Linear particle accelerators are elaborate machines that demand a thorough comprehension of their beam physics interactions to enhance performance. Traditionally, physics simulations model the physics interactions inside a machine but they are computationally intensive. A novel solution to the long runtimes of physics simulations is replacing the intensive computations with a machine learning model that predicts the results instead of simulating them. Simple neural networks take milliseconds to compute the results. The ability to make physics predictions in almost real time opens a world of online models that can predict diagnostics which typically are destructive to the beam when measured. This research entailed the incorporation of an innovative simulation infrastructure for the SLAC FACET-II group, aimed at optimizing existing physics simulations through advanced algorithms. The new infrastructure saves the simulation data at each step in optimization and then improves the input parameters to achieve a more desired result. The data generated by the simulation was then used to create a machine learning model to predict the parameters generated in the simulation. The machine learning model was a simple feedforward neural network and showed success in accurately predicting parameters such as beam emittance and bunch length from varied inputs.

One of the Grand Challenges in beam physics is development of virtual particle accelerators for beam prediction. Virtual accelerators rely on efficient and effective methodologies grounded in theory, simulation, and experiment. We will address one sample methodology, extending the understanding and the control of deleterious effects, for example, emittance growth. We employ the application of the Sparse Identification of Nonlinear Dynamical systems algorithm–previously presented at NAPAC’22 and IPAC’23–to identify emittance growth dynamics caused by nonuniform, empirical distributions in phase space in a linear, hard-edge, periodic FODO lattice. To gain further understanding of the evolution of emittance growth as the beam’s distribution approaches steady state, we compare our results to theoretical predictions describing the final state emittance growth due to collective and N-body mode interaction of space charge nonuniformities as a function of free-energy and space-charge intensity. Finally, we extend our methodology to a broader range of virtual and real experiments to identify the growth(decay) of (un)desired beam parameters.

The model of spin depolarization invoking isolated resonances hinges on a closed-form solution of energy ramping with the Single Resonance Model by Froissart and Stora. However, for non-resonant orbital tunes, resonant depolarization by single resonance crossing is impossible in the SRM while using a pair of Siberian Snakes since the amplitude-dependent spin tune is then fixed to one-half. Polarization loss in RHIC demonstrates that the isolated resonances model is not a good approximation of polarization dynamics with two Siberian Snakes. We therefore extend the model in which a pair of resonances in close proximity push the amplitude-dependent spin tune away from one-half in the presence of Siberian Snakes, allowing the crossing of higher-order spin resonances associated with depolarization. We present results from applying Machine Learning methods that establish spin transport models with two overlapping resonances from tracking data.

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

The Super Proton Synchrotron at CERN serves the fixed-target experiments of the North Area, providing protons and ions via slow extraction, and employs the crystal shadowing technique to significantly minimize losses. Over the past three operational years, the use of a crystal, positioned upstream of the electrostatic septum to shadow its blade, has allowed to achieve a 25% reduction in losses. Additionally, a novel non-local shadowing technique, utilizing a different crystal location, has successfully halved these losses. While using a single crystal in this location resulted in a temporary 50% reduction in slow extraction losses at nominal intensity, this effect was not sustainable beyond a few hours. This limitation is primarily attributed to the magnetic non-reproducibility and hysteresis inherent to the SPS main dipoles and quadrupoles. In this paper, we introduce the application of the Rank-Weighted Gaussian Process Ensemble to the setup of shadowing. We demonstrate its superior efficiency and effectiveness in comparison to traditional Bayesian optimization and other numerical methods, particularly in managing the complex dynamics of local and non-local shadowing.

Magnetic hysteresis, eddy currents, and manufacturing imperfections pose significant challenges for beam operation in multi-cycling synchrotrons. Addressing the dynamic dependency of magnetic fields on cycling history is a current limitation for control room tools using existing models. This paper outlines recent advancements to solve this, presenting the outcome of operational tests utilizing data-driven approaches and an overview of the next steps. Notably, artificial neural networks, including long short-term memory networks, transformers and other time series analysis architectures, are employed to model static and dynamic effects in the main dipole magnets of the CERN SPS. These networks capture hysteresis and eddy current decays based on measured magnetic field and data from the real-time magnetic measurement system of the SPS main dipoles. Cycle-by-cycle feed-forward corrections are implemented through the CERN accelerator controls infrastructure, which propagate corrections of magnetic fields to corresponding adjustments in the current of the power converters feeding the magnets.

