Virtual beam diagnostics relies on computationally intensive beam dynamics simulations where high-dimensional charged particle beams evolve through the accelerator. We propose Latent Evolution Model (LEM), a hybrid machine learning framework with an autoencoder that projects high-dimensional phase spaces into lower-dimensional representations, coupled with transformers to learn temporal dynamics in the latent space. This approach provides a common foundational framework addressing multiple interconnected challenges in beam diagnostics. For forward modeling, a Conditional Variational Autoencoder (CVAE) encodes 15 unique projections of the 6D phase space into a latent representation, while a transformer predicts downstream latent states from upstream inputs. For inverse problems, we address two distinct challenges: (a) predicting upstream phase spaces from downstream observations by utilizing the pretrained CVAE with transformers trained on reversed temporal sequences, and (b) estimating RF settings from the latent space of the trained LEM using a dedