CNN 束流光学 储存环

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ProtoDUNE-SP is the single-phase DUNE Far Detector prototype that is under construction and will be operated at the CERN Neutrino Platform (NP) starting in 2018. ProtoDUNE-SP, a crucial part of the DUNE effort towards the construction of the first DUNE 10-kt fiducial mass far detector module (17 kt total LAr mass), is a significant experiment in its own right. With a total liquid argon (LAr) mass of 0.77 kt, it represents the largest monolithic single-phase LArTPC detector to be built to date. It's technical design is given in this report.

This paper presents a novel approach for constructing neural networks which model charged particle beam dynamics. In our approach, the Taylor maps arising in the representation of dynamics are mapped onto the weights of a polynomial neural network. The resulting network approximates the dynamical system with perfect accuracy prior to training and provides a possibility to tune the network weights on additional experimental data. We propose a symplectic regularization approach for such polynomial neural networks that always restricts the trained model to Hamiltonian systems and significantly improves the training procedure. The proposed networks can be used for beam dynamics simulations or for fine-tuning of beam optics models with experimental data. The structure of the network allows for the modeling of large accelerators with a large number of magnets. We demonstrate our approach on the examples of the existing PETRA III and the planned PETRA IV storage rings at DESY.

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Modeling of large-scale research facilities is extremely challenging due to complex physical processes and engineering problems. Here, we adopt a data-driven approach to model the longitudinal phase-space-diagnostic beamline at the photoinector of the European XFEL with an encoder-decoder neural-network model. A deep convolutional neural network (decoder) is used to build images, measured on the screen, from a small feature map generated by another neural network (encoder). We demonstrate that the model, trained only with experimental data, can make high-fidelity predictions of megapixel images for the longitudinal phase-space measurement without any prior knowledge of photoinjectors or electron beams. The prediction significantly outperforms existing methods. We also show the scalability and interpretability of the model by sharing the same decoder with more than one encoder, used for different setups of the photoinjector, and propose a pragmatic way to model a facility with various diagnostics and working points. This opens the door to a way of accurately modeling a photoinjector using neural networks and experimental data. The approach can possibly be extended to the whole accelerator and even other types of scientific facility.

A machine learning model was created to predict the electron spectrum generated by a GeV-class laser wakefield accelerator. The model was constructed from variational convolutional neural networks, which mapped the results of secondary laser and plasma diagnostics to the generated electron spectrum. An ensemble of trained networks was used to predict the electron spectrum and to provide an estimation of the uncertainty of that prediction. It is anticipated that this approach will be useful for inferring the electron spectrum prior to undergoing any process that can alter or destroy the beam. In addition, the model provides insight into the scaling of electron beam properties due to stochastic fluctuations in the laser energy and plasma electron density.

The beam interruptions (interlocks) of particle accelerators, despite being necessary safety measures, lead to abrupt operational changes and a substantial loss of beam time. A novel time series classification approach is applied to decrease beam time loss in the High-Intensity Proton Accelerator complex by forecasting interlock events. The forecasting is performed through binary classification of windows of multivariate time series. The time series are transformed into Recurrence Plots which are then classified by a Convolutional Neural Network, which not only captures the inner structure of the time series but also uses the advances of image classification techniques. Our best-performing interlock-to-stable classifier reaches an Area under the ROC Curve value of 0.71±0.01 compared to 0.65±0.01 of a Random Forest model, and it can potentially reduce the beam time loss by 0.5±0.2 s per interlock.

We present a general adaptive latent space tuning approach for improving the robustness of machine learning tools with respect to time variation and distribution shift. We demonstrate our approach by developing an encoder-decoder convolutional neural network-based virtual 6D phase space diagnostic of charged particle beams in the HiRES ultrafast electron diffraction (UED) compact particle accelerator with uncertainty quantification. Our method utilizes model-independent adaptive feedback to tune a low-dimensional 2D latent space representation of ∼1 million dimensional objects which are the 15 unique 2D projections (x,y),...,(z,p_{z}) of the 6D phase space (x,y,z,p_{x},p_{y},p_{z}) of the charged particle beams. We demonstrate our method with numerical studies of short electron bunches utilizing experimentally measured UED input beam distributions.

At present, a variety of image-based diagnostics are used in particle accelerator systems. Often times, these are viewed by a human operator who then makes appropriate adjustments to the machine. Given recent advances in using convolutional neural networks (CNNs) for image processing, it should be possible to use image diagnostics directly in control routines (NN-based or otherwise). This is especially appealing for non-intercepting diagnostics that could run continuously during beam operation. Here, we show results of a first step toward implementing such a controller: our trained CNN can predict multiple simulated downstream beam parameters at the Fermilab Accelerator Science and Technology (FAST) facility's low energy beamline using simulated virtual cathode laser images, gun phases, and solenoid strengths.

Machine learning (ML) models of accelerator systems ('surrogate models') are able to provide fast, accurate predictions of accelerator physics phenomena. However, approaches to date typically do not include measured input diagnostics, such as the initial beam distributions, which are critical for accurately representing the beam evolution through the system. In addition, these inputs often vary over time, and models that can account for these changing conditions are needed. As beam time for measurements is often limited, simulations are in some cases needed to provide sufficient training data. These typically represent the designed machine before construction; however, the behavior of the installed components may be quite different due to changes over time or static differences that were not modeled. Therefore, surrogate models that can leverage both simulation and measured data successfully are needed. We introduce an approach based on convolutional neural networks that uses the drive laser distribution and scalar settings as inputs for a photoinjector system model (here, the linac coherent light source II, LCLS-II, injector frontend). The model is able to predict scalar beam parameters and the transverse beam distribution downstream, taking into account the impact of time-varying non-uniformities in the initial transverse laser distribution. We also introduce and evaluate a transfer learning procedure for adapting the surrogate model from the simulation domain to the measurement domain, to account for differences between the two. Applying this approach to our test case results in a model that can predict test sample outputs within a mean absolute percent error of 9%. This is a substantial improvement over the model trained only on simulations, which has an error of 261% when applied to measured data. While we focus on the LCLS-II Injector frontend, these approaches for improving ML-based online modeling of injector systems could be easily adapted to other accelerator facilities.

