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Particle accelerator operation requires simultaneous optimization of multiple objectives. Multi-Objective Optimization (MOO) is particularly challenging due to trade-offs between the objectives. Evolutionary algorithms, such as genetic algorithm (GA), have been leveraged for many optimization problems, however, they do not apply to complex control problems by design. This paper demonstrates the power of differentiability for solving MOO problems using a Deep Differentiable Reinforcement Learning (DDRL) algorithm in particle accelerators. We compare DDRL algorithm with Model Free Reinforcement Learning (MFRL), GA and Bayesian Optimization (BO) for simultaneous optimization of heat load and trip rates in the Continuous Electron Beam Accelerator Facility (CEBAF). The underlying problem enforces strict constraints on both individual states and actions as well as cumulative (global) constraint for energy requirements of the beam. A physics-based surrogate model based on real data is developed. This surrogate model is differentiable and allows back-propagation of gradients. The results are evaluated in the form of a Pareto-front for two objectives. We show that the DDRL outperforms MFRL, BO, and GA on high dimensional problems.

Next-generation accelerator concepts which hinge on the precise shaping of beam distributions, demand equally precise diagnostic methods capable of reconstructing beam distributions within 6-dimensional position-momentum spaces. However, the characterization of intricate features within 6-dimensional beam distributions using conventional diagnostic techniques necessitates hundreds of measurements, using many hours of valuable beam time. Novel phase space reconstruction techniques are needed to substantially reduce the number of measurements required to reconstruct detailed, high-dimensional beam features in order to resolve complex beam phenomena, and as feedback in precision beam shaping applications. In this study, we present a novel approach to reconstructing detailed 6-dimensional phase space distributions from experimental measurements using generative machine learning and differentiable beam dynamics simulations. We demonstrate that for a collection of synthetic beam distribution test cases that this approach can be used to resolve 6-dimensional phase space distributions using basic beam manipulations and as few as 20 2-dimensional measurements of the beam profile, without the need for prior data collection or model training. We also demonstrate an application of the reconstruction method in an experimental setting at the Argonne Wakefield Accelerator, where it is able to reconstruct the beam distribution and accurately predict previously unseen measurements 75x faster than previous methods.

Ultrafast electron diffraction using MeV energy beams(MeV-UED) has enabled unprecedented scientific opportunities in the study of ultrafast structural dynamics in a variety of gas, liquid and solid state systems. Broad scientific applications usually pose different requirements for electron probe properties. Due to the complex, nonlinear and correlated nature of accelerator systems, electron beam property optimization is a time-taking process and often relies on extensive hand-tuning by experienced human operators. Algorithm based efficient online tuning strategies are highly desired. Here, we demonstrate multi-objective Bayesian active learning for speeding up online beam tuning at the SLAC MeV-UED facility. The multi-objective Bayesian optimization algorithm was used for efficiently searching the parameter space and mapping out the Pareto Fronts which give the trade-offs between key beam properties. Such scheme enables an unprecedented overview of the global behavior of the experimental system and takes a significantly smaller number of measurements compared with traditional methods such as a grid scan. This methodology can be applied in other experimental scenarios that require simultaneously optimizing multiple objectives by explorations in high dimensional, nonlinear and correlated systems.

Tuning particle accelerators is a challenging and time-consuming task that can be automated and carried out efficiently using suitable optimization algorithms, such as model-based Bayesian optimization techniques. One of the major advantages of Bayesian algorithms is the ability to incorporate prior information about beam physics and historical behavior into the model used to make control decisions. In this work, we examine incorporating prior accelerator physics information into Bayesian optimization algorithms by utilizing fast executing, neural network models trained on simulated or historical datasets as prior mean functions in Gaussian process models. We show that in ideal cases, this technique substantially increases convergence speed to optimal solutions in high-dimensional tuning parameter spaces. Additionally, we demonstrate that even in non-ideal cases, where prior models of beam dynamics do not exactly match experimental conditions, the use of this technique can still enhance convergence speed. Finally, we demonstrate how these methods can be used to improve optimization in practical applications, such as transferring information gained from beam dynamics simulations to online control of the LCLS injector, and transferring knowledge gained from experimental measurements across different operating modes, such as accelerating different ion species at the ATLAS heavy ion accelerator.

