A measurable chaos indicator is used as the online optimization objective in tuning a complicated nonlinear system—the National Synchrotron Light Source-II storage ring. Through analyzing the Shannon entropy in measured Poincaré maps, not only can the commonly used nonlinear characterizations be extracted, but more importantly, the chaos can be quantified and then used for an online regularization of these maps. The method itself is general and applicable to other tunable nonlinear systems as well.

In this paper we expand the technique of characterizing nonlinear optics from off-energy closed orbits (NOECO) to cover harmonic sextupoles in storage rings. The existing NOECO technique has been successfully used to correct the chromatic sextupole errors on the MAX-IV machine (Olsson et al., 2020), however, it does not account for harmonic sextupoles, which are still widely used on many other machines. By generating vertical dispersion with chromatic skew quadrupoles, a measurable chromatic function dependence on harmonic sextupoles can be observed on hybrid dispersive orbits. Proof of concept of this technique was accomplished by simulations and beam measurements on the National Synchrotron Light Source II (NSLS-II) storage ring.

This paper reports recent lattice characterization results obtained at the National Synchrotron Light Source II (NSLS-II) storage ring, conducted without reliance on a lattice model. A pair of beam position monitors (BPMs) with bunch-by-bunch (B x B) resolution, were recently installed in a section of the storage ring free of magnetic fields. The new BPM pair measured the beam, or bunch's transverse Poincar & eacute; map precisely after the beam was excited. Linear one-turn-matrices (OTM) were then derived, and from these, the 4-dimensional coupled Twiss parameters were extracted at the locations of the BPM pair. By normalizing beam oscillation amplitudes with the Twiss parameters, the global action-variables were obtained. These action-variables facilitated the measurement of the local Twiss parameters observed by other BPMs independent on lattice model. This method is general, and particularly useful in certain scenarios such as a round beam mode in a diffraction-limited light source ring. We applied it to assess both weakly and strongly coupled lattices at the NSLS-II ring. Through analysis of the strongly coupled lattice, the quadrupole tilt errors were estimated to be less than 400 mu rad. Utilizing the BPMs' B x B resolution, for the first time we observed the variations of the linear lattice along a long bunch-train.

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.

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-beta 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.

For some synchrotron light source beamline applications, a round beam is preferable to a flat one. A conventional method of obtaining a round beam in an electron storage ring is to shift its tune close to a linear difference resonance. The linearly coupled beam dynamics is analyzed with perturbation theories, which have certain limitations. In this paper, we adopt the solution by linear matrices (SLIM) analysis to calculate exact beam sizes to design round beam lattices. The SLIM analysis can deal with a generally linearly coupled accelerator lattice. The effects of various coupling sources on beam emittances and sizes can be studied within a self-consistent frame. Both the on-and off-resonance schemes to obtain round beams are explained with examples. The SLIM formalism for two widely used magnet models: combined function bending magnets, and planar wigglers and undulators, is also derived.

A data-driven chaos indicator concept is introduced to characterize the degree of chaos for nonlinear dynamical systems. The indicator is represented by the prediction accuracy of surrogate models established purely from data. It provides a metric for the predictability of nonlinear motions in a given system. When using the indicator to implement a tune-scan for a quadratic Hénon map, the main resonances and their asymmetric stop-band widths can be identified. When applied to particle transportation in a storage ring, as particle motion becomes more chaotic, its surrogate model prediction accuracy decreases correspondingly. Therefore, the prediction accuracy, acting as a chaos indicator, can be used directly as the objective for nonlinear beam dynamics optimization. This method provides a different perspective on nonlinear beam dynamics and an efficient method for nonlinear lattice optimization. Applications in dynamic aperture optimization are demonstrated as real world examples.

Background: Stroke is known to affect both men and women; however, incidence and outcomes differ between them. Therefore, the discovery of novel, sex-specific, blood-based biomarkers for acute ischemic stroke (AIS) patients has the potential to enhance the understanding of the etiology of this deadly disease in the content of sex. The objective of this study was to identify serum metabolites associated with male and female AIS patients. Methods: Metabolites were measured with the use of untargeted, reverse-phase ultra-performance liquid chromatography-tandem mass spectrometry quantification from blood specimens collected from AIS patients. Samples were collected from 36 patients comprising each of 18 men and women with matched controls. Metabolic pathway analysis and principal component analysis (PCA) was used to differentiate metabolite profiles for male and female AIS patients from the control, while logistic regression was used to determine differences in metabolites between male and female AIS patients. Results: In female AIS patients, 14 distinct altered metabolic pathways and 49 corresponding metabolites were identified, while 39 metabolites and 5 metabolic pathways were identified in male patients. Metabolites that are predictive of ischemic stroke in female patients were 1-(1-enyl-palmitoyl)-2-arachidonoyl-GPC (P-16:0/20:4) (AUC = 0.914, 0.765–1.000), 1-(1-enyl-palmitoyl)-2-palmitoyl-GPC (P-16:0/16:0) (AUC = 0.840, 0.656–1.000), and 5,6-dihydrouracil (P-16:0/20:2) (AUC = 0.815, 0.601–1.000). Significant metabolites that were predictive of stroke in male patients were 5alpha-androstan-3alpha,17beta-diol disulfate (AUC = 0.951, 0.857–1.000), alpha-hydroxyisocaproate (AUC = 0.938, 0.832–1.000), threonate (AUC = 0.877, 0.716–1.000), and bilirubin (AUC = 0.817, 0.746–1.000). Conclusions: In the current study, the untargeted serum metabolomics platform identified multiple pathways and metabolites associated with male and female AIS patients. Further research is necessary to characterize how these metabolites are associated with the pathophysiology in male and female AIS patients.