Abstract Machine learning (ML) tools are able to learn relationships between the inputs and outputs of large complex systems directly from data. However for time-varying systems, the predictive capabilities of ML tools degrade if the systems are no longer accurately represented by the data with which the ML models were trained. For complex systems, re-training is only possible if the changes are slow relative to the rate at which large numbers of new input-output training data can be non-invasively recorded. In this work, we present an approach to deep learning for time-varying systems which does not require re-training. Our approach is to include adaptive feedback in the architecture of deep generative convolutional neural networks (CNN). The feedback is based only on available system output measurements and is applied in the encoded low-dimensional dense layers of the encoder-decoder CNNs. Our approach is inspired by biological systems in which separate groups of neurons interact and are controlled and synchronized by external feedbacks. We demonstrate this approach by developing an inverse model of a complex charged particle accelerator system, mapping output beam measurements to input beam distributions, while both the accelerator components and the unknown input beam distribution vary rapidly with time. We demonstrate our methods on experimental measurements of the input and output beam distributions of the HiRES ultra-fast electron diffraction (UED) beam line at Lawrence Berkeley National Laboratory. Our method can be successfully used to aid both physics and ML-based surrogate online models to provide non-invasive beam diagnostics. We also demonstrate our method for automatically tracking the time varying quantum efficiency map of a particle accelerator’s photocathode.

Abstract The transverse cross-sectional size and emittance are critical beam parameters that characterize the performance of the accelerator and assess the state of the beam. Inspired by the success of machine learning in image processing tasks, we have crafted a bespoke measurement system with a primary focus on accurately determine the transverse cross-sectional size and emittance of the beam. The system utilizes a beam spot detector to convert the beam spot to a light spot image, which is then projected onto the CCD camera through the telecentric lens for the acquisition. The image data collected by the camera is subsequently imported into the EPICS database developed based on ADAravis software. We employ the Gaussian fitting technique on the collected images to accurately calculate the cross-sectional size of the beam. Furthermore, by incorporating the four-level iron scanning method, the lateral emittance of the beam is calculated in a comprehensive manner. To suppress the salt and pepper noise introduced due to the presence of dark current and beam shooting phenomena on the transmission line, we propose a novel fully convolutional neural network (FCN) design with preactivated residual units. The test conducted at HLS-II confirms that the measurement uncertainty of this system is superior to 27.5 μm. Moreover, when operating at an electron beam energy of 800 MeV, the measured emittance of the accelerator is found to be 38.515 nm·rad, a value closely aligning with the theoretical value of 36.2 nm·rad. These compelling results provide strong evidence supporting the reliability of the emittance measurement algorithm, making it suitable for deployment in the forthcoming terahertz accelerator.

Abstract A physics-informed generative convolutional neural network (CNN)-based 6D phase space diagnostic is presented which generates all 15 unique 2D projections ( x, y ), ( x, y′ ),...,( z, E ) of a charged particle beam’s 6D phase space ( x, y, z, x′, y′, E ). The CNN is trained by supervised learning over a wide range of input beam distributions, accelerator parameters, and the associated 6D beam phase spaces at multiple accelerator locations. The CNN is applied in an un-supervised adaptive manner without knowledge of the input beam distribution or accelerator parameters and is robust to their unknown time variation. Adaptive feedback automatically tunes the low-dimensional latent space of the encoder-decoder CNN to predict the 6D phase space based only on 2D ( z, E ) longitudinal phase space measurements from a device such as a transverse deflecting RF cavity (TCAV). This method has the potential to provide diagnostics beyond the existing state of the art at many accelerator facilities. Studies are presented for two very different accelerators: the 5-meter-long ultra-fast electron diffraction (UED) HiRES compact accelerator at LBNL and the kilometer long plasma wakefield accelerator FACET-II at SLAC.

With the advent of increased computational resources and improved algorithms, machine learning-based models are being increasingly applied to complex problems in particle accelerators. However, such data-driven models may provide overly confident predictions with unknown errors and uncertainties. For reliable deployment of machine learning models in high-regret and safety-critical systems such as particle accelerators, estimates of prediction uncertainty are needed along with accurate point predictions. In this investigation, we evaluate Bayesian neural networks (BNN) as an approach that can provide accurate predictions along with reliably quantified uncertainties for particle accelerator problems, and compare their performance with bootstrapped ensembles of neural networks. We select three accelerator setups for this evaluation: a storage ring, a photoinjector, and a linac. The problems span different data volumes and dimensionalities (e.g., scalar predictions as well as image outputs). It is found that BNN provide accurate predictions of the mean along with reliable estimates of predictive uncertainty across the test cases. In this vein, BNN may offer an attractive alternative to deterministic deep learning tools to generate accurate predictions with quantified uncertainties in particle accelerator applications.

Machine learning techniques are used in various scientific and industry fields as a powerful tool for data analysis and automatization. The presentation is devoted to exploration of relevant machine learning methods for beam diagnostics. The target is to provide an insight into modern machine learning techniques, which can be applied to improve current beam diagnostics and general applications in accelerators. Possible concepts for future applications are also presented.