Beams with cross-plane coupling or extreme asymmetries between the two transverse phase spaces are often encountered in particle accelerators. Flat beams with large transverse-emittance ratios are critical for future linear colliders. Similarly, magnetized beams with significant cross-plane coupling are expected to enhance the performance of electron cooling in hadron beams. Preparing these beams requires precise control and characterization of the four-dimensional transverse phase space. In this study, we employ generative phase space reconstruction (GPSR) techniques to rapidly characterize magnetized and flat-beam phase-space distributions using a conventional quadrupole-scan method. The reconstruction technique is experimentally demonstrated on an electron beam produced at the Argonne Wakefield Accelerator and successfully benchmarked against conventional diagnostics techniques. Specifically, we show that predicted beam parameters from the reconstructed phase-space distributions (e.g. as magnetization and flat beam emittances) are in excellent agreement with those measured from the conventional diagnostic methods.

Accelerator physics relies on numerical algorithms to solve optimization problems in online accelerator control and tasks such as experimental design and model calibration in simulations. The effectiveness of optimization algorithms in discovering ideal solutions for complex challenges with limited resources often determines the problem complexity these methods can address. The accelerator physics community has recognized the advantages of Bayesian optimization algorithms, which leverage statistical surrogate models of objective functions to effectively address complex optimization challenges, especially in the presence of noise during accelerator operation and in resource-intensive physics simulations. In this review article, we offer a conceptual overview of applying Bayesian optimization techniques towards solving optimization problems in accelerator physics. We begin by providing a straightforward explanation of the essential components that make up Bayesian optimization techniques. We then give an overview of current and previous work applying and modifying these techniques to solve accelerator physics challenges. Finally, we explore practical implementation strategies for Bayesian optimization algorithms to maximize their performance, enabling users to effectively address complex optimization challenges in real-time beam control and accelerator design.

In this article we examine recent developments in the research area concerning the creation of end-to-end models for the complete optimization of measuring instruments. The models we consider rely on differentiable programming methods and on the specification of a software pipeline including all factors impacting performance -- from the data-generating processes to their reconstruction and the extraction of inference on the parameters of interest of a measuring instrument -- along with the careful specification of a utility function well aligned with the end goals of the experiment. Building on previous studies originated within the MODE Collaboration, we focus specifically on applications involving instruments for particle physics experimentation, as well as industrial and medical applications that share the detection of radiation as their data-generating mechanism., Comment: 70 pages, 17 figures. To be submitted to journal

Transverse beam emittance plays a key role in the performance of high brightness accelerators. Characterizing beam emittance is often done using a quadrupole scan, which fits beam matrix elements to experimental measurements using first order optics. Despite its simplicity at face value, this procedure is difficult to automate due to practical limitations. Key issues that must be addressed include maintaining beam size measurement validity by keeping beams within the radius to diagnostic screens, ensuring that measurement fitting produces physically valid results, and accurately characterizing emittance uncertainty. We describe a demonstration of the Bayesian Exploration technique towards solving this problem at the Argonne Wakefield Accelerator, enabling a turnkey, autonomous quadrupole scan tool that can be used to quickly measure beam emittances at various locations in accelerators with limited operator input.

Current physics models used to interpret experimental measurements of particle beams require either simplifying assumptions to be made in order to ensure analytical tractability, or black box optimization methods to perform model based inference. This reduces the quantity and quality of information gained from experimental measurements, in a system where measurements have a limited availability. However differentiable physics modeling, combined with machine learning techniques, can overcome these analysis limitations, enabling accurate, detailed model creation of physical accelerators. Here we examine two applications of differentiable modeling, first to characterize beam responses to accelerator elements exhibiting hysteretic behavior, and second to characterize beam distributions in high dimensional phase spaces., Comment: arXiv admin note: text overlap with arXiv:2209.04505, arXiv:2202.07747

Bayesian optimization has been shown to be a powerful tool for solving black box problems during online accelerator optimization. The major advantage of Bayesian based optimization techniques is the ability to include prior information about the problem to speed up optimization, even if that information is not perfectly correlated with experimental measurements. In parallel, neural network surrogate system models of accelerator facilities are increasingly being made available, but at present they are not widely used in online optimization. In this work, we demonstrate the use of an approximate neural network surrogate model as a prior mean for Gaussian processes used in Bayesian optimization in a realistic setting. We show that the initial performance of Bayesian optimization is improved by using neural network surrogate models, even when surrogate models make erroneous predictions. Finally, we quantify requirements on surrogate prediction accuracy to achieve optimization performance when solving problems in high dimensional input spaces.