In the light source community, a round beam rather than a flat one is preferable for many beamline users. A conventional method of shifting machine’s tune close to a difference resonance to obtain approximately round beams is usually analyzed with perturbation theories. In this paper, we adopt the Solution by LInear Matrices (SLIM) analysis to exactly calculate beam sizes when the linear coupling is present. The SLIM analysis can deal with a generally linearly coupled accelerator lattice, and the effects of various coupling sources on beam emittances and sizes are studied within a selfconsistent frame. Both the onand off-resonance schemes to obtain round beams are explained with examples. The formalism for two magnet models, combined-function bending magnets, planar wigglers and undulators, which are widely used on light source storage rings, are derived.

A numerical method to design nonlinear double- and multibend achromat (DBA and MBA) lattices with approximate invariants of motion is investigated. The search for such nonlinear lattices is motivated by Fermilab's Integrable Optics Test Accelerator, whose design is based on an integrable Hamiltonian system with two invariants of motion. While it may not be possible to design an achromatic lattice for a dedicated synchrotron light source storage ring with one or more exact invariants of motion, it is possible to tune the sextupoles and octupoles in existing double- and multibend achromat lattices to produce approximate invariants. In our procedure, the lattice is tuned while minimizing the turn-by-turn fluctuations of the Courant-Snyder actions ${J}_{x}$ and ${J}_{y}$ at several distinct amplitudes, while simultaneously minimizing diffusion of the on-energy betatron tunes. The resulting lattices share some important features with integrable ones, such as a large dynamic aperture, trajectories confined to invariant tori, robustness to resonances and errors, and a large amplitude-dependent tune spread. Compared to the nominal National Synchrotron Light Source-II lattice, the single- and multibunch instability thresholds are increased and the bunch-by-bunch feedback gain can be reduced.

A fast dynamic aperture (DA) optimization method for storage rings has been developed through the use of reversal integration. Even if dynamical systems have an exact reversal symmetry, a numerical forward integration differs from its reversal. For a chaotic trajectory, cumulative round-off errors are scaled, which results in an exponential growth on the difference. The exponential effect is a generic chaos indicator which represents the sensitivity of the chaotic motion to its initial condition. The chaos indicator of the charged particle motion can be obtained by comparing the forward integrations of particle trajectories with corresponding reversals, a.k.a. "backward integrations.'' The indicator is observable even through short-term particle tracking simulations. Therefore, adopting it as an objective function could speed up optimization. The DA of the National Synchrotron Light Source II storage ring, and another test diffraction-limited light source ring, were optimized using this method for the purpose of demonstration.

A numerical method to construct quasi-invariants (QI) has been explored in doubleand multibend achromat (DBA and MBA) lattices. The Fermilab’s Integrable Optics Test Accelerator (IOTA) and the University of Maryland Electron Ring (UMER) built with exact invariants, pave the way for discovery of a new type of nonlinear lattice. But it might be impossible to construct exact invariants in various achromatic lattices for dedicated synchrotron light source storage rings. Quasi-invariants, however, were found to be constructible by tuning the sextupoles and octupoles in the DBA and MBA lattices. In our exploration, QIs were constructed by confining the simulated trajectories to tori in the phase space at a certain Poincaré section, while simultaneously maintaining monochromatic betatron tunes. The lattices with QIs share some important features as integrable ones, such as a large dynamic aperture, confined trajectory tori, robustness to resonances and errors, and a large amplitude-dependent tune-spread.

Surrogate models have been widely used in studying nonlinear dynamical systems, including modern particle accelerators. A different perspective of viewing beam dynamical system from the prediction discrepancy of surrogate models is presented. The prediction accuracy was observed worse when particle motion is more chaotic. Therefore, such property can be used as a chaos indicator in beam dynamical system optimization. This new method was demonstrated with the National Synchrotron Light Source II storage ring.