We discuss the implementation of a suite of virtual diagnostics at the FACET-II facility currently under commissioning at SLAC National Accelerator Laboratory. The diagnostics will be used for the prediction of the longitudinal phase space along the linac, spectral reconstruction of the bunch profile, and non-destructive inference of transverse beam quality (emittance) while using edge radiation at the injector dogleg and bunch compressor locations. These measurements will be folded into adaptive feedbacks and Machine Learning (ML)-based reinforcement learning controls to improve the stability and optimize the performance of the machine for different experimental configurations. In this paper we describe each of these diagnostics with expected measurement results that are based on simulation data and discuss progress towards implementation in regular operations.

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Recently, reinforcement learning (RL) algorithms have been applied to a wide range of control problems in accelerator commissioning. In order to achieve efficient and fast control, these algorithms need to be highly efficient, so as to minimize the online training time. In this paper, we incorporated the beam position monitor trend into the observation space of the twin delayed deep deterministic policy gradient (TD3) algorithm and trained two different structure agents, one based on physical prior knowledge and the other using the original TD3 network architecture. Both of the agents exhibit strong robustness in the simulated environment. The effectiveness of the agent based on physical prior knowledge has been validated in a real accelerator. Results show that the agent can overcome the difference between simulated and real accelerator environments. Once the training is completed in the simulated environment, the agent can be directly applied to the real accelerator without any online training process. The RL agent is deployed to the medium energy beam transport section of China Accelerator Facility for Superheavy Elements. Fast and automatic orbit correction is being tested with up to ten degrees of freedom. The experimental results show that the agents can correct the orbit to within 1 mm. Moreover, due to the strong robustness of the agent, when a trained agent is applied to different lattices of different particles, the orbit correction can still be completed. Since there are no online data collection and training processes, all online corrections are done within 30 s. This paper shows that, as long as the robustness of the RL algorithm is sufficient, the offline learning agents can be directly applied to online correction, which will greatly improve the efficiency of orbit correction. Such an approach to RL may find promising applications in other areas of accelerator commissioning.

The Linac coherent light source x-ray free-electron laser is a complex scientific apparatus which changes configurations multiple times per day, necessitating fast tuning strategies to reduce setup time for successive experiments. To this end, we employ a Bayesian approach to maximizing x-ray laser pulse energy by controlling groups of quadrupole magnets. A Gaussian process model provides probabilistic predictions for the machine response with respect to control parameters, enabling a balance of exploration and exploitation in the search for the global optimum. We show that the model parameters can be learned from archived scans, and correlations between devices can be extracted from the beam transport. The result is a sample-efficient optimization routine, combining both historical data and knowledge of accelerator physics to significantly outperform existing optimizers.

The Large Hadron Collider (LHC) is one of the largest scientific instruments ever built. Since opening up anew energy frontier for exploration in 2010, it has gathered a global user community of about 9000 scientists working in fundamental particle physics and the physics of hadronic matter at extreme temperature and density. To sustain and extend its discovery potential, the LHC will need a major upgrade in the 2020s. This will increase its instantaneous luminosity (rate of collisions) by a factor of five beyond the original design valueand the integrated luminosity (totalnumber of collisions) by a factor ten. The LHC is already a highly complexand exquisitely optimised machine so this upgrade must be carefully conceived and will require new infrastructures(underground and on surface)and over a decade to implement. The new configuration, known as High Luminosity LHC (HL-LHC), relies on a number of key innovations that push accelerator technology beyond its present limits. Among these are cutting-edge 11–12Tesla superconducting magnets, compact superconducting cavities for beam rotation with ultra-precise phase control, new technology and physical processes for beam collimation and 100 metre-long high-power superconducting links with negligible energy dissipation, all of which required several years of dedicated R&D; effort on a global international level. The present document describes the technologies and components that will be used to realise the projectand is intended to serve as the basis for the detailed engineering design of the HL-LHC.

Abstract Plasma-based accelerators use the strong electromagnetic fields that can be supported by plasmas to accelerate charged particles to high energies. Accelerating field structures in plasma can be generated by powerful laser pulses or charged particle beams. This research field has recently transitioned from involving a few small-scale efforts to the development of national and international networks of scientists supported by substantial investment in large-scale research infrastructure. In this New Journal of Physics 2020 Plasma Accelerator Roadmap, perspectives from experts in this field provide a summary overview of the field and insights into the research needs and developments for an international audience of scientists, including graduate students and researchers entering the field.

Data-driven science and technology offer transformative tools and methods to science. This review article highlights the latest development and progress in the interdisciplinary field of data-driven plasma science (DDPS), i.e., plasma science whose progress is driven strongly by data and data analyses. Plasma is considered to be the most ubiquitous form of observable matter in the universe. Data associated with plasmas can, therefore, cover extremely large spatial and temporal scales, and often provide essential information for other scientific disciplines. Thanks to the latest technological developments, plasma experiments, observations, and computation now produce a large amount of data that can no longer be analyzed or interpreted manually. This trend now necessitates a highly sophisticated use of high-performance computers for data analyses, making artificial intelligence and machine learning vital components of DDPS. This article contains seven primary sections, in addition to the introduction and summary. Following an overview of fundamental data-driven science, five other sections cover widely studied topics of plasma science and technologies, i.e., basic plasma physics and laboratory experiments, magnetic confinement fusion, inertial confinement fusion and high-energy-density physics, space and astronomical plasmas, and plasma technologies for industrial and other applications. The final section before the summary discusses plasma-related databases that could significantly contribute to DDPS. Each primary section starts with a brief introduction to the topic, discusses the state-of-the-art developments in the use of data and/or data-scientific approaches, and presents the summary and outlook. Despite the recent impressive signs of progress, the DDPS is still in its infancy. This article attempts to offer a broad perspective on the development of this field and identify where further innovations are required.

