Using a simplified multi spin resonances model we study the how the interference of spin resonances near a strong intrinsic spin resonance crossing effect the polarization transmission as a function of emittance for a lattice with more than two snakes.

We are presenting a design of a 2-18 GeV electron synchrotron accelerator made of permanent non-linear combined function magnets with fixed betatron tunes. It is based on the successfully commissioned CBETA Energy Recovery Linac where we used a single return beam line based on Fixed Field Alternating gradient (FFA) principle. The 2 GeV injection energy electrons come from the Recirculating Llnear Accelerator (RLA) with 500 MeV linac and a single FFA linear combined function magnet beam line to return electrons to the linac. The electron collision energy uses the same single beam line avoiding the RF accelerating cavities during selected number of turns.

We study coherent transverse beam oscillations in the EIC electron storage ring (ESR), to specify the tolerance for high-frequency ripple of the magnet power supplies. To avoid unacceptable proton emittance growth from the oscillating beam-beam kick from the electrons, the amplitude of these oscillations at the proton betatron frequency needs to be limited to about 1e-4 fraction of the beam size at the interaction point. We show that the oscillations potentially caused by the ESR magnet dipole power supply ripple could be substantial, but still tolerable, if we account for the eddy current shielding in the vacuum chamber. Beam size oscillations, potentially caused by the rippling quadrupole magnet power supplies are also studied and appear manageable.

Electron storage rings in synchrotron light sources are typically composed of 𝑁 identical sectors that repeat over the ring. Transverse plane betatron frequencies are not an integer harmonic of the beam revolution frequency to avoid that accelerator imperfection effects are turn-by-turn amplified causing beam losses. Consequently, orbit variations induced by ring parameters not affecting beam energy, do not show periodicity equal to 𝑁, while variations affecting energy do generate dispersion orbits with 𝑁 periodicity. In the relativistic case, the beam energy in a ring is set by its closed orbit length (defined by the RF frequency) jointly with the field in bend magnets. Ring thermal expansion/compression causes energy variations and periodic dispersion orbits. In the frequency domain, the real-time amplitude of these orbits can be determined from their 𝑁 spectral line magnitude and phase. This info can be used in orbit feedbacks to adjust the RF to remove orbit dispersion components avoiding conflict with the corrector magnet action. Initial measurements performed at the Advanced Light Source in Berkeley to validate the technique are presented. Additional application possibilities are also discussed.

We present a novel concept of the Fixed-Field-Alternating (FFA) permanent magnet small racetrack proton accelerator with kinetic energy range between 10-250 MeV. The horizontal and vertical tunes are fixed within the energy range providing very fast cycling with a frequency of 400 Hz to 1.3 KHz. The injector is commercially available cyclotron with RF frequency of 65 MHz. The permanent magnet synchrotron has a shape of a racetrack where the two arcs are made of combined function permanent non-linear fields magnets to provide fixed betatron tunes for the extraordinary kinetic energy range between 10 and 250 MeV.

Data driven methods have proved to be a useful tool for analyzing Hamiltonian systems. The symplectic condition is a strong constraint on Hamiltonian systems and it is therefore useful to implement this constraint into neural networks to ensure the accuracy of long term predictions about the system. One such method is the use of SympNets*, linear, activation, and gradient layers that guarantee the symplectic condition is met without the use of symplectic integration or extra gradient calculations. Data driven methods are also useful for calculating Koopman operators which aim to simplify nonlinear dynamical systems into linear ones. By using SympNets, one can ensure that the transformation described by the Koopman operator is symplectic, reversible, and more easily trained.

Proton polarization is preserved in the AGS by using helical dipoles partial snakes to avoid depolarizing vertical resonances. These same helical dipoles also drive numerous (82) weak horizontal resonances that result in polarization loss. These horizontal resonances occur at the same energy (and therefore frequency) as depolarizing resonances driven by linear betatron coupling. A new scheme has therefore been implemented to correct the snake-driven resonances with the placement of skew quadrupoles in the AGS ring powered to cancel the resonance driving term at each horizontal resonance crossing. The skew quadrupoles are required to pulse independently for each resonance to account for the variation of drive term phasing with energy. Fifteen thin skew quadrupoles have been installed in the AGS ring to implement this correction. We describe the correction principle, the magnet design and commissioning results from RHIC Run 24.

The Future Circular electron-positron Collider, FCC-ee, is a design study for a 90 km circumference luminosity-frontier and highest-energy e+e- collider. It foresees four operation modes optimized for producing different particles by colliding high-brightness lepton beams. Operating such a machine presents unique challenges, including stored beam energies up to 17.5 MJ, a value about two orders of magnitude higher than any lepton collider to date. Given the high stored beam energy, unavoidable beam losses pose a serious risk of damage. Thus, an adequate protection system has to be implemented. To address this challenge, a beam collimation system to protect the sensitive equipment of this machine is indispensable. This paper presents the studies that led to a new collimation system baseline and a collimation performance evaluation under selected beam loss scenarios.

