Review of nonlinear resonances in accelerators and storage rings; including a discussion of chaos, particle diffusion and dynamic aperture

SPS-II was designed for low emittance storage ring with compact Double-Triple Bend Achromat (DTBA) cell. To ensure sufficient machine performance, realistic machine imperfections were simulated and incorporated into the optimization process.Thus the lattice solutions were made robust against imperfections, thereby reducing the machine’s sensitivity. The solution with sufficient dynamic aperture and lifetime can be found in the presence of imperfections. The simulation steps and optimization will be discussed in this work.

Beam based alignment (BBA) plays an important role in the commissioning of the light sources. To speed up the BBA, a BBA method using AC excitation, called fast BBA (FBBA), has been proposed and is tested in several existing light sources. In the FBBA, the beam orbit is sinusoidally modulated at around 10Hz by AC correctors, and the change in the beam response when a target quadrupole magnet strength is changed is measured using fast beam position monitors (BPM) at about 10kHz. To apply FBBA to light source commissioning, a simulation study of FBBA using random variables as response functions was performed to calculate the optimal corrector strength and variation of the strength of a quadrupole as a function of the BPM noise. We also improved the FBBA and found that a new FBBA scheme using two AC correctors of different frequencies separated by 1/2π betatron phase for one plane (horizontal or vertical) can suppress the BPM offset error by up to 10.

Since synchrotron radiation sources have many advanced characteristics such as high radiation power, high brightness, broad spectral range, transverse coherence, and excellent time structure, they have become powerful tools for exploring microscopic material structures. With the growing demand for industrial researches, several dedicated industrial light sources are under operation or construction around the world. Zhejiang Industrial Photon Source (ZIPS) is designed to provide a scientific platform for industrial applications within the X-ray region in China. As a preliminary design, the ZIPS storage ring adopts a modified Triple-Bend Achromat (TBA) lattice with an energy of 2.6 GeV and a low emittance of 3.88 nm · rad. Details of the lattice design are presented in this paper.

SuperKEKB is an asymmetric lepton collider with 7-GeV electron and 4-GeV positron beams. The current vertical beta function (βy) at the collision point is set to 1 mm. Experimental results confirm that reducing βy leads to narrower dynamic apertures in both the horizontal and vertical directions, which in turn decreases the beam injection efficiency. This study presents a numerical investigation aimed at improving injection efficiency to achieve higher beam luminosity.

The Future Circular Collider (FCC-ee) at CERN requires a betatron and momentum collimation system for reducing particle backgrounds in the detectors, and for protecting the machine in case of excessive beam losses. The system is composed of primary and secondary collimators, which will be housed in one of the technical insertions of the 91 km ring. In this paper, we present a first assessment of the beam-induced power deposition in the collimators using FLUKA Monte Carlo simulations. We show that dedicated shower absorbers are needed in the collimation insertion, which intercept secondary particles from the halo collimators and reduce the energy leakage to the environment. A first optimization of the shower absorber configuration is presented, considering different absorber positions and absorber lengths. We demonstrate that the power absorption of the betatron collimation system can be increased from about 50% to over 80% by adding two shower absorbers between primary and secondary collimators.

Local coupling correction in Interaction Regions (IRs) and global coupling correction based on Base-Band Tune (BBQ) measurement have been performed routinely for RHIC operation. However, one still observes significant residual local coupling measured by beam position data. For the Electron-Ion Collider (EIC) project, betatron decoupling for the hadron beam needs to be improved to maintain a large horizontal to vertical beam emittance ratio (12:1). In this paper, we will analyze the cause for noticeable residual coupling in RHIC and propose an integrated local and global betatron coupling correction based on beam position measurements. We will also present experimental results from ML-based optimization of the local and global coupling in RHIC.

The SIS100 synchrotron, currently under construction as part of the FAIR project, is set to play a pivotal role in advancing high-intensity ion beam research. Reaching the FAIR design intensities for low charge-state heavy ions, e.g. the reference ion U28+ will, however, be challenging due to limitations of the existing SIS18 synchrotron serving as injector to SIS100. In the long-term, the integration of a new linear accelerator capable of delivering high-intensity ion beams at energies up to 200 MeV/u would open the possibility of direct multi-turn injection (MTI) into SIS100, bypassing the SIS18. This paper investigates the MTI process for U28+ beams, aiming to accumulate up to 5x1E11 particles per cycle with high efficiency and minimal particle losses on the electrostatic septum. We present a theoretical analysis of horizontal-plane MTI, outline achievable beam performance, and discuss system requirements. Additionally, the proposed layout and parameters of the MTI equipment are detailed.