Uncovering the mechanisms of physics is driving a new paradigm in artificial intelligence (AI) discovery. Today, physics has enabled us to understand the AI paradigm in a wide range of matter, energy, and space-time scales through data, knowledge, priors, and laws. At the same time, the AI paradigm also draws on and introduces the knowledge and laws of physics to promote its own development. Then this new paradigm of using physical science to inspire AI is the physical science of artificial intelligence (PhysicsScience4AI, PS4AI). Although AI has become the driving force for development in various fields, there is still a “black box” phenomenon that is difficult to explain in the field of AI deep learning. This article will briefly review the connection between relevant physics disciplines (classical mechanics, electromagnetism, statistical physics, quantum mechanics) and AI. It will focus on discussing the mechanisms of physics disciplines and how they inspire the AI deep learning paradigm, and briefly introduce some related work on how AI solves physics problems. PS4AI is a new research field. At the end of the article, we summarize the challenges facing the new physics-inspired AI paradigm and look forward to the next generation of artificial intelligence technology. This article aims to provide a brief review of research related to physics-inspired AI deep algorithms and to stimulate future research and exploration by elucidating recent advances in physics.

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Understanding the concept of dynamic aperture provides essential insights into nonlinear beam dynamics, beam losses, and the beam lifetime in circular particle accelerators. This comprehension is crucial for the functioning of modern hadron synchrotrons like the CERN Large Hadron Collider and the planning of future ones such as the Future Circular Collider. The dynamic aperture defines the extent of the region in phase space where the trajectories of charged particles are bounded over numerous revolutions, the actual number being defined by the physical application. Traditional methods for calculating the dynamic aperture depend on computationally demanding numerical simulations, which require tracking over multiple turns of numerous initial conditions appropriately distributed in phase space. Prior research has shown the efficiency of a multilayer perceptron network in forecasting the dynamic aperture of the CERN Large Hadron Collider ring, achieving a remarkable speed-up of up to 200-fold compared to standard numerical tracking tools. Building on recent advancements, we conducted a comparative study of various deep learning networks based on BERT, DenseNet, ResNet and VGG architectures. The results demonstrate substantial enhancements in the prediction of the dynamic aperture, marking a significant advancement in the development of more precise and efficient surrogate models of beam dynamics.

Inevitably, various errors occur in an actual storage ring, such as magnetic field errors, magnet misalignments, and ground settlement deformation, which cause closed orbit distortion and tuning shift. Therefore, linear optics calibration is an essential procedure for storage rings. In this paper, we introduce a new method using machine learning to calibrate linear optics. This method is different from the traditional linear optics from closed orbit (LOCO) method, which is based on singular value decomposition (SVD). The machine learning model does not need to be computed by SVD. Our study shows that the machine-learning-based method can significantly reduce the difference between the model response matrix and the measurement response matrix by adjusting the strength of the quadrupoles.

We discuss the various beam dynamics problems in muon collider systems, starting from the proton accelerator needed to generate the muon beams and proceeding through the muon storage ring.

The term beta-beam has been coined for the production of a pure beam of electron neutrinos or their antiparticles through the decay of radioactive ions circulating in a storage ring. This concept requires radioactive ions to be accelerated to as high Lorentz gamma as 150. The neutrino source itself consists of a storage ring for this energy range, with long straight sections in line with the experiment(s). Such a decay ring does not exist at CERN today, nor does a high-intensity proton source for the production of the radioactive ions. Nevertheless, the existing CERN accelerator infrastructure could be used as this would still represent an important saving for a beta-beam facility.

Physics of enhanced optical cooling of particle beams in storage rings, nonlinear features of cooling and requirements to ring lattices, optical and laser systems are discussed

A general procedure for construction of the formalism of quantum beam optics for any particle is reviewed. The quantum formalism of spin-1/2 particle beam optics is presented starting {\em ab initio} with the Dirac equation. As an example of application the case of normal magnetic quadrupole lens is discussed. In the classical limit the quantum formalism leads to the well-known Lie algebraic formalism of classical particle beam optics.

In this manuscript, we provide a summary of accelerator design and the key challenges of the CEPC accelerator, both of which are laid out in detail in the Conceptual Design Report (CDR) released in November 2018. We also outline future directions and challenges. In the Addendum, we briefly describe the planning and the international organization of the CEPC. The next step for the CEPC team is to perform detailed technical design studies. Effective international collaboration would be crucial at this stage. This submission for consideration by the ESPP is part of our dedicated effort in seeking international collaboration and support.

Of the tens of thousands of particle accelerators in operation worldwide, the vast majority are not used for particle physics, but instead for applications. Some applications such as radiotherapy for cancer treatment are well-known, while others are more surprising: food irradiation using electron beams, or the hardening of road tarmac. The uses of particle beams are constantly growing in number including in medicine, industry, security, environment, and cultural heritage preservation. This lecture aims to give a broad sweep of the many uses of particle accelerators, covering technologies ranging in size from a few centimetres for industrial electron linacs through to large synchrotron light sources of hundreds of metres circumference operating as national and international facilities. We finish by discussing some of the challenges facing accelerators used in wider society.

This document summarizes the findings of the Accelerator Working Group (AWG) of the International Scoping Study (ISS) of a Future Neutrino Factory and super-beam Facility. The work of the group took place at three plenary meetings along with three workshops, and an oral summary report was presented at the NuFact06 workshop held at UC-Irvine in August, 2006. The goal was to reach consensus on a baseline design for a Neutrino Factory complex. One aspect of this endeavor was to examine critically the advantages and disadvantages of the various Neutrino Factory schemes that have been proposed in recent years.

Depending on the application people use time-domain or frequency-domain signals in order to measure or describe processes. First we will look at the definition of these terms, produce some mathematical background and then apply the tools to measurements made in the accelerator domain. We will first look at signals produced by a single bunch passing once through a detector (transfer line, linac), then periodic single bunch passages (circular accelerator) and at the end multi-bunch passages in a circular accelerator.