In non-linear optics, achieving integrability can enhance the dynamic aperture in storage rings. We analyze turn-by-turn phase-space data from our Danilov-Nagaitsev lattice implementation at Fermilab's Integrable Optics Test Accelerator using machine learning. AI Poincaré estimates conserved quantities from experimental data without prior knowledge of the invariant structure, showing qualitative agreement with theoretical predictions. Additionally, one of the two learned invariants exhibits comparable or better conservation compared to known theoretical expressions.

The complexity of the GSI/FAIR accelerator facility demands a high level of automation in order to maximize time for physics experiments. Accelerator laboratories world-wide are exploring a large variety of techniques to achieve this, from classical optimization to reinforcement learning. This paper reports on the first results of using Geoff at GSI for automatic optimization of various beam manipulations. Geoff (Generic Optimization Framework & Frontend) is an open-source framework that harmonizes access to the above automation techniques and simplifies the transition towards and between them. It is maintained as part of the EURO-LABS project in cooperation between CERN and GSI. In dedicated beam experiments, the beam loss of the multi-turn injection into the SIS18 synchrotron has been reduced from 40% to 10% in about 15 minutes, where manual adjustment can take up to 2 hours. Geoff has also been used successfully at the GSI Fragment Separator (FRS) for beam steering. Further experimental activities include closed orbit correction for specific broken-symmetry high-transition-energy SIS18 optics with Bayesian optimization in comparison to traditional SVD-based correction.

The International Linear Collider (ILC) is a next-generation electron-positron collider designed to operate at center-of-mass energies ranging from 250 GeV to 1 TeV, providing opportunities for exploring physics beyond the Standard Model. A critical component of the ILC is the E-driven positron source, which requires sophisticated technology to produce large quantities of positrons. Traditional accelerator design methods involve sequential optimization, which is inefficient and challenging for achieving global optimization. This study introduced the use of the Tree-structured Parzen Estimator (TPE) algorithm, a black-box optimization method, to improve the design efficiency of the ILC E-driven positron source. By implementing the TPE algorithm using Optuna, we optimized up to 8 parameters, achieving a positron capture efficiency of 1.42, significantly higher than the 1.20 efficiency obtained through manual optimization. This substantial improvement is expected to meet the safety standards for target destruction. The optimization process was also expedited, reducing the time from about a week to approximately half a day. These results demonstrate the potential of machine learning techniques in accelerator design, offering a more comprehensive global optimization by exploring a broader parameter space and avoiding local minima.

Following the decommissioning of the Main Injector Neutrino Oscillation Search (MINOS) experiment, muon and hadron monitors have emerged as essential diagnostic tools for the NuMI Off-axis nu_mu Appearance (NOvA) experiment at Fermilab. For this study, we use a combination of muon monitor simulation and measurement data to study the monitor responses to variations in proton beam and lattice parameters. We also apply pattern-recognition algorithms to develop machine-learning-based models to establish correlations between muon monitor signals, primary beam parameters, and neutrino flux at the detectors.

Transfer maps of different ion optical elements are usually obtained via ray tracing methods without taking into account the imperfections and misalignments of the optics. Normally beam profile monitors do not measure the full 6D phase-space, but only a portion of it. To verify the beam phase-space, we have constructed an Ion Optics Test Stand (IOTS) that is located at the Low Energy Branch (LEB) of the Jozef Stefan Institute in Ljubljana, Slovenia [1]. The IOTS consists of two Allison emittance scanners (AES) [2] with an electrode sandwiched between them, and is supplied by the LEB with a variety of ion beams with energies up to 20 keV. This allows us to automatically measure the 6D beam phase-space before and after the electrode and determine the electrodes transfer map. We will discuss the status of the IOTS, the emittance scanners, electrode transfer map measurements with them, and describe an example of AES--Einzel lens--AES test configuration. We will also show how the phase-space measurements performed with the IOTS can be used as a training ground of Machine Learning (ML) tools designed for ion optics optimization with respect to a preferred transport metric.