The ESRF-EBS storage ring is operated with constant vertical emittance at 10 pm. The emittance blow-up is obtained with a magnetic shaker exciting the beam with a noise in a range of frequencies including the betatron tunes. The amplitude of the shaker is tuned by a feedback depending on the measured emittance. The coherent oscillations given to the beam by the shaker at each turn become incoherent thanks to the chromaticity and the amplitude detuning. Simulations and measurements have been performed to assess the efficiency of the emittance blow-up as a function of the chromaticities.

Beam based alignment (BBA) plays an important role in the commissioning of the fourth generation light source but it takes a lot of time with several hundreds of BPMs. To speed up BBA, a method using AC excitation, called fast BBA, has been proposed and is tested in several 3rd generation light sources. We have recently also proposed and tested a new BBA based on the neural network machine learning. In this paper, we will compare these new BBAs with conventional BBA in term of error, speed and some other aspects such as the betatron coupling.

2023 was the last year of operation for the Cooler Synchrotron (COSY) in Jülich, Germany. To prepare for the extraction of polarized protons at a momentum of 1950 MeV/c to an external target, full advantage of the most recent developments of the COSY control system was taken along with the established hardware of COSY. Challenges in beam development included the operation close to transition energy as well as seven depolarizing resonances (4 intrinsic and 3 imperfection resonances) which have to be crossed during the acceleration. To overcome the intrinsic resonances tune jumps were carried out with the Q-jump quadrupole system of COSY*. To identify the correct time window for the jump, the precise measurement of the tune** during the acceleration ramp was used. We present how the recent developments in the control system, along with the established techniques, enabled us to successfully accelerate and extract the polarized beam.

In 2023, the LHC started its Run 3 operation with 208Pb82+ beams at 6.8 ZTeV, with a substantially higher number of bunches compared to past runs. Several new hardware systems were used operationally for the first time with high-intensity beams, including bent crystal collimators in the betatron cleaning insertion. Crystal-assisted collimation reduces the leakage of secondary ion fragments to the downstream dispersion suppressors, therefore decreasing the risk of quenching superconducting magnets. Nevertheless, one of the limitations encountered during the 2023 run were events with fast beam losses impacting the collimation system, which triggered multiple premature beam aborts on Beam Loss Monitors (BLMs). In this contribution, we present energy deposition simulations for these events, performed with the FLUKA tool, aiming to quantify the quench margin for the fast loss regime (~30 ms). To assess the predictive ability of the model, benchmarks against 2023 measurements are presented. The studies provide an important input for fine-tuning BLM thresholds in future heavy-ion runs, therefore increasing the tolerance to beam losses and hence the LHC availability.

We present the results of the first experiments on 6-dimensional phase-space tracking of a single electron in a storage ring, using a linear multi-anode photomultiplier tube for simultaneously measuring transverse coordinates and arrival times of synchrotron-radiation pulses. This technology makes it possible to fully reconstruct turn-by-turn positions and momentums in all three planes for a single particle. Complete experimental particle tracking enables the first direct measurements of dynamical properties, including invariants, amplitude and energy dependence of tunes with exceptional precision, and chaotic behavior.

Observation of Schottky signals provides information on important beam and machine parameters, such as transverse emittance, betatron tune, and first-order chromaticity. However, the so-far developed theory of Schottky spectra does not include the impact of the higher-order chromaticity, known to be non-negligible in the case of the Large Hadron Collider (LHC). In this contribution, we expand the theory of Schottky spectra to also take into account second-order chromaticity. Analytical results are compared with macro-particle simulations and the errors resulting from neglecting second-order chromaticity are assessed for the case of the LHC.

In preparation for PIP2, there has been interest in running the Fermilab Booster at a higher current more indicative of the PIP2 era operation. In July 2023 an experiment was performed to study collective instabilities over the transition crossing at the Fermilab Booster. Over the transition crossing, the synchrotron tune becomes small and synchro-betatron instabilities become possible. During the experiment, an intensity threshold was observed, above which a dipole instability with losses concentrated in the tail of the bunch. These losses are consistent with the Convective Instability.

During Run 2 and Run 3 of the Large Hadron Collider (LHC), slow losses from electron cloud (e-cloud) effects have been systematically observed during the full duration of fills with closely-spaced proton bunches. In particular, these effects had been found to depend strongly on the crossing angle of the two beams and the value of the betatron functions in the interaction points. Due to this observation, the main cause of this effect was attributed to the non-linear forces induced by electron clouds forming in the vacuum chamber of the LHC Inner Triplet quadrupole magnets. In this contribution, electron cloud buildup simulations reveal that the induced forces depend strongly on the transverse coordinates of the beam particles, on time, as well as on the longitudinal coordinate within the Inner Triplet. Finally, non-linear maps are generated based on the buildup simulations, and the effect of these forces on the motion of the protons is simulated.

