Momentum Aperture Research Articles

Dual-energy electron storage ring

A dual-energy electron storage ring is a novel concept initially proposed to cool hadron beams at high energies. The design consists of two closed rings operating at significantly different energies: the low-energy ring and the high-energy ring. These two rings are connected by an energy recovery linac (ERL) that provides the necessary energy difference. The ERL features superconducting radio-frequency (SRF) cavities that first accelerate the beam from the low energy EL to the high energy EH and then decelerate the beam from EH to EL in the next pass. The different SRF cavities in the ERL section can be adjusted based on the applications. In this paper, we present a possible layout of a dual-energy electron storage ring. The preliminary optics of the ring is designed to optimize chromaticity correction, dynamic aperture, momentum aperture, beam lifetime, radiation damping, and intrabeam scattering effects. The primary focus of this paper is on the stability conditions and beam dynamics studies associated with this storage ring. 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.

Optimization of chromatic optics in the electron storage ring of the Electron-Ion Collider

We have developed a new chromatic compensation scheme for the electron storage ring with two low-beta interaction regions in the Electron-Ion Collider. The hybrid scheme consists of the modular chromatic matching of periodic systems and beamlines. The first-order chromatically matched solutions are linearly parameterized with the local linear chromaticities that control the higher order chromatic beatings. The parameterization enables an efficient optimization of dynamic aperture. As a result, we successfully achieve the 1% design criterion for the momentum aperture in the ring.

Application of a machine learning based algorithm to online optimization of the nonlinear beam dynamics of the Argonne Advanced Photon Source

A machine learning-based optimization algorithm, the multigeneration Gaussian process optimizer, is used to optimize the nonlinear beam dynamics of the Advanced Photon Source storage ring. The dynamic aperture (DA) and the local momentum aperture (LMA) are first optimized separately with sextupole knobs. Solutions found with these optimizations are used to seed the initial population of seeds in two-objective optimizations that simultaneously optimize the DA and LMA, which lead to a distribution of solutions with different DA and LMA performances, from which a setting suitable for operation can be selected.

Design of a diffraction-limited storage ring lattice using longitudinal gradient bends and reverse bends

Diffraction-limited storage ring (DLSR) light sources are being developed towards the goal of reaching the diffraction-limited emittances. To reduce the emittances, multi-bend achromat (MBA) lattices with many bend unit cells are used in DLSR designs. The bend unit cell with the combination of longitudinal gradient bend (LGB) and reverse bend (RB) can achieve much lower emittance, which has produced the SLS-2 7BA lattice (Streun et al., 2018). In this paper, a 6BA lattice with LGB/RB unit cells is designed for a DLSR with an energy of 2.2 GeV and 20 periods. An ultra-low natural emittance of 36 pm⋅rad is achieved for the designed DLSR, and the beta functions at straight sections are also relatively low so as to enhance the radiation brightness of insertion devices. The optimized dynamic aperture is relatively large, larger than 4 mm in the horizontal direction, and the momentum aperture is also reasonable. Besides, the intra-beam scattering effect is estimated and discussed.

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.

Storage ring nonlinear dynamics optimization with multi-objective multi-generation Gaussian process optimizer

Nonlinear beam dynamics optimization is essential in a low emittance storage ring design. Multi-objective optimization algorithms are needed in order to simultaneously optimize the dynamic aperture and the momentum aperture. In this study we demonstrate the application of a highly efficient stochastic optimization algorithm, the multi-generation Gaussian process optimizer (MG-GPO), to storage ring nonlinear dynamics optimization by successfully applying the method to the SPEAR3 upgrade lattice. It is shown that the new method, owing to its capability of selecting high rank candidates from a large number of trial solutions, converges significantly faster than the commonly used traditional algorithms, multi-objective genetic algorithms (MOGA) and particle swarm optimization (PSO).

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.

Simulation study of longitudinal injection scheme for HALS with a higher harmonic cavity system

Longitudinal injection is a promising on-axis injection scheme for diffraction-limited storage rings. In the latest version of the Hefei advanced light source (HALS), both the dynamic aperture and momentum aperture have been optimized. A longitudinal injection scheme was investigated on the HALS using a double-frequency radio frequency system. To evaluate the injection performance, various errors were considered. A series of tracking simulations were conducted, and the injection efficiency was obtained under different error levels.

Energy acceptance and on momentum aperture optimization for the Sirius project

A fast objective function to calculate Touschek lifetime and on momentum aperture is essential to explore the vast search space of strength of quadrupole and sextupole families in Sirius. Touschek lifetime is estimated by using the energy aperture (dynamic and physical), RF system parameters and driving terms. Non-linear induced betatron oscillations are considered to determine the energy aperture. On momentum aperture is estimated by using a chaos indicator and resonance crossing considerations. Touschek lifetime and on momentum aperture constitute the objective function, which was used in a multi-objective genetic algorithm to perform an optimization for Sirius.