A novel beam diagnostics technique to detect fast beam transient instabilities and glitches has been developed at National Synchrotron Light Source II (NSLS-II). Vertical spikes of beam size and centroid have been observed occasionally and randomly during high current operations. These spikes are believed to be caused by ion instabilities associated with vacuum activity localized in the ring. With the functionality of gated beam position monitor (BPM), the newly developed technique utilizes turn-by-turn (TBT) data to detect beam centroid glitches. Whenever one turn trajectory deviates from a predefined window, a global control event is generated to trigger an online TBT data acquisition. The data acquisition is synchronized for all BPMs around the ring. In the meantime, the bunch-by-bunch (BxB) data, which is acquired from a single dedicated feedback BPM, has also been collected for analyzing possible coupled bunch instabilities (CBI). In addition to CBI caused mainly by ion bursts, other types of fast transient motions, such as, the top-off residual disturbance and fast orbit disturbance, have been captured with the new tool. The sources of the glitches can be approximately localized with the synchronized TBT data from multiple BPMs around the ring.

With a Bayesian Gaussian regression approach, a systematic method for analyzing a storage ring's beam position monitor (BPM) system requirements has been developed. The ultimate performance of a ring-based accelerator, based on brightness or luminosity, is determined not only by global parameters, but also by local beam properties at some particular points of interest (POI). BPMs used for monitoring the beam properties, however, can not be located at these points. Therefore, the underlying and fundamental purpose of a BPM system is to predict whether the beam properties at POIs reach their desired values. The prediction process is a regression problem with BPM readings as the training data, but containing random noise. A Bayesian Gaussian regression approach can determine the probability distribution of the predictive errors, which can be used to conversely analyze the BPM system requirements. This approach is demonstrated by using turn-by-turn data to reconstruct a linear optics model, and predict the brightness degradation for a ring-based light source. The quality of BPMs was found to be more important than their quantity in mitigating predictive errors.

With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. Starting from the Bayes' theorem, a complete linear optics model is simplified as "likelihood functions" and "prior probability distributions". Under some assumptions, the least square algorithm and then the Jacobian matrix approach can be re-derived. The coherence of the correction algorithm is ensured through specifying a self-consistent regularization coefficient to prevent overfitting. Optimal weights for different correction objectives are obtained based on their measurement noise level. A new technique has been developed to resolve degenerated quadrupole errors when observed at a few select BPMs. A necessary condition of being distinguishable is that their optics response vectors seen at these specific BPMs should be near-orthogonal.

With the aid of machine learning techniques, the genetic algorithm has been enhanced and applied to the multi-objective optimization problem presented by the dynamic aperture of the National Synchrotron Light Source II (NSLS-II) Storage Ring. During the evolution processes employed by the genetic algorithm, the population is classified into different clusters in the search space. The clusters with top average fitness are given “elite” status. Intervention on the population is implemented by repopulating some potentially competitive candidates based on the experience learned from the accumulated data. These candidates replace randomly selected candidates among the original data pool. The average fitness of the population is therefore improved while diversity is not lost. Maintaining diversity ensures that the optimization is global rather than local. The quality of the population increases and produces more competitive descendants accelerating the evolution process significantly. When identifying the distribution of optimal candidates, they appear to be located in isolated islands within the search space. Some of these optimal candidates have been experimentally confirmed at the NSLS-II storage ring. The machine learning techniques that exploit the genetic algorithm can also be used in other population-based optimization problems such as particle swarm algorithm.

Methods of characterization of a storage ring's lattice have traditionally been intrusive to routine operations. More importantly, the lattice seen by particles can drift with the beam current due to collective effects. To circumvent this, we have developed a novel approach for dynamically characterizing a storage ring's lattice that is transparent to operations. Our approach adopts a dedicated filling pattern which has a short, separate diagnostic bunch train (DBT). Through the use of a bunch-by-bunch feedback system, the DBT can be selectively excited on demand. Gated functionality of a beam position monitor system is capable of collecting turn-by-turn data of the DBT, from which the lattice can then be characterized after excitation. As the DBT comprises only about one percent of the total operational bunches, the effects of its excitation are negligible to users. This approach allows us to localize the distributed quadrupolar wakefields generated in the storage ring vacuum chamber during beam accumulation. While effectively transparent to operations, our approach enables us to dynamically control the beta beat and phase beat, and unobtrusively optimize performance of the National Synchrotron Light Source-II accelerator during routine operations.

The injector for the National Synchrotron Light Source II (NSLS-II) storage ring consists of a 3 GeV booster synchrotron and a 200 MeV S-band linac. The linac was designed to produce either a single bunch with a charge of 0.5 nC of electrons or a train of bunches up to 300 ns long containing a total charge of 15 nC. The booster was designed to accelerate up to 15 nC each cycle in a train of bunches up to 300 ns long. Linac commissioning was completed in April 2012. Booster commissioning was started in November 2013 and completed in March 2014. All of the significant design goals were satisfied including beam emittance, energy spread, and transport efficiency. While the maximum booster charge accelerated was only 10 nC, this has proven to be more than sufficient for storage ring commissioning and operation. The injector has operated reliably during storage ring operation since then. Results will be presented showing measurements of linac and booster operating parameters achieved during commissioning and initial operation. Operating experience and reliability during the first year of NSLS-II operation will be discussed.