The 2D Orszag-Tang vortex magnetohydrodynamics (MHD) problem is studied through the use of physics-constrained convolutional neural networks (PCNNs). The density and the magnetic field are forecasted, and we also predict magnetic field given the velocity field of the fluid. We examined the incorporation of various physics constraints into the PCNNs: absence of magnetic monopoles, non-negativity of density and use of only relevant variables. Translation equivariance was present from the convolutional architecture. The use of a residual architecture and data augmentation was found to increase performance greatly. The most accurate models were incorporated into the simulation, with reasonably accurate results. For the prediction task, the PCNNs were evaluated against a physics-informed neural network (PINN), which had the ideal MHD induction equation as a soft constraint. The use of PCNNs for MHD has the potential to produce physically consistent real-time simulations to serve as virtual diagnostics in cases where inferences must be made with limited observables.

Coherent synchrotron radiation has a significant impact on electron storage rings and bunch compressors, inducing energy spread and emittance growth in a bunch. While the physics of the phenomenon is well-understood, numerical calculations are computationally expensive, severally limiting their usage. Here, we explore utilizing neural networks (NNs) to model the 3D wakefields of electrons in circular orbit in the steady state condition. We demonstrate that NNs can achieve a significant speed-up, while also accurately reproducing the 3D wakefields. NN models were developed for both Gaussian and general bunch distributions. These models can potentially aid in the design and optimization of accelerator apparatuses by enabling rapid searches through parameter space.

A particle accelerator is a time-varying complex system whose various components are regularly perturbed by external disturbances. The tuning of the accelerator can be a time-consuming process involving manual adjustment of multiple components, such as RF cavities, to minimize beam loss due to time-varying drifts. The high dimensionality of the system (~100 amplitude and phase RF settings in the LANSCE accelerator) makes it difficult to achieve optimal operation. The time-varying drifts and the dimensionality make system parameter estimation a challenging optimization problem. In this work, we propose a variational autoencoded latent regression (VAELR) model for robust estimation of system parameters using 2D unique projections of a charged particle beam's 6D phase space. In VAELR, VAE projects the phase space projections into a lower-dimensional latent space, and a dense neural network maps the latent space onto the space of system parameters. The trained network can predict system parameters for unseen phase space projections. Furthermore, VAELR can generate new projections by randomly sampling the latent space of VAE and also estimate the corresponding system parameters.

Addressing the charged particle beam diagnostics in accelerators poses a formidable challenge, demanding high-fidelity simulations in limited computational time. Machine learning (ML) based surrogate models have emerged as a promising tool for non-invasive charged particle beam diagnostics. Trained ML models can make predictions much faster than computationally expensive physics simulations. In this work, we have proposed a temporally structured variational autoencoder model to autoregressively forecast the spatiotemporal dynamics of the 15 unique 2D projections of 6D phase space of charged particle beam as it travels through the LANSCE linear accelerator. In the model, VAE embeds the phase space projections into a lower dimensional latent space. A long-short-term memory network then learns the temporal correlations in the latent space. The trained network can evolve the phase space projections across further modules provided the first few modules as inputs. The model predicts all the projections across different modules with low mean squared error and high structural similarity index.

Phase space reconstruction using Neural-Networks and differentiable simulation* is a robust beam diagnostic method to obtain complete 4D phase space including the coupling terms such as (x-y’) and (y-x’). In the first experimental demonstration, it was verified that the RMS beam envelope and normalized emittance from the reconstructed phase space are quantitatively similar to those from the conventional beam diagnostics such as quadrupole scan. In addition, here we show the demonstration of the phase space for the i) flat and ii) magnetized beam where the beam has i) very large ratio in between horizontal and vertical emittances (e.g., enx/eny >>1) and ii) transverse coupling induced by non-zero solenoid magnetic field at the cathode (known-as canonical momentum-dominated beam). Through the demonstrations using the experimental data achieved at the Argonne Wakefield Accelerator Facility (AWA), we successfully obtained the information such that the measured flat beam indeed has the emittance ratio larger than 70 with minimized transverse coupling. In addition, we were able to obtain the magnetization from the reconstructed phase space. Moreover, we will compare the beam parameters obtained from the phase space reconstruction and conventional diagnostics and discuss the uncertainty of the parameters.