The existing synchrotron SIS18 will serve as an injector for the FAIR (Facility for Antiproton and Ion Research) complex in booster mode operation. FAIR requires high-intensity beams, placing stringent demands on increasing beam currents in SIS18. Operational experience has shown that significantly increasing beam intensity in SIS18 necessitates both a higher current from UNILAC and improved injection efficiency into SIS18. Currently, injection into the SIS18 synchrotron is performed using conventional multi-turn injection (MTI) in the horizontal plane. To significantly enhance beam intensity in SIS18, we propose implementing a two-plane multi-turn injection scheme. This method aims to boost beam intensity to the desired levels (e.g., uranium beams exceeding 1x1E11 per cycle), even within the current capabilities of UNILAC. This paper discusses how MTI gain can be increased with high efficiency through a two-dimensional technique of painting Lissajous-like patterns in horizontal-vertical space using an inclined electrostatic septum. Simulation examples are presented, illustrating the characteristics of the beam created in SIS18 and the potential effects of space charge forces.

The High-Luminosity LHC (HL-LHC) project foresees nearly doubling the design beam intensity of CERN's Large Hadron Collider (LHC). A particularly pressing issue is the observation of significant beam losses at the flat bottom in the Super Proton Synchrotron (SPS) that delivers these beams to the LHC. These losses arise from multiple factors: uncaptured beam losses that are generated during the bunch rotation in the Proton Synchrotron (PS) before the transfer to the SPS; large transient beam loading effects in the RF system during multi-turn SPS injections; and the diffusion of over-populated transverse tails, which reach aperture limitations. Dedicated beam measurements were carried out in the SPS as a first step towards untangling these losses. These studies aimed to disentangle the various loss mechanisms, with a focus on the halo population and potential correlations between transverse and off-momentum tails.

APPLE-II type elliptically polarized undulators (EPUs) are critical for producing elliptically polarized light in modern synchrotron light sources. However, residual skew quadrupole components from manufacturing imperfections can couple horizontal betatron motion and dispersion to the vertical plane, changing beam size and degraded beam quality. This paper introduces a Bayesian optimization-based approach to correct these coupling effects for EPU66 at the Taiwan Photon Source (TPS). By constructing a two-dimensional coupling feed-forward table as a function of EPU gap and phase. Experimental implementation and verification with the closest-tune approach demonstrate the efficacy of this method. This article details the optimization process, mathematical framework, and experimental results, establishing a practical strategy for EPU coupling correction in TPS.

Betatron radiation is the spontaneous emission of radiation produced by the betatron oscillations of electrons in a plasma during the Laser Wakefield Acceleration (LWFA) process. A high-intensity and ultra-short laser pulse is focused on a supersonic gas jet, simultaneously creating a plasma, injecting, and accelerating electrons, which then emit this radiation. In the framework of the EuPRAXIA project, EuAPS (EuPRAXIA Advanced Photon Source) will be the first user-oriented radiation source based on betatron radiation developed at LNF-INFN Frascati in collaboration with CNR and the University of Rome Tor Vergata. This radiation source has a wide range of applications, including materials science, medical and biological research. The user facility aims to deliver 1-10 keV photons using a compact laser-driven plasma accelerator operating in a self-injection mechanism, which occurs in highly nonlinear laser-plasma interaction. In this contribution, we present the expected parameters of the source and the result of several dedicated experimental campaigns conducted within the EuAPS project to provide the preliminary characterization of the x-rays betatron radiation source.

Ion accelerators use electron cooling to improve luminosity and beam lifetime. However, extremely low momentum spread in a cold beam weakens Landau damping, enabling the development of instabilities and potentially decreasing lifetime. To combat this, the NICA Booster electron cooling system allows to generate electron beams with oscillating energy to increase the momentum spread in ion beams. Here we describe the implementation of the energy oscillation technique and provide numerical calculations predicting the achievable momentum spread.

Determining the betatronic waist shift and the $\beta^*$ at the interaction points through K-modulation in the Large Hadron Collider presents considerable challenges. This paper introduces a novel method for the measurement of these quantities, based on luminosity measurements and the van der Meer technique for reconstructing transverse bunch profiles. The strategy involves colliding multiple bunches with distinct emittances, performing emittance scans, and subsequently shifting the collision point along the longitudinal plane via RF cogging. This shows promising potential to reduce uncertainties in the optics parameters at the interaction point and to obtain measurements of the absolute beam emittance. The first measurement using this technique was carried out at the Large Hadron Collider, with the analysis and findings discussed in detail.