Integrable systems possess a hidden symmetry associated with the existence of conserved quantities known as integrals of motion. These systems play an important role in understanding general dynamics in accelerators and have potential for future designs. This work will cover two automated methods for finding integrable symplectic maps of the plane. The first algorithm is based on the observation that the evolution of an integrable system in phase space is confined to a lower-dimensional submanifold of a specific type. The second algorithm relies on an analysis of dynamical variables. Both methods rediscover some of the famous McMillan-Suris integrable mappings and ultra-discrete Painlev\'e equations. Over 100 new integrable families are presented and analyzed, some of which are isolated in the space of parameters, while others are families with one parameter (or the ratio of parameters) being either continuous or discrete. In addition, the newly discovered maps are related to a general 2D symplectic map through the use of discrete perturbation theory. A method is proposed for constructing smooth near-integrable dynamical systems based on mappings with polygon invariants.

The SSRF storage ring has been upgraded to an asymmetric lattice containing two super-bend cells, two double-mini-βy optics (DMB) cells and a superconducting wiggler (SCW) in 2019. Due to the destruction in structural symmetry, the restoration of linear optics becomes an essential issue in commissioning and routine beam dynamics maintenance. During the initial commissioning, the linear optics were well corrected with the LOCO method even though the SCW had not yet been installed. Recently, it has been found that the setups of some quadrupole power supplies tend to exceed the limits and deviate significantly from the intrinsic theoretical values, and the beta-functions and the tunes cannot be commendably recovered, leading to degradation of the storage ring performance. In this paper, the linear optics correction of the SSRF storage ring is introduced, the difficulties of the linear optics correction in asymmetric lattice are investigated, and the improved correction method and related application results are introduced.

Thomas Jefferson National Accelerator Facility (Jefferson Lab) currently studies the feasibility of upgrading its energy to 22GeV. It considers addition of six more linac passes. The highest energy passes will share two new arcs designed using the Fixed-Field Alternating Gradient (FFA) technology. The FFA arcs are built using permanent combined-function magnets. They will be connected to the linacs through transition sections that will match the optics of all six passes to the linacs. With the high number of constraints and the limited space available, we are investigating a parametric resonance technique to match the optics quasi-independently at each energy. A resonance is excited at each individual energy to selectively control its optics. The resonant dipole and quadrupole kick harmonics are imposed for all energies simultaneously using Panofsky corrector magnets placed throughout the FFA arcs. This paper presents the current progress on that transition section design.

Space charge has been a limiting effect for low energy accelerators inducing emittance growth and tune spread. Tune shift and tune spread parameters are important for avoiding resonances, which limits intensity of the beam. Circular modes are round beams with intrinsic flatness that are generated through strong coupling, where intrinsic flatness can be transformed to real plane flatness through decoupling. It is understood that flat beams increase the quality parameters of a beam due to one of the plane emittances being smaller than the other plane since luminosity and beam brightness depend inversely on the beam emittances. We show that circular mode beams manifest smaller space charge tune spread compared to uncorrelated round beams, which allows better systematic control of operating point of the beam. Minimized tune spread allows flexible operating points on the tune map. We also dedicate current and intrinsic flatness ratio limits on circular modes, which increase quality parameters without detrimental effects on the emittance increase.

The Nonlinear Injection Kicker (NIK) scheme for the Taiwan Photon Source (TPS) has been under study as a potential replacement for the current bump-based injection scheme. The evaluation encompasses three phases of the NIK scheme. In phases I and II, the orig-inal Booster to Storage Ring Transfer Line (BTS) is utilized to assess the performance of a prototype NIK. Phase III involves the redesigning of the BTS within the NIK injection scheme, thereby freeing up space occupied by the original four kickers used in the bump-based injection, for the insertion of devices. The positions of the NIKs, considerations, and limitations regarding the design of the new BTS, as well as other related issues, are thoroughly discussed.

Transverse bunch-by-bunch (BxB) feedback system has been designed, fabricated, installed, and tested with beam at the Advanced Photon Source Upgrade (APS-U) storage ring. The transverse feedback system (TFB) is designed to suppress coupled bunch instabilities and single bunch instabilities. It adapted a stripline kicker design which has the same profile as the APS-U injection/extraction kickers. The system uses digital controllers which provide powerful diagnostics, in addition to its major functionality for feedback control. This paper presents the status of the TFB system including early beam commissioning results.

A method to simultaneously determine the magnetic centers of multiple magnets with beam-based measurements is proposed. Similar to the quadrupole modulation system (QMS) method that is widely used for beam-based alignment measurement, the strengths of the group of selected magnets are modulated. The orbit shifts induced by the modulation are used to deduce the kicks applied at the magnet locations with the help of orbit response matrix calculated with the lattice model. By varying the beam orbit at the magnets, with a pair of corrector of magnets or local orbit bumps, and repeating the modulation measurement at each orbit, the magnet centers can be determined through fitting the calculated kicks versus the beam orbit. Demonstration of the method on a storage ring is presented. The method can also been applied to nonlinear magnets.