Linear particle accelerators are elaborate machines that demand a thorough comprehension of their beam physics interactions to enhance performance. Traditionally, physics simulations model the physics interactions inside a machine but they are computationally intensive. A novel solution to the long runtimes of physics simulations is replacing the intensive computations with a machine learning model that predicts the results instead of simulating them. Simple neural networks take milliseconds to compute the results. The ability to make physics predictions in almost real time opens a world of online models that can predict diagnostics which typically are destructive to the beam when measured. This research entailed the incorporation of an innovative simulation infrastructure for the SLAC FACET-II group, aimed at optimizing existing physics simulations through advanced algorithms. The new infrastructure saves the simulation data at each step in optimization and then improves the input parameters to achieve a more desired result. The data generated by the simulation was then used to create a machine learning model to predict the parameters generated in the simulation. The machine learning model was a simple feedforward neural network and showed success in accurately predicting parameters such as beam emittance and bunch length from varied inputs.

Semi-deterministic optimization problems are common in operating complex lasers and accelerator facilities. In these problems, a few optimal solutions exist that can achieve satisfactory system performance for a specific system state. Typically, online optimizations are performed to find these optimal solutions, which can be time-consuming and must be repeated when the system state changes. In this paper, we propose a high-efficient optimization method called method, which can directly map any given system state to the optimal solution based on the optimization criterion. We demonstrate the effectiveness of our method in several real-life optimization scenarios, including simulations and experiments conducted at SLAC and LBNL. Our proposed method can significantly reduce the optimization time and cost and provide a more efficient solution for accelerator facility operations. Moreover, an 8-beam, diffractive coherent beam combiner is phase-controlled by the method, from random states, showing fast optimization of the complex laser system without labeling target patterns as demonstrated in previous publications.

Betatron radiation is a form of synchrotron radiation emitted by moving or accelerated electron or positron-like charged particles. As a valuable tool it can provide useful information about their trajectories, momentum and acceleration. It has good potential as a novel non-destructive diagnostic for laser-driven plasma wakefield acceleration (LWFA) and beam-driven plasma wakefield acceleration (PWFA). Since information about the properties of the beam is encoded in the betatron radiation, measurements using the Maximum Likelihood Estimation (MLE) method, rich information about the beam parameters (beam spot size, emittance, charge, energy etc.) can be extracted. Machine learning (ML) techniques can then be applied to improve the accuracy of these measurements. It has already been observed that betatron radiation can give an insight into the change in plasma density. The QUASAR Group, based at the Cockcroft Institute on Daresbury Sci-Tech campus, is planning to build on and expand an existing collaboration with UCLA and also to apply the technique for the AWAKE experiment at CERN. In this work, a hybrid ML-MLE approach is attempted to optimize the use of these diagnostics and obtain a deep insight into the beam’s parameters e.g. beam spot sizes where ML and MLE individually have their limitations.

One of the Grand Challenges in beam physics is development of virtual particle accelerators for beam prediction. Virtual accelerators rely on efficient and effective methodologies grounded in theory, simulation, and experiment. We will address one sample methodology, extending the understanding and the control of deleterious effects, for example, emittance growth. We employ the application of the Sparse Identification of Nonlinear Dynamical systems algorithm–previously presented at NAPAC’22 and IPAC’23–to identify emittance growth dynamics caused by nonuniform, empirical distributions in phase space in a linear, hard-edge, periodic FODO lattice. To gain further understanding of the evolution of emittance growth as the beam’s distribution approaches steady state, we compare our results to theoretical predictions describing the final state emittance growth due to collective and N-body mode interaction of space charge nonuniformities as a function of free-energy and space-charge intensity. Finally, we extend our methodology to a broader range of virtual and real experiments to identify the growth(decay) of (un)desired beam parameters.