Low Emittance Lattice Research Articles

Design study of a low emittance complex bend achromat lattice

Light sources worldwide have experienced rapid growth in the last decades, pushing toward higher brightness with lower emittance to meet growing demands from the user community. The quest for higher brightness motivates the development of low-emittance ring lattices. At this point, all fourth-generation storage ring light sources employ variations of the multibend achromat (MBA) lattice. In this paper, we discuss an extension of this approach, known as complex bend achromat lattice in relation to the future NSLS-II upgrade. A detailed approach for the lattice design will be described and the developed lattice will be presented. The advantages of using our complex bend approach are evident in reaching a natural emittance as low as 23 pm at a beam energy of 3 GeV, providing a straight section of 8.4 m for long insertion devices, and acquiring a ratio of about 50% of free space with respect to the ring circumference. The design includes the use of permanent magnets largely reducing the need for power supplies. Our new approach provides an extension to the MBA concept for the next-generation light source lattice design. Published by the American Physical Society 2024

Simultaneous correction of high order geometrical driving terms with octupoles in synchrotron light sources

As the next generation of light sources is pushing toward high-brightness storage rings with ultralow emittance, the control of the beam nonlinear dynamics becomes increasingly challenging. Nonlinear perturbations, arising from sextupole cross talks, set the limit to the achievable dynamic performance of the machine. Octupoles can be an efficient mean to tackle the remaining resonant driving terms generated to the second order by the lattice sextupoles. However, they have been used sparingly in light sources because of a lack of control on higher order effects. In this paper, we discuss the optimal positioning of octupoles, with respect to the sextupoles present in the lattice, for a local and simultaneous compensation of all fourth order on-momentum phase and amplitude dependent driving terms, using only three families of octupoles. In addition, higher order geometrical terms are also minimized, including among others, second-order tune shift with amplitude. This study is a continuation of past research made on the optimal use of octupoles for the operation of future light sources. The correction method was built on observations made on a simple model, then applied to a realistic low-emittance lattice, designed in the framework of the upgrade of the National Synchrotron Light Source II, to demonstrate its potential.

Modelling the effects of optical vibrations on photon beam parameters using ray-tracing software.

A method to simulate beam properties observed at the beamline sample-point in the presence of motion of optical components has been developed at Diamond Light Source. A series of stationary ray-tracing simulations are used to model the impact on the beam stability caused by dynamic motion of optical elements. Ray-tracing simulations using SHADOW3 in OASYS, completed over multiple iterations and stitched together, permit the modelling of a pseudo-dynamic beamline. As beamline detectors operating at higher frequencies become more common, beam stability is crucial. Synchrotron ring upgrades to low-emittance lattices require increased stability of beamlines in order to conserve beam brightness. By simulating the change in beam size and position, an estimate of the impact the motion of various components have on stability is possible. The results presented in this paper focus on modelling the physical vibration of optical elements. Multiple beam parameters can be analysed in succession without manual input. The simulation code is described and the initial results obtained are presented. This method can be applied during beamline design and operation for the identification of optical elements that may introduce large errors in the beam properties at the sample-point.

Mathieu unit cell as a template for low emittance lattices

The multi-bend achromat (MBA), which often serves as a building block for modern low-emittance storage rings, is composed of a repetition of unit cells with optimized optical functions for low emittance in the achromat center, as well as end cells for dispersion and optics matching to insertion devices. In this work, we describe the simplest stable class of unit cells that are based on a longitudinal Fourier expansion, transforming Hill equations to Mathieu equations. The resulting cell class exhibits continuously changing dipolar and quadrupolar moments along the beam path. Although this elementary model is defined by only three parameters, it captures a significant amount of notions that are applied in the design of MBAs. This is especially interesting as Mathieu cells can be viewed as an elementary extension of Christofilos' original model of alternating-gradient focusing, while their sinusoidal bending and focusing functions lend themselves to future applications in undulator-like structures. Mathieu cells can be used to estimate the range of reasonable cell tunes and put an emphasis on the combination of longitudinal gradient bending and reverse bending, as well as on strong horizontal focusing to reach emittances lower than the classic theoretical minimum emittance cell. Furthermore, the lowest emittances in this model are accompanied by small absolute momentum compaction factors.