These notes provide an overview of Fixed-Field Alternating-Gradient (FFAG) accelerators for medical applications. We begin with a review of the basic principles of this type of accelerator, including the scaling and non-scaling types, highlighting beam dynamics issues that are of relevance to hadron ac- celerators. The potential of FFAG accelerators in the field of hadron therapy is discussed in detail, including an overview of existing medical FFAG designs. The options for FFAG treatment gantries are also considered.

This paper gives an introduction of longitudinal beam dynamics for circular accelerators. After briefly discussing some types of circular accelerators, it focuses on particle motion in synchrotrons. It summarizes the equations of motion, discusses phase-space matching during beam transfer, and introduces the Hamiltonian of longitudinal motion.

The ILC Technology Network (ITN) was established in 2022 by the ILC International Development Team, a subcommittee of the International Committee for Future Accelerators, to advance engineering studies toward the realisation of the International Linear Collider (ILC). While the ITN work packages focus on engineering activities for the ILC, their topics are also relevant to a broad range of accelerator applications in particle physics and beyond. These work packages are being carried out now by laboratories in Asia and Europe in close collaboration. This report summarises the current status of the ITN activities.

We summarize the community-based consensus for improvements concerning education, public outreach, and inclusion in Accelerator Science and Engineering that will enhance the workforce in the USA. The improvements identified reflect the product of discussions held within the 2021-2022 Snowmass community planning process by topical group AF1: Beam Physics and Accelerator Education within the Accelerator Frontier. Although the Snowmass process centers on high-energy physics, this document outlines required improvements for the entire U.S. accelerator science and engineering enterprise because education of those entering and in the field, outreach to the public, and inclusion are inextricably linked.

The radio-frequency (RF) system is the key element that generates electric fields for beam acceleration. To keep the system reliable, a highly sophisticated protection scheme is required, which also should be designed to ensure a good balance between beam availability and machine safety. Since RF systems are complex, incorporating high-voltage and high-power equipment, a good portion of machine downtime typically comes from RF systems. Equipment and component damage in RF systems results in long and expensive repairs. Protection of RF system hardware is one of the oldest machine protection concepts, dealing with the protection of individual high-power RF equipment from breakdowns. As beam power increases in modern accelerators, the protection of accelerating structures from beam-induced faults also becomes a critical aspect of protection schemes. In this article, an overview of the RF system is given, and selected topics of failure mechanisms and examples of protection requirements are introduced.

These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics. The main objective of these notes is to introduce a student who is familiar with concepts in linear algebra and partial differential equations to select topics in deep learning. These lecture notes exploit the strong connections between deep learning algorithms and the more conventional techniques of computational physics to achieve two goals. First, they use concepts from computational physics to develop an understanding of deep learning algorithms. Not surprisingly, many concepts in deep learning can be connected to similar concepts in computational physics, and one can utilize this connection to better understand these algorithms. Second, several novel deep learning algorithms can be used to solve challenging problems in computational physics. Thus, they offer someone who is interested in modeling a physical phenomena with a complementary set of tools.

The identification of the constrained dynamics of mechanical systems is often challenging. Learning methods promise to ease an analytical analysis, but require considerable amounts of data for training. We propose to combine insights from analytical mechanics with Gaussian process regression to improve the model's data efficiency and constraint integrity. The result is a Gaussian process model that incorporates a priori constraint knowledge such that its predictions adhere to Gauss' principle of least constraint. In return, predictions of the system's acceleration naturally respect potentially non-ideal (non-)holonomic equality constraints. As corollary results, our model enables to infer the acceleration of the unconstrained system from data of the constrained system and enables knowledge transfer between differing constraint configurations.

Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is tackling their ill-posed nature. Bayesian inference provides a principled approach for overcoming this by formulating the inverse problem into a statistical framework. However, it is challenging to apply when inferring fields that have discrete representations of large dimensions (the so-called "curse of dimensionality") and/or when prior information is available only in the form of previously acquired solutions. In this work, we present a novel method for efficient and accurate Bayesian inversion using deep generative models. Specifically, we demonstrate how using the approximate distribution learned by a Generative Adversarial Network (GAN) as a prior in a Bayesian update and reformulating the resulting inference problem in the low-dimensional latent space of the GAN, enables the efficient solution of large-scale Bayesian inverse problems. Our statistical framework preserves the underlying physics and is demonstrated to yield accurate results with reliable uncertainty estimates, even in the absence of information about underlying noise model, which is a significant challenge with many existing methods. We demonstrate the effectiveness of proposed method on a variety of inverse problems which include both synthetic as well as experimentally observed data.

We propose to optimize the nonlinear beam dynamics of existing and future storage rings with direct online optimization techniques. This approach may have crucial importance for the implementation of diffraction limited storage rings. In this paper considerations and algorithms for the online optimization approach are discussed. We have applied this approach to experimentally improve the dynamic aperture of the SPEAR3 storage ring with the robust conjugate direction search method and the particle swarm optimization method. The dynamic aperture was improved by more than 5 mm within a short period of time. Experimental setup and results are presented.

In the SSRF Phase-II beamline project, a Superconducting Wiggler (SW) will be installed in the electron storage ring. It may greatly impact on the beam dynamics due to the very high magnetic field. The emittance growth becomes a main problem, even after a well correction of the beam optics. A local achromatic lattice is studied, in order to combat the emittance growth and keep the good performance of the SSRF storage ring, as well as possible. Other effects of the SW are simulated and optimized as well, including the beta beating, the tune shift, the dynamic aperture, and the field error effects.