The 4th generation synchrotron light source, BESSY III, is expected to enable high-impact applications for users in life science, material science, energy and catalysis materials, and more. Currently in its Conceptual Design Report (CDR) phase, the feasibility of BESSY III's ambitious parameter range necessitates a thorough assessment of "collective effects". These phenomena can either compromise beam stability or degrade beam quality, potentially hindering the expected performance. In this work, we present recent estimations of the Intra Beam Scattering (IBS) and Touschek lifetime for the BESSY III lattice. The IBS leads to an increase in longitudinal and transverse emittances, it is described through the IBS growth rates and equilibrium emittances. Both quantities were computed with the ibsEmittance module from elegant and a newly implemented module in Xsuite. The Touschek effect induces beam losses along the storage ring resulting in a shorter beam lifetime. Its effect was computed using pyAT. Finally, the impact of different emittance coupling factors is studied to mitigate both effects, laying the first stone for future studies with higher-harmonic cavities.

The VEPP-2000 collider is a compact machine, which uses the round-beam concept to achieve high luminosity. Its compact size (24 m in circumference) limits the free space between the magnetic elements. Only 4 BPMs are installed in the ring with large phase advance between them (~2 pi). The key to improve its luminosity is to reduce the power of resonances. The implementing of the RDT measurement technique with our limitations is discussed. The presented experimental data gives basic information on the location of the considered magnetic perturbation causing the RDT.

This work presents the results of single-bunch-instability measurements in the Diamond storage ring. A streak camera was used to measure the bunch lengthening with current, whilst transverse multi-bunch feedback (TMBF) was utilised to quantify the charge-dependent betatron tune shifts and the head-tail instability thresholds. The results show that increasing chromaticity can be used to mitigate head-tail instabilities which can allow to accumulate higher charge in a single bunch. Using TMBF to suppress single-bunch instabilities is discussed.

The transverse beam halo population in the Large Hadron Collider (LHC) has been found to carry a significant fraction of the total stored beam energy, potentially reaching several percent. With the anticipated increase in beam brightness for the High Luminosity LHC (HL-LHC), this poses an increasing risk to machine safety, particularly during abrupt orbit shifts or critical component failures. A comprehensive understanding and an accurate modelling of the transverse beam halo are crucial for simulations of beam losses around the ring as a consequence of such failure scenarios in the HL-LHC era. Various models, including Gaussian, double-Gaussian, and q-Gaussian distributions, have been used to describe the LHC beam halos for fitting the measured distributions. This paper provides an in-depth analysis of halo modelling based on collimator scraping measurements from the LHC operational Run 2 and Run 3, and evaluates the accuracy and representativeness of these different distribution models.

The Direct Diode Detection (3D) method for transverse tune measurement, which was developed at CERN, has been implemented in numerous hadron machines and has recently been tested in electron machines. This method can provide orders of magnitude greater sensitivity to betatron oscillations than conventional beam position measurement approaches, which is particularly useful in fast-ramping synchrotrons such as the Booster of the BESSY~II light source. Typical systems used for tune measurement in an electron storage ring, which rely on the beam being in a relatively steady state, are not well-suited for fast-ramping machines; in order to measure the tune throughout the full acceleration ramp using conventional beam position approaches in the BESSY~II Booster, it is necessary to use large external excitation which disturbs injection into the storage ring. Here we describe tune measurement in the BESSY~II Booster using diode detectors, which allows for tune measurements during the full acceleration ramp with little to no external excitation and therefore no disturbance to user operation.

The Beam Loss Monitoring System (BLM) of the Large Hadron Collider (LHC) protects the accelerator against energy deposition from beam losses. One of the most critical moments regarding beam losses is the start of the beam acceleration. During this process, particles outside the bucket will not be captured in the first seconds of the start of ramp thus being lost at the machine aperture. This is expected to be the moment of minimum beam lifetime in the LHC cycle. During Run 3, losses from these off-momentum particles triggered some beam dumps. Several studies are on-going to assess a possible limitation from this loss scenario. This contribution quantifies the beam power lost at that moment and how the losses are distributed along the accelerator by the use of a dedicated BLM loss pattern recognition algorithm.