Realizing low-emittance lattice solutions with Complex Bends

A concept of new lattice element called “Complex Bend” is recently proposed at NSLS-II. Replacing the regular dipoles in the Double-Bend Achromat lattice by Complex Bends significantly reduces the beam emittance. The first attempt of lattice design for potential NSLS- II upgrade based on Complex Bend, is described. Compared with the current NSLS-II lattice, the new solution modifies only three of the six girders per cell. The linear optics has been matched keeping unchanged the lattice parameters at the straight sections, where the light-generating insertion devices are located. The Complex Bend gradient is limited by 250 T/m assuming possible use of permanent magnets. The lattice provides 65 pm emittance without damping wigglers, use of which results in further decrease of the emittance.

Nonlinear dynamics optimization with particle swarm algorithm for CANDLE storage ring low emittance lattice

Recently developed low emittance lattice of CANDLE storage ring was suffering from the typical issue of complicated nonlinear beam dynamics resulting in lowered dynamic and momentum apertures. In order to improve these characteristics of the new lattice, an optimization of nonlinear dynamics, by the usage of multi-objective particle swarm algorithm, was performed. Two optimization scenarios, with different number of objectives, were considered. This paper presents the main aspects and results of the conducted optimization procedure.

Low emittance lattice design from first principles: Reverse bending and longitudinal gradient bends

The well-known relaxed theoretical minimum emittance (TME) cell is commonly used in the design of multi-bend achromat (MBA) lattices for the new generation of diffraction limited storage rings. But significantly lower emittance at moderate focusing properties can be achieved by combining longitudinal gradient bends (LGB) and reverse bends (RB) in a periodic lattice unit cell. LGBs alone, however, are of rather limited gain. We investigate the emittance achievable for different unit cell classes as a function of the cell phase advance in a most general framework, i.e. with a minimum of assumptions on the particular cell optics. Each case is illustrated with a practical example of a realistic lattice cell, eventually leading to the LGB/RB unit cell of the baseline lattice for the upgrade of the Swiss Light Source.

Numerical optimization of a low emittance lattice cell

In the lattice designs for the next generation storage ring light sources, longitudinal gradient bending magnets and anti-bending magnets have been adopted. A logical question raised by the trend of varying the longitudinal distribution of dipole strength is: what are the optimal distributions of the dipole and quadrupole fields in a lattice cell for the purpose of minimizing the natural emittance? We studied this problem by numerically optimizing the dipole and quadrupole distributions of the normalized cell optics using the particle swarm optimization algorithm. The results reveal the features of the longitudinal field variation of the optimized cell and show that when the quadrupole gradient is increased enough, the cell tends to split into two identical cells with similar features.

Complex bend: Strong-focusing magnet for low-emittance synchrotrons

Modern synchrotron light sources are competing intensively to increase x-ray brightness and, eventually, approach the diffraction limit, which sets the final goal of lattice emittance. All recent synchrotron facility upgrades follow the multibend achromat approach by arranging small horizontal beta function and dispersion inside discrete bending dipoles. In this paper we propose a concept of a lattice element that we call ``complex bend,'' which has the potential of becoming a main building block for low emittance lattices. The complex bend is a sequence of dipole poles interleaved with strong alternate focusing so as to maintain the beta function and dispersion oscillating at low values. Comprising the ring lattice with complex bends, instead of regular dipoles, will minimize the $H$-function and reduce horizontal emittance while localizing bending to a small fraction of the storage ring circumference, which should provide more space for insertion devices. In this paper we present the details of the complex bend, considerations regarding the choice of optimal parameters, and thoughts for its practical realization. We focus here on complex bend physics and engineering design, rather than integration of this complex bend into a specific ring lattice.

Magnetic field of longitudinal gradient bend

The longitudinal gradient bend is an effective method for reducing the natural emittance in light sources. It is, however, not a common element. We have analyzed its magnetic field and derived a set of formulae. Based on the derivation, we discuss how to model the longitudinal gradient bend in accelerator codes that are used for designing electron storage rings. Strengths of multipole components can also be evaluated from the formulae, and we investigate the impact of higher order multipole components in a very low emittance lattice.

Design of a Superconducting Longitudinal Gradient Bend Magnet for the SLS Upgrade

The Paul Scherrer Institute is planning a major upgrade of the Swiss Light Source (SLS-2) with the development of a new storage ring lattice providing ultralow emittance while maintaining the locations of the undulator-based beam lines, in order to meet the growing demand of the users for higher photon flux and brilliance. The preliminary design of the lattice features a multibend achromat with seven bending magnets in each of the 12 arcs. This compact low-emittance lattice will include the use of high field longitudinal gradient bends (LGB), whose design and fabrication are particularly challenging. The superconducting dipole will have a hyperbolic longitudinal field variation with a narrow peak (FWHM of about 40-70 mm) to limit energy spread and the radiated power. The total magnet length should not exceed 400 mm with a field integral of around 0.6 Tm. The peak field value at the beam position has to be around 6 T. The LGB has to host a room temperature vacuum chamber and an antichamber to release the synchrotron radiation. This requirement determines the magnet aperture and with it the peak field at the conductor location that drives the choice of the superconducting material for the winding. In this paper, the design of the LGB magnet is presented.

Low emittance lattice design with Robinson wiggler in the arc section

Beam emittance reduction is an effective method to increase the brightness of a synchrotron light source. Robinson wiggler can play a role in the beam emittance reduction by increasing the horizontal damping partition number. A replacement of the quadrupoles in the arc section with short combined function dipoles will construct a single-periodic Robinson wiggler in the SSRF storage ring. This scheme provides a lower beam emittance, without occupying any straight section. Detailed analysis is presented in this paper.

A conceptual design of circular Higgs factory

Similar to a super B-factory, a circular Higgs factory (CHF) will require strong focusing systems near the interaction points and a low-emittance lattice in the arcs to achieve a factory luminosity. At electron beam energy of 125 GeV, beamstrahlung effects during the collision pose an additional challenge to the collider design. In particular, a large momentum acceptance at the 2% level is necessary to retain an adequate beam lifetime. This turns out to be the most challenging aspect in the design of a CHF. In this paper, an example will be provided to illustrate the beam dynamics in a CHF, emphasizing the chromatic optics. Basic optical modules and advanced analysis will be presented. Most importantly, we will show that 2% momentum aperture is achievable.

Sub-nm emittance lattice design for CANDLE storage ring

The most effective way to increase the brilliance of synchrotron light sources is the reduction of beam emittance. Following the recent developments in low emittance lattice design, a new sub-nm emittance lattice based on implementation of multi-band achromat concept and application of longitudinal gradient bending magnets was developed for CANDLE storage ring. The paper presents the main design considerations, linear and non-linear beam dynamics aspects of the new lattice proposed.

Sextupole Magnets With Variable Tilting Angle for SuperKEKB

SuperKEKB, which is an electron-positron collider with a design peak luminosity of 8 × 10 35 /(cm 2 s), is under construction. The luminosity is 40 times higher than the world record set by its predecessor, KEKB B-factory. The design of SuperKEKB is based on the “nanobeam scheme,” which is a low-emittance lattice. To achieve the low-emittance beam, the chromaticity of X-Y coupling at the interaction point (IP) should be controlled. Skew sextupole magnets are found to be effective in reducing the beam size at the IP during the KEKB operation. A novel idea of tilting normal sextupole magnets to control the ratio of the skew to the normal field component has been proposed for the positron ring at SuperKEKB. This paper presents the design and the fabrication of the tilting sextupole magnet system.

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.

Design of a multi-bend achromat lattice for 3 GeV synchrotron light source

We present a lattice design for a low-emittance and high-brilliance 3GeV synchrotron light source that has been widely investigated in the world. We show the design results for a MBA (Multi-Bend Achromat) lattice with an emittance of 1.3nm and 282.4m circumference. Each cell has 5 bending magnets that consist of outer two with bending angle of 4.5° and inner three with bending angle of 7°. The lattice is designed to be flexible and consists of 12 straight sections in which one straight section has a length of 5.9m.We have studied the dynamic aperture in the lattice with machine errors. It is shown that the designed low-emittance lattice provides sufficient dynamic aperture after COD correction. We present the results of variations of emittance, energy spread and dynamic aperture due to in-vacuum undulators in the straight sections.We performed particle tracking after the beam injection to investigate the efficiency of the injection scheme. We show the designed results of an injection scheme that shows the space allocation in injection section and the particle motions of injected beam. Our designed lattice provides a good optimization in terms of the emittance and brilliance as a light source for 3GeV energy and circumference of 28m.

Low emittance lattice for the storage ring of the Turkish Light Source Facility TURKAY**Supported by Turkish Republic Ministry of Development (DPT2006K120470)

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.

Design of a low-emittance lattice for 3.5 GeV synchrotron light source

We investigate a lattice design for a low-emittance, high-brilliance intermediate energy synchrotron light source that is being intensively performed in the world. We present the design results in detail for a non-achromatic double bend achromat lattice with an emittance of 1.1 nm and 597.6 m circumference. Each superperiod has 4 straight sections, 7 m, 5.4 m, and 2 × 2.8 m in length, giving a total of 60 straight sections in the ring. The lattice is designed to be flexible and also provides an achromatic optics with an emittance of 3.2 nm. The lattice provides high brilliance at a photon energy of a few tens of keV, which meets the requirements of hard X-ray synchrotron radiation users. We investigated the dynamic aperture in the lattice with machine errors using a simulation method that achieves the optimal tune for the ring. The low-emittance lattice provides sufficient dynamic aperture after closed orbit distortion correction. We show an estimate of variations of emittance, energy spread, and dynamic aperture due to a wiggler in the straight sections. We present the design of an injection scheme for full energy injection, the space allocation in injection section, and the particle dynamics of injected beam. Particle tracking after beam injection was performed to examine the validity of the injection scheme. Our design lattice shows good optimization in terms of the emittance, number of straight sections, brilliance, and circumference as a light source for 3.5 GeV beam energy.

Sirius: A 5BA Low-Emittance Lattice with Superbends for the New Brazilian Synchrotron Light Source

Starting in the late 1980s and into the 1990s, Brazil developed its own technology for the production of synchrotron light, designing and building UVX, a light source based on a 1.37 GeV electron storage ring with a circumference of 93 m and natural emittance of 100 nm.rad [1]. Over more than 15 years of routine operation for users, the expansion capabilities for this light source, either in terms of new beamlines or upgrades to its accelerators, have reached fundamental limits that can no longer be overcome. The first discussions about a new low-emittance light source for Brazil started in 2006 among the scientific and accelerator communities during the 16th LNLS Annual Users Meeting. In November 2008, a decision by the Brazilian Federal Government was taken to fund preliminary studies for this new source, leading to the final decision to fund the whole project in 2011. The proposed new synchrotron light source, Sirius, is based on a 3 GeV electron storage ring with a circumference of 518 m, a natural emittance of 0.28 nm.rad, and a total of 20 straight sections, of which 18 are for insertion devices. The new facility is being built at the same LNLS site as shown in Figure 1.