApEn analysis is a technique used to quantify the amount of regularity and the unpredictability of fluctuations with respect to time-series data. The ApEn, when applied as a chaos indicator, can then be used for nonlinear lattice optimization and analysis. The National Synchrotron Light Source II (NSLS-II) electron storage ring lattice was used as an example of a real-world application of our technique. Published by the American Physical Society 2024

Linear optics compensation for the HEX superconducting wiggler at NSLS-II

At the NSLS-II ring, a 1.2 m long superconducting wiggler with the maximum 4.34T magnetic field has been installed at a low-β straight section (cell 27) to drive the high energy engineering X-ray scattering (HEX) beamline. To mitigate the potential performance degradation due to the linear optics distortion, a local compensation scheme was adopted and confirmed with the online beam measurement. A feedforward control to enable a dynamic compensation of the linear optics distortion was deployed. It can maintain the storage ring lattice performance when the device main coil current ramps.

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

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

Designing the EIC electron storage ring lattice for a wide energy range

The Electron-Ion Collider (EIC) will collide electrons with hadrons at center-of-mass energies up to 140 GeV (in the case of electron-proton collisions). A 3.8-kilometer electron storage ring is being designed, which will store electrons with a range of energies up to 18 GeV for collisions at one or two interaction points. At energies up to 10 GeV the arcs will be tuned to provide 60 degree phase advance per cell in both planes, whereas at top energy of 18 GeV a 90 degree phase advance per cell will be used, which largely compensates for the horizontal emittance increase with energy. The optics must be matched at three separate energies, and the different phase-advance requirements in both the arc cells and the straight sections make this challenging. Moreover, the spin rotators must fulfill requirements for polarization and spin matching at widely different energies while satisfying technical constraints. In this paper these challenges and proposed solutions are presented and discussed.

Lattice design of the UVSOR-IV storage ring

We are designing a storage ring lattice for the future plan of UVSOR. As a candidate, we have designed a storage ring of 1 GeV electron energy, which is higher than the present value, 750 MeV. The magnetic lattice is based on a compact double bend achromat cell, which consists of two bending magnets and four focusing magnets, all of which are of combined function. The circumference is 82.5 m. The emittance is 4 nm in the achromatic condition, which becomes lower in the non-achromatic condition. The lattice has moderately large dynamic aperture with four sextupole families. The lattice of 6-fold symmetry has six straight sections of 4 m long and six of 1.5 m long. Undulators can radiate nearly diffraction-limited light in VUV. If we install high field multipole wigglers at the short straight sections, they can provide high flux tender X-rays. We are expecting usage of a laser-based accelerator as the injector, which might be developed in the next decade. As an alternative plan, we have designed a traditional injector, which consists of a linear accelerator and a booster synchrotron that can be constructed inside of the storage ring.

Online optimisation of the MAX IV 3 GeV storage ring octupoles

The MAX IV 3 GeV storage ring lattice contains three separate families of octupole magnets. During the lattice design, they served the purpose of minimising the amplitude-dependent tune shift. Ensuring the optimal settings of the octupoles is important in order to achieve the desired machine performance in terms of transverse dynamic acceptance and momentum acceptance. This paper describes the online optimisation process used to find octupole settings which improve the Touschek lifetime, and better recreate the desired amplitude-dependent tune shift, as well as their effect on transverse dynamic acceptance and momentum acceptance.

Equilibrium parameters in coupled storage ring lattices and practical applications

We calculate equilibrium emittances and damping times due to the emission of synchrotron radiation for coupled storage ring lattices by evaluating the projections of the commonly used synchrotron radiation integrals onto the normal modes of the coupled motion. Orbit distortion is included by calculating off-axis contributions to the radiation integrals. We provide explicit formulae for fast forward calculation, which have been implemented into the interactive lattice design code OPA.

