Hadron Collider Rings offer unprecedented opportunities to address fundamental scientific questions in particle and nuclear physics. To achieve these ambitious goals, the colliders must deliver exceptionally high levels of luminosity, hence require high intensity hadron beam in the ring, which leads to high beam-beam parameter, as well as comparable space charge effects. This study focuses on nonlinear effects that impact the beam dynamics within the hadron accelerator ring, including weak-strong beam-beam interactions and their interplay with space charge effects. Accurately predicting these non-linearities, particularly resonances arising during multi-turn acceleration, is critical for long beam lifetime and optimal accelerator performance. This work presents an initial attempt to develop an optimized approach that integrates space charge effects across the entire ring length while incorporating localized beam-beam interactions at specific interaction points.

Performance drift over long periods of operation due to changes in machines settings or the environment has been a longstanding problem for particle accelerators. Algorithms which are capable of tuning machine settings while keeping the performance within a desired threshold can be used to compensate for such drifts. We have developed a modified version of the Multi-Generation Gaussian Process Optimizer (MG-GPO) which is capable of tuning accelerator settings during user operation. The modified algorithm uses Gaussian Process regression to predict the performance of potential trial settings and removes ones with a high probability of giving too poor of a performance before selection for evaluation on the machine. The modified MG-GPO has been tested on analytic functions and applied to the SPEAR3 kicker-bump matching problem as a proof of concept. It is expected that the modified MG-GPO will be applied to maintain optimal trajectory of the beam injected into the SPEAR3 storage ring.

Modern particle accelerator optimization requires sophisticated computational methods to address the inherently stochastic nature of beam dynamics. This research develops a framework applying AD to SDEs that specifically addresses beam dynamics challenges in particle accelerators, focusing on accurately modeling and optimizing beam behavior in regimes dominated by stochastic processes. By incorporating key physical phenomena such as synchrotron radiation, wakefield effects, and quantum excitation, the framework aims to provide auto differentiation on the figure of merit of the phase space evolution and beam dynamics. The methodology will enable effective optimization method in a dynamic system with stochastic process.

Performance drift over long periods of operation due to changes in machines settings or the environment has been a longstanding problem for particle accelerators. Algorithms which are capable of tuning machine settings while keeping the performance within a desired threshold can be used to compensate for such drifts. We have developed a modified version of the Multi-Generation Gaussian Process Optimizer (MG-GPO) which is capable of tuning accelerator settings during user operation. The modified algorithm uses Gaussian Process regression to predict the performance of potential trial settings and removes ones with a high probability of giving too poor of a performance before selection for evaluation on the machine. The modified MG-GPO has been tested on analytic functions and applied to the SPEAR3 kicker-bump matching problem as a proof of concept. It is expected that the modified MG-GPO will be applied to maintain optimal trajectory of the beam injected into the SPEAR3 storage ring.

Modern particle accelerator optimization requires sophisticated computational methods to address the inherently stochastic nature of beam dynamics. This research develops a framework applying AD to SDEs that specifically addresses beam dynamics challenges in particle accelerators, focusing on accurately modeling and optimizing beam behavior in regimes dominated by stochastic processes. By incorporating key physical phenomena such as synchrotron radiation, wakefield effects, and quantum excitation, the framework aims to provide auto differentiation on the figure of merit of the phase space evolution and beam dynamics. The methodology will enable effective optimization method in a dynamic system with stochastic process.

A major obstacle to collaboration on accelerator projects has been the sharing of lattice description files among modeling codes. To address this problem, a standardized lattice description called the Particle Accelerator Lattice Standard (PALS) is being developed. PALS development is a community-wide international effort involving accelerator physicists from multiple institutions. Along with the standard, interface packages written in commonly used languages will be developed. The importance for developing PALS is due to the increase in scale and complexity of new machines bringing an ever greater need for global collaboration, as well as interfacing with the data-driven activities using artificial intelligence and machine learning. The proposed Particle Accelerator Lattice Standard aims to promote: (i) portability between applications, (ii) a unified open-access description for scientific data (publishing and archiving), (iii) a unified description for post-processing, visualization and analysis. We will present an introduction to the effort, an overview of the standard, examples of applications, and discuss plans and future involvements from the community.

We present a method to construct high-order polynomial approximate invariants (AI) for non-integrable Hamiltonian dynamical systems, and apply it to a modern ring-based particle accelerator. Taking advantage of a special property of one-turn transformation maps in the form of a square matrix, AIs can be constructed order-by-order iteratively. Evaluating AI with simulation data, we observe that AI's fluctuation is actually a measure of chaos. Through minimizing the fluctuations, the stable region of long-term motions, i.e., the dynamic aperture of the accelerator, could be enlarged.

JuTrack is a high-performance accelerator modeling and particle tracking package developed in the Julia programming language. With compiler-level automatic differentiation (AD), JuTrack enables fast and precise derivative computations for arbitrary differentiable simulation functions. It supports efficient modeling of complex collective effects such as space-charge forces, wakefields, and beam-beam interactions. Beyond conventional tracking simulations, JuTrack also incorporates a machine learning–based module for self-field modeling and convenience interface that brings data-driven and physics-driven model together. In this paper, we demonstrate the capability and performance of JuTrack through a broad set of beam dynamics applications and optimization across various accelerator types, including a synchrotron light source, a heavy-ion linear accelerator, and the colliders. Built on Julia’s high-performance architecture and user-friendly syntax, JuTrack provides a powerful tool for beam dynamics studies and accelerator design optimization.

A measurable chaos indicator is used as the online optimization objective in tuning a complicated nonlinear system - the National Synchrotron Light Source-II (NSLS-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.

Hadron Collider Rings offer unprecedented opportunities to address fundamental scientific questions in particle and nuclear physics. To achieve these ambitious goals, the colliders must deliver exceptionally high levels of luminosity, hence require high intensity hadron beam in the ring, which leads to high beam-beam parameter, as well as comparable space charge effects. This study focuses on nonlinear effects that impact the beam dynamics within the hadron accelerator ring, including weak-strong beam-beam interactions and their interplay with space charge effects. Accurately predicting these non-linearities, particularly resonances arising during multi-turn acceleration, is critical for long beam lifetime and optimal accelerator performance. This work presents an initial attempt to develop an optimized approach that integrates space charge effects across the entire ring length while incorporating localized beam-beam interactions at specific interaction points.

The Electron-Ion Collider (EIC), to be constructed at Brookhaven National Laboratory, will collide polarized high-energy electron beams with polarized proton and ion beams, achieving luminosities of up to 1 × 10^34 cm^−2 s^−1 in the center-of-mass energy range of 20-140 GeV. Crab cavities will be used in both EIC rings to compensate for the geometric luminosity loss due to the large crossing angle of 25 mrad in the interaction region. For the baseline design, a local crabbing scheme is adopted for both EIC rings, where crab cavities will be installed on both sides of the interaction region, and the ideal horizontal phase advance between the interaction point and the crab cavities is 90 degrees. In this article, we will study the feasibility of using a global crabbing scheme for each EIC ring, and, in particular, the case where the crab cavities in the Electron Storage Ring (ESR) will not be available during the early EIC commissioning. In this scenario, we need to reduce the electron beam's beam-beam parameter to avoid electron loss during injection.