Analytical approach to chromatic correction in the final focus system of circular colliders

A conventional final focus system in particle accelerators is systematically analyzed. We find simple relations between the parameters of two focus modules in the final telescope. Using the relations, we derive the chromatic Courant-Snyder parameters for the telescope. The parameters are scaled approximately according to $({L}^{*}/{\ensuremath{\beta}}_{y}^{*})\ensuremath{\delta}$, where ${L}^{*}$ is the distance from the interaction point to the first quadrupole, ${\ensuremath{\beta}}_{y}^{*}$ the vertical beta function at the interaction point, and $\ensuremath{\delta}$ the relative momentum deviation. Most importantly, we show how to compensate its chromaticity order by order in $\ensuremath{\delta}$ by a traditional correction module flanked by an asymmetric pair of harmonic multipoles. The method enables a circular Higgs collider with 2% momentum aperture and illuminates a path forward to 4% in the future.

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.

Genetic algorithm for chromaticity correction in diffraction limited storage rings

A multi-objective genetic algorithm is developed for optimizing nonlinearities in diffraction limited storage rings. This algorithm determines sextupole and octupole strengths for chromaticity correction that deliver optimized dynamic aperture and beam lifetime. The algorithm makes use of dominance constraints to breed desirable properties into the early generations. The momentum aperture is optimized indirectly by constraining the chromatic tune footprint and optimizing the off-energy dynamic aperture. The result is an effective and computationally efficient technique for correcting chromaticity in a storage ring while maintaining optimal dynamic aperture and beam lifetime. This framework was developed for the Swiss Light Source (SLS) upgrade project.

Measuring and optimizing the momentum aperture in a particle accelerator

Particle motion in storage rings is confined by various aperture limits, the size of which restricts the performance of the ring in terms of injection efficiency, lifetime, etc. Intrabeam scattering makes particles sweep a large portion of the phase space, where their motion may eventually be resonantly or chaotically excited to large amplitudes leading to collision with the vacuum chamber. We report here the studies performed at the Advanced Light Source (ALS) on the on- and off-momentum particle motion that provides a good understanding of these limitations. Using off-momentum simulations and experiments together with frequency map analysis, we could precisely correlate beam loss areas with resonance locations. The very good agreement between simulations and experiments allowed us to provide guidance for avoiding these dangerous areas. This analysis results in predictive improvements of the momentum aperture, which actually led to a lifetime increase of 25% at the ALS for very high bunch charge.

Momentum Precooling in the Debuncher Ring for the Fermilab Tevatron-I Project

The design of the antiproton source for the Fermilab Tevatron-I project (TeV-I) incorporates two separate rings. The Accumulator Ring uses a stochastic cooling/stacking system to accumulate a sufficient number of antiprotons for use in the Tevatron collider. The Debuncher Ring rotates buckets and debunches antiproton pulses from the production target. This requires, in the Debuncher, a choice of lattice transition energy very near the beam energy, resulting in very narrow spread in the circulation frequency. If the energy spread could be further reduced in the Debuncher before the beam is transferred to the Accumulator, operational improvements would result in: (1) the reduction of stochastic cooling power in the Accumulator; (2) the acceptance of a larger momentum bite of antiprotons in the Debuncher (thus more antiprotons); and (3) the reduction of momentum aperture in the Accumulator. This note describes a quick investigation of the feasibility of precooling within the framework of technically achievable parameters.

The variation of γt with Δp/p in the CERN ISR

The variation of the transition energy γt moc2 across the momentum aperture in the ISR has been determined by measuring the non-linear change of the revolution frequency as a function of the radial displacement and the momentum deviation and by measuring the phase oscillation frequency variation across the aperture while operating close to transition energy. The ratio of the relative slopes of γt and γ was found to be dγttc ≈ -0.75. This value could be changed to nearly zero by strongly exciting the sextupole magnets. All measurements are in good agreement with each other and with computations carried out with a modified version of the program AGS. The change of γt across the aperture causes an area change of the empty buckets while traversing the beam during phase displacement acceleration. This leads to a momentum blow-up.

Beam Transfer from the AGS to ISABELLE

The ISABELLE design current is built up by repetitive transfer of charge from the AGS. To do this, a momentum stacking method similar to the one used at the ISR has been chosen. The AGS beam bunches are synchronously transferred from the AGS into waiting rf buckets on the injection orbit at the ISA, and then slowly accelerated into the previously established debunched beam stack. This process is repeated until all the available momentum aperture in the ISA is filled up, whereupon the beam stack is rebunched and accelerated to the desired operating energy.