Proposed methods for measuring the electric dipole moment (EDM) of the proton use an intense, polarized proton beam stored in an all-electric storage ring "trap". At the "magic" kinetic energy of 232.792 MeV, proton spins are "frozen", for example always parallel to the instantaneous particle momentum. This paper describes an accelerator simulation code, ETEAPOT, a new component of the Unified Accelerator Libraries (UAL), to be used for long term tracking of particle orbits and spins in electric bend accelerators, in order to simulate EDM storage ring experiments. Though qualitatively much like magnetic rings, the non-constant particle velocity in electric rings give them significantly different properties, especially in weak focusing rings. Like the earlier code TEAPOT (for magnetic ring simulation) this code performs \emph{exact tracking in an idealized (approximate) lattice} rather than the more conventional approach, which is \emph{approximate tracking in a more nearly exact lattice.} The BMT equation describing the evolution of spin vectors through idealized bend elements is also solved exactly---original to this paper. Furthermore the idealization permits the code to be exactly symplectic (with no artificial "symplectification"). Any residual spurious damping or anti-damping is sufficiently small to permit reliable tracking for the long times, such as the 1000 seconds assumed in estimating the achievable EDM precision.

I describe a new scheme for selectively isolating high density low longitudinal emittance beam particles in a storage ring from the rest of the beam without emittance dilution. I discuss the general principle of the method, called longitudinal momentum mining, beam dynamics simulations and results of beam experiments. Multi-particle beam dynamics simulations applied to the Fermilab 8 GeV Recycler (a storage ring) convincingly validate the concepts and feasibility of the method, which I have demonstrated with beam experiments in the Recycler. The method presented here is the first of its kind.

For high bunch intensities the long-range beam-beam interactions are strong enough to provoke effects on the orbit. As a consequence the closed orbit changes. The closed orbit of an unperturbed machine with respect to a machine where the beam-beam force becomes more and more important has been studied and the results are presented in this paper.

We argue that storage rings can be used for the detection of low-frequency gravitational-wave background. We explain the systematic shrinkage of the machine circumference of the storage ring of the SPring-8, observed by Takao and Shimada (Proceedings of EPAC 2000, Vienna, 2000, p.1572), by the influence of the relic gravitational-wave background. We show that the systematic shrinkage of the machine circumference can be explained by a relic gravitational-wave background even if it is treated as a stochastic system incoming on the plane of the machine circumference from all quarters of the Universe. We show that the rate of the systematic shrinkage of the machine circumference does not depend on the radius of the storage ring and it should be universal for storage rings with any radius.

We studied the coupled beam motion in a storage ring between the transverse and longitudinal directions introduced by crab cavities. Analytic form of the linear decoupling transformation is derived. The equilibrium bunch distribution in an electron storage ring with a crab cavity is given, including contribution to the eigen-emittance induced by the crab cavity. Application to the short pulse generation scheme using crab cavities is considered.

Three-dimensional spiral injection enables beam storage in ultra-compact rings with nanosecond revolution periods. We report first storage of a $297 \, \mathrm{keV/}c$ electron beam in a $22 \,\mathrm{cm}$ weak-focusing ring with a $4.7\,\mathrm{ns}$ revolution period using a $140\,\mathrm{ns}$ kicker pulse. A scintillating-fiber detector observes signals $>5σ$ above noise for $\geq 1\, \mathrm{μs}$, and varying the weak-focusing field potential shifts the stored-beam region, consistent with Monte Carlo predictions, validating beam storage. This proof-of-principle opens a path to ultra-compact storage rings for next-generation precision measurements.

Magnet errors in storage rings significantly degrade beam performance, impacting the brightness and stability of the light source. Therefore, beam-based correction is crucial for the safe operation of machines and the stability of radiated photons. Unlike traditional correction methods such as linear optics from closed orbit, this paper proposes a machine learning (ML) framework to directly predict quadrupole/sextupole gradient errors and misalignment from beam position monitor-measured optics functions and closed-orbit distortion data. Based on a four-bend achromat storage ring lattice, we generate training datasets through ELEGANT numerical simulations and compare regression performance of Linear Regression, Support Vector Machine, Radial Basis Function Neural Network and Densely Connected Convolutional Network. Results demonstrate that ML models can effectively predict magnet errors and reconstruct ideal optics. This approach offers a novel strategy for accelerating storage ring commissioning and optimization, online diagnostics, and dynamic compensation for next-generation diffraction-limited rings.

Precision searches for the electric dipole moment of protons in storage ring experiments call for beam-position monitoring in the picometer range. We present the relevant fully quantum mechanical derivation of radiofrequency-driven collective oscillations of a beam in a storage ring.

SPARC collaboration at FAIR pursues the worldwide unique research program by utilizing storage ring and trapping facilities for highly-charged heavy ions. The main focus is laid on the exploration of the physics at strong, ultra-short electromagnetic fields including the fundamental interactions between electrons and heavy nuclei as well as on the experiments at the border between nuclear and atomic physics. Very recently SPARC worked out a realization scheme for experiments with highly-charged heavy-ions at relativistic energies in the High-Energy Storage Ring HESR and at very low-energies at the CRYRING coupled to the present ESR. Both facilities provide unprecedented physics opportunities already at the very early stage of FAIR operation. The installation of CRYRING, dedicated Low-energy Storage Ring (LSR) for FLAIR, may even enable a much earlier realisation of the physics program of FLAIR with slow anti-protons.

Real-time, bunch-by-bunch monitoring of transverse position, longitudinal phase, and bunch length is crucial for beam control in diffraction-limited storage rings, where complex collective dynamics pose unprecedented diagnostic challenges. This study presents a neural network framework that simultaneously predicts these parameters directly from beam position monitor waveforms. The hybrid architecture integrates specialized Multi-Layer Perceptron (MLP), Convolutional Neural Network (CNN), and Long Short-Term Memory with Attention (LSTM-Attention) sub-networks, overcoming key limitations of traditional methods such as serial processing chains and batch-mode operation. Validated on experimental data from the Shanghai Synchrotron Radiation Facility and Hefei Light Source, the model achieves high prediction accuracy with a sub-millisecond latency of 0.042 ms per bunch. This performance demonstrates its potential as a core tool for real-time, multi-parameter diagnostics and active feedback in next-generation light sources.