Characterizing the phase space distribution of particle beams in accelerators is a central part of accelerator understanding and performance optimization. However, conventional reconstruction-based techniques either use simplifying assumptions or require specialized diagnostics to infer high-dimensional ($>$ 2D) beam properties. In this Letter, we introduce a general-purpose algorithm that combines neural networks with differentiable particle tracking to efficiently reconstruct high-dimensional phase space distributions without using specialized beam diagnostics or beam manipulations. We demonstrate that our algorithm accurately reconstructs detailed 4D phase space distributions with corresponding confidence intervals in both simulation and experiment using a single focusing quadrupole and diagnostic screen. This technique allows for the measurement of multiple correlated phase spaces simultaneously, which will enable simplified 6D phase space distribution reconstructions in the future.

Particle accelerators are invaluable discovery engines in the chemical, biological and physical sciences. Characterization of the accelerated beam response to accelerator input parameters is of-ten the first step when conducting accelerator-based experiments. Currently used techniques for characterization, such as grid-like parameter sampling scans, become impractical when extended to higher dimensional input spaces, when complicated measurement constraints are present, or prior information is known about the beam response is scarce. In this work, we describe an adaptation of the popular Bayesian optimization algorithm, which enables a turn-key exploration algorithm that replaces parameter scans and minimizes prior information needed about the measurements' behavior and associated measurement constraints. We experimentally demonstrate that our algorithm autonomously conducts an adaptive, multi-parameter exploration of input parameter space,while navigating a highly constrained, single-shot beam phase-space measurement. In addition to applications in accelerator-based scientific experiments, this algorithm addresses challenges shared by many scientific disciplines and is thus applicable to autonomously conducting experiments over a broad range of research topics.

Particle accelerators require constant tuning during operation to meet beam quality, total charge and particle energy requirements for use in a wide variety of physics, chemistry and biology experiments. Maximizing the performance of an accelerator facility often necessitates multi-objective optimization, where operators must balance trade-offs between multiple objectives simultaneously, often using limited, temporally expensive beam observations. Usually, accelerator optimization problems are solved offline, prior to actual operation, with advanced beamline simulations and parallelized optimization methods (NSGA-II, Swarm Optimization). Unfortunately, it is not feasible to use these methods for online multi-objective optimization, since beam measurements can only be done in a serial fashion, and these optimization methods require a large number of measurements to converge to a useful solution.Here, we introduce a multi-objective Bayesian optimization scheme, which finds the full Pareto front of an accelerator optimization problem efficiently in a serialized manner and is thus a critical step towards practical online multi-objective optimization in accelerators.This method uses a set of Gaussian process surrogate models, along with a multi-objective acquisition function, which reduces the number of observations needed to converge by at least an order of magnitude over current methods.We demonstrate how this method can be modified to specifically solve optimization challenges posed by the tuning of accelerators.This includes the addition of optimization constraints, objective preferences and costs related to changing accelerator parameters.

Present-day and next-generation accelerators, particularly for applications in driving wakefield-based schemes, require longitudinal beam shaping and attendant longitudinal characterization for experimental optimization. Here we present a diagnostic method which reconstructs the longitudinal beam profile at the location of a wakefield-generating source. The methods presented derive the longitudinal profile of a charged particle beam solely from measurement of the time-resolved centroid energy change due to wakefield effects. The reconstruction technique is based on a deconvolution algorithm that is fully generalizable to any analytically or numerically calculable Green's function for the wakefield excitation mechanism. This method is shown to yield precise features in the longitudinal current distribution reconstruction. We demonstrate the accuracy and efficacy of this technique using simulations and experimental examples, in both plasmas and dielectric structures, and compare to the experimentally measured longitudinal beam parameters as available. The limits of resolution and applicability to relevant scenarios are also examined., Comment: Submitted to PRAB

Plasma wakefields can enable very high accelerating gradients for frontier high energy particle accelerators, in excess of 10 GeV/m. To overcome limits on total acceleration achievable, specially shaped drive beams can be used in both linear and nonlinear plasma wakefield accelerators (PWFA), to increase the transformer ratio, implying that the drive beam deceleration is minimized relative to acceleration obtained in the wake. In this Letter, we report the results of a nonlinear PWFA, high transformer ratio experiment using high-charge, longitudinally asymmetric drive beams in a plasma cell. An emittance exchange process is used to generate variable drive current profiles, in conjunction with a long (multiple plasma wavelength) witness beam. The witness beam is energy-modulated by the wakefield, yielding a response that contains detailed spectral information in a single-shot measurement. Using these methods, we generate a variety of beam profiles and characterize the wakefields, directly observing beam-loaded transformer ratios up to R=7.8. Furthermore, a spectrally-based reconstruction technique, validated by 3D particle-in-cell simulations, is introduced to obtain the drive beam current profile from the decelerating wake data.