Study of solution diversity in multi-objective optimization of storage ring lattice

Evolutionary algorithms, including multi-objective genetic algorithm (MOGA) and multi-objective particle swarm optimization (MOPSO), have been widely used for storage ring lattice designs, showing good performance in searching the optimal objective function values (i.e. Pareto front). Mathematically, different variable values can have the same objective function value, which is called many-to-one mapping. Different from focusing on the convergence of Pareto front, in this paper we study the diversity of variables in the optimization of storage ring lattice and make a comparison between MOGA and MOPSO. Two different lattices are taken as study examples. The study shows that the lattice solutions with almost the same objectives and different variables can show difference in some storage ring properties, which is beneficial for lattice selection. Besides, compared to MOPSO, MOGA gives a wider distribution of optimal lattice solutions in the variable space, though both algorithms can obtain almost the same Pareto front.

Design and commissioning of the new SSRF storage ring lattice with asymmetric optics

Lattice upgrade, consisting of replacing the conventional bending magnets with super-bend locally, constructing two double-mini-βy optics (DMB) and installing a superconducting wiggler (SCW), was implemented in the Beamline-Project of Shanghai Synchrotron Radiation Facility (SSRF). The symmetry of the SSRF storage ring was completely destroyed, forcing the global optics to be modified. The lattice of the new SSRF storage ring, matching the new elements perfectly, was designed. Sufficient dynamic aperture and energy acceptance were obtained by elaborate lattice design and nonlinear optimization. Study on beam dynamics, including the closed orbit correction, the linear optics correction, the coupling correction, the chromaticity correction and the nonlinear dynamic optimization, achieved good results for the new lattice. The critical step in the study is the restoration of the linear beam optics, which greatly restored the machine performance. The resulting beam parameters, as well as the operation status, are also presented.

Progress with the Diamond-II Storage Ring Lattice

Progress with the Diamond-II Storage Ring Lattice

Design of beam optics for a Super Tau-Charm Factory

Beam optics design for a Super Tau-Charm Factory (STCF) that planning in China is presented in this paper. This STCF is an electron-positron circular collider characterized with high luminosity, wide energy ranges as well as high longitudinally polarized electron beam. In order to achieve high luminosity, the recently proposed collision scheme based on large Piwinski angle and crab waist sextupole will be adopted. In this paper, the beam optical parameters and their design basis for the STCF storage ring lattice are given. In addition, the preliminary dynamic aperture and beam-beam simulation are studied to get a luminosity more than 0.5 × 1035 cm-2 s-1 at the optimized energy 2 GeV.

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

For the High Energy Photon Source (HEPS), a green-field fourth-generation storage ring light source, the preliminary 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. 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. The modified lattice satisfies the requirements from hardware and engineering design.

Magnetic design of a new source for bending magnet beamlines at ultra-low emittance ILSF ring

The Iranian Light Source Facility (ILSF) is a 3-GeV third-generation synchrotron radiation laboratory in the basic design phase. The storage ring (SR) is based on a five-bend achromat (5BA) lattice, which provides ultra-low horizontal emittance of 0.27 nm rad. It is recommended to use short-length wigglers for hard x-ray generation because of the ILSF storage ring straight section limitations. This article describes the magnetic design and optimization of the three-pole wiggler and its beam dynamics effects on the SR lattice that have been investigated for the ILSF. The 3D modeling and flux calculations have been carried out by the Radia, SPECTRA and SRW Codes.

Linear optics and coupling correction of ILSF storage ring lattice

The Iranian Light Source Facility (ILSF) is a 3 GeV synchrotron radiation facility, which is in the design stage. The ILSF storage ring design is based on a five-bend achromat lattice providing an ultralow horizontal beam emittance of 0.27 nm-rad. Inevitable errors like imperfection of magnetic field and misalignment of magnets will introduce various destructive effects on the performance of the machine. The possibility of correcting the errors should be thoroughly examined before settling the design. In this paper, we have tried to estimate the errors as realistic as possible based on the results obtained from the simulation of the elements and the accuracy of the predicted equipment for fabrication and alignment. The influence of errors on the lattice is investigated. Closed orbit distortion, beta beating and betatron coupling are corrected and improvement made in the lattice functions and machine performance will be presented.