Application of electron cooling at ion energies above a few GeV has been limited due to reduction of electron cooling efficiency with energy and difficulty in producing and accelerating a high-current high-quality electron beam. A high-current storage-ring electron cooler offers a solution to both of these problems by maintaining high cooling beam quality through naturally-occurring synchrotron radiation damping of the electron beam. However, the range of ion energies where storage-ring electron cooling can be used has been limited by low electron beam damping rates at low ion energies and high equilibrium electron energy spread at high ion energies. This paper reports a development of a storage ring based cooler consisting of two sections with significantly different energies: the cooling and damping sections. The electron energy and other parameters in the cooling section are adjusted for optimum cooling of a stored ion beam. The beam parameters in the damping section are adjusted for optimum damping of the electron beam. The necessary energy difference is provided by an energy recovering SRF structure. A prototype linear optics of such storage-ring cooler and initial tracking simulations are presented and some potential issues such as coherent synchrotron radiation and beam break up are discussed.

The High-Energy Storage Ring (HESR) of the future International Facility for Antiproton and Ion Research (FAIR) at GSI in Darmstadt is planned as an antiproton synchrotron and storage ring in the momentum range from 1.5 to 15 GeV/c. An important feature of this new facility is the combination of phase space cooled beams with dense internal targets (e.g. pellet targets), resulting in demanding beam parameter of two operation modes: high luminosity mode with peak luminosities up to 2*10^32 cm-2 s-1, and high resolution mode with a momentum spread down to 10^-5, respectively. To reach these beam parameters very powerful phase space cooling is needed, utilizing high-energy electron cooling and high-bandwidth stochastic cooling. The effect of beam-target scattering and intra-beam interaction is investigated in order to study beam equilibria and beam losses for the two different operation modes.

Ultimate storage rings (USRs), with electron emittance smaller than 100 pm.rad and on the scale of the diffraction limit for hard X-rays in both transverse planes, have the potential to deliver photons with much higher brightness and higher transverse coherence than that projected for the rings currently operational or under construction. Worldwide efforts have been made to design and to build light sources based on USRs. How to obtain a round beam, i.e. beam with equivalent transverse emittances, is an important topic in USR studies. In this paper, we show that a locally-round beam can be achieved by using a pair of solenoid and anti-solenoid with a circularly polarized undulator located in between. Theoretical analysis and application of this novel method, particularly to one of the Beijing Advanced Photon Source storage ring design having natural emittance of 75 pm.rad, are presented.

The Beam Loss Monitors (BLM) are designed to measure the position and amount of beam loss in accelerators. In this article, we have studied the 3 GeV electron losses in the storage ring and secondary particles from the losses on the beam pipe. We have compared ionization chamber, NaI and Si radiation detectors as BLM and selected Si detector for further studies. We have calculated electron deflection angle due to magnetic field mismatches in dipole magnets, quadrupoles and sextupoles and assumed that electron beam is deflected and hit the beam pipe with the angle of 3 degrees with respect to the beam axis. The number and energy of photons and secondary particles on beam pipe and in Si detector are calculated by the MCNP code and reported in this paper.

In order to improve the stability of synchrotron radiation, we developed a new method of machine learning-based closed orbit feedback and piloted it in the storage ring of the Shanghai Synchrotron Radiation Facility (SSRF). In our experiments, not only can the machine learning-based closed orbit feedback carry out horizontal, vertical and RF frequency feedback simultaneously, but it also has better convergence and convergence speed than the traditional Slow Orbit Feed Back (SOFB) system. What's more, the residual values of the correctors' currents variations after correction can be almost ignored. This machine learning-based new method is expected to establish a new closed orbit feedback system and improve the orbit stability of the storage ring in daily operation.

A new scheme for the two-dimensional cooling of ion beams in storage rings is suggested in which ions interact with a counterpropagating broad-band laser beam. The interaction region in the direction of the ion movement is much less then the wavelength of the ion betatron oscillations. The laser beam in the orbit plane has sharp flat edge directed to the ion beam and the width of the laser beam of the order of the ion beam width. Laser beam radial position is being displaced with some velocity at first from inside and then from outside to the ion beam and decreases both betatron and synchrotron oscillations.

Position sensitive beam monitors are indispensable for the beam diagnostics in storage rings. Apart from their applications in the measurements of beam parameters, they can be used in non-destructive in-ring decay studies of radioactive ion beams as well as enhancing precision in the isochronous mass measurement technique. In this work, we introduce a novel approach based on cavities with elliptical cross-section, in order to compensate for existing limitations in ion storage rings. The design is aimed primarily for future heavy ion storage rings of the FAIR project. The conceptual design is discussed together with simulation results.

We describe an approach to learning optimal control policies for a large, linear particle accelerator using deep reinforcement learning coupled with a high-fidelity physics engine. The framework consists of an AI controller that uses deep neural nets for state and action-space representation and learns optimal policies using reward signals that are provided by the physics simulator. For this work, we only focus on controlling a small section of the entire accelerator. Nevertheless, initial results indicate that we can achieve better-than-human level performance in terms of particle beam current and distribution. The ultimate goal of this line of work is to substantially reduce the tuning time for such facilities by orders of magnitude, and achieve near-autonomous control.

Present understanding of accelerator optics is based mainly on classical mechanics and electrodynamics. In recent years quantum theory of charged-particle beam optics has been under development. In this paper the newly developed formalism is outlined.

This lecture is a brief introduction to charged particle accelerators. The aim is to provide the reader with basic concepts and tools needed to describe the motion of charged particles under the action of guiding and focussing fields, with an emphasis on those aspects that are relevant to understanding and quantifying how accelerator vacuum systems affect accelerator performance. Even though the focus is on electron accelerators and, in particular, electron storage rings used as synchrotron light sources, most of the concepts described are of general application to a wider class of particle accelerators.

This paper gives an overview of the particle transport theory essentials, the basics of particle-material interaction simulation, physical quantities needed to simulate particle transport and interactions in materials, Monte Carlo simulation flow, response of additive detectors, statistical weights and other techniques to minimize statistical errors. Effects in materials under irradiation, materials response related to component lifetime and performance are considered with a focus on high-energy and high-power accelerator applications. Implementation of simulation of particle-material interactions in the modern Monte Carlo codes along with the code s main features and results of recent benchmarking are described.

The use of nonlinear lattices with large betatron tune spreads can increase instability and space charge thresholds due to improved Landau damping. Unfortunately, the majority of nonlinear accelerator lattices turn out to be nonintegrable, producing chaotic motion and a complex network of stable and unstable resonances. Recent advances in finding the integrable nonlinear accelerator lattices have led to a proposal to construct at Fermilab a test accelerator with strong nonlinear focusing which avoids resonances and chaotic particle motion. This presentation will outline the main challenges, theoretical design solutions and construction status of the Integrable Optics Test Accelerator underway at Fermilab.

As part of the Snowmass'21 planning exercise, the Advanced Accelerator Concepts community proposed developing multi-TeV linear colliders and considered beam-beam effects for these machines. Such colliders operate under a high disruption regime with an enormous number of electron-positron pairs produced from QED effects. Thus, it requires a self-consistent treatment of the fields produced by the pairs, which is not implemented in state-of-the-art beam-beam codes such as GUINEA-PIG. WarpX is a parallel, open-source, and portable particle-in-cell code with an active developer community that models QED processes with photon and pair generation in relativistic laser-beam interactions. However, its application to beam-beam collisions has yet to be fully explored. In this work, we benchmark the luminosity spectra, photon spectra, and coherent production process from WarpX against GUINEA-PIG in the ILC and ultra-tight collision scenarios. Our performance comparison demonstrates a significant speed-up advantage of WarpX, ensuring a more robust and efficient modeling of electron-positron collisions at multi-TeV energies.

Fermilab's Integrable Optics Test Accelerator is an electron storage ring designed for testing advanced accelerator physics concepts, including implementation of nonlinear integrable beam optics and experiments on optical stochastic cooling. The machine is currently under construction at the Advanced Superconducting Test Accelerator facility. In this report we present the goals and the current status of the project, and describe the details of machine design. In particular, we concentrate on numerical simulations setting the requirements on the design and supporting the choice of machine parameters.

The PASER is potentially a very attractive method for particle acceleration, in which energy from an active medium is transferred to a charged particle beam. The effect is similar to the action of a maser or laser with the stimulated emission of radiation being produced by the virtual photons in the electromagnetic field of the beam. We have been investigating the possibility of developing a demonstration PASER operating at X-band. The less restrictive beam transport and device dimensional tolerances required for working at X-band rather than optical frequencies as well as the widespread application of X-band hardware in accelerator technology all contribute to the attractiveness of performing a PASER demonstration experiment in this frequency range. Key to this approach is the availability of a new class of active materials that exhibit photoinduced electron spin polarization. We will report on the status of active material development and measurements, numerical simulations, and progress towards a planned microwave PASER acceleration experiment at the Argonne Wakefield Accelerator facility.

We have made the first observation of a charged particle beam by means of its electro-optical effect on the propagation of laser light in a birefringent crystal at the Brookhaven National Laboratory Accelerator Test Facility. Polarized infrared light was coupled to a LiNbO3 crystal through a polarization maintaining fiber of 4 micron diameter. An electron beam in 10ps bunches of 1mm diameter was scanned across the crystal. The modulation of the laser light during passage of the electron beam was observed using a photodiode with 45GHz bandwidth. The fastest rise time measured, 120ps, was made in the single shot mode and was limited by the bandwidth of the oscilloscope and the associated electronics. Both polarization dependent and polarization independent effects were observed. This technology holds promise of greatly improved spatial and temporal resolution of charged particle beams.

We briefly give some of the characteristics of the beam-driven, plasma-based particle accelerator known as the plasma wakefield accelerator (PWFA). We also mention some of the major results that have been obtained since the birth of the concept. We focus on high-energy particle beams where possible.

We analyze the use of a relativistic laser pulse with a controlled frequency chirp incident on a rising plasma density gradient to drive an acceleration structure for proton and light-ion acceleration. The Chirp Induced Transparency Acceleration (ChITA) scheme is described with an analytical model of the velocity of the snowplow at critical density on a pre-formed rising plasma density gradient that is driven by a positive-chirp in the frequency of a relativistic laser pulse. The velocity of the ChITA-snowplow is shown to depend upon rate of rise of the frequency of the relativistic laser pulse represented by $\frac{ε_0}θ$ where, $ε_0 = \frac{Δω_0}{ω_0}$ and chirping spatial scale-length, $θ$, the normalized magnetic vector potential of the laser pulse $a_0$ and the plasma density gradient scale-length, $α$. We observe using 1-D OSIRIS simulations the formation and forward propagation of ChITA-snowplow, being continuously pushed by the chirping laser at a velocity in accordance with the analytical results. The trace protons reflect off of this propagating snowplow structure and accelerate mono-energetically. The control over ChITA-snowplow velocity allows the tuning of accelerated proton energies.

Operation, upgrade and development of accelerators for Intensity Frontier face formidable challenges in order to satisfy both the near-term and long-term Particle Physics program. Here we discuss key issues and R&D required for the Intensity Frontier accelerators.