A micro-focusing and high-flux-throughput beamline design using a bending magnet for microscopic XAFS at the High Energy Photon Source.

An optical design study of a bending-magnet beamline, based on multi-bend achromat storage ring lattices, at the High Energy Photon Source, to be built in Beijing, China, is described. The main purpose of the beamline design is to produce a micro-scale beam from a bending-magnet source with little flux loss through apertures. To maximize the flux of the focal spot, the synchrotron source will be 1:1 imaged to a virtual source by a toroidal mirror; a mirror pair will be used to collimate the virtual source into quasi-parallel light which will be refocused by a Kirkpatrick-Baez mirror pair. In the case presented here, a beamline for tender X-rays ranging from 2.1 keV to 7.8 keV, with a spot size of approximately 7 µm (H) × 6 µm (V) and flux up to 2 × 1012 photons s-1, can be achieved for the purpose of X-ray absorption fine-structure (XAFS)-related experiments, such as scanning micro-XAFS and full-field nano-XAFS.

The Higgs Factory muon collider superconducting magnets and their protection against beam decay radiation

A low-energy medium-luminosity Muon Collider (MC) is being studied as a possible Higgs Factory (HF). Electrons from muon decays will deposit more than 300 kW in superconducting (SC) magnets of the HF collider ring. This imposes significant challenges to SC magnets used in the HF storage ring (SR) and interaction regions (IR). Conceptual designs of SC dipole and quadrupole magnets are described which provide high operating gradient and field in a large aperture to accommodate the large size of muon beams (due to low β*), as well as a cooling system to intercept the large heat deposition from the showers induced by decay electrons. The distribution of heat deposition in the main elements of HF SR lattice requires large-aperture magnets to accommodate thick high-Z absorbers to protect the SC coils. Based on the developed MARS15 model and intensive simulations, a sophisticated protection system from radiation was designed for the collider SR and IR to bring the peak power density in the SC coils well below the quench limit and reduce the dynamic heat deposition in the cold mass of SC magnets by a factor of 100. The radiation protection system consists of tight tungsten masks in the magnet interconnect regions and elliptical tungsten liners in the magnet aperture optimized for each magnet. These elements reduce also the background particle fluxes in the collider detector.

Longitudinal and transverse dynamics of ions from residual gas in an electron accelerator

The ion cloud produced from residual gas in an electron accelerator can degrade machine performances and produce instabilities. The ion dynamics in an accelerator is governed by the beam-ion interaction, magnetic fields and eventual mitigation strategies. Due to the fact that the beam has a nonuniform transverse size along its orbit, the ions move longitudinally and accumulate naturally at some points in the accelerator. In order to design effective mitigation strategies it is necessary to understand the ion dynamics not only in the transverse plane but also in the longitudinal direction. After introducing the physics behind the beam-ion interaction, we show how to get accumulation points for a realistic electron storage ring lattice. Simulations of the ion cloud dynamics, including the effect of magnetic fields on the ions, clearing electrodes and clearing gaps are shown. Longitudinal ion trapping due to the magnetic mirror effect in the dipole fringe fields is also detailed. Finally, the effectiveness of clearing electrode using longitudinal clearing fields is discussed and compared to clearing electrodes producing transverse field only.

Constrained multi-objective optimization of storage ring lattices

The storage ring lattice optimization is a class of constrained multi-objective optimization problem, where in addition to low beam emittance, a large dynamic aperture for good injection efficiency and improved beam lifetime are also desirable. The convergence and computation times are of great concern for the optimization algorithms, as various objectives are to be optimized and a number of accelerator parameters to be varied over a large span with several constraints. In this paper, a study of storage ring lattice optimization using differential evolution is presented. The optimization results are compared with two most widely used optimization techniques in accelerators—genetic algorithm and particle swarm optimization. It is found that the differential evolution produces a better Pareto optimal front in reasonable computation time between two conflicting objectives-beam emittance and dispersion function in the straight section. The differential evolution was used, extensively, for the optimization of linear and nonlinear lattices of Indus-2 for exploring various operational modes within the magnet power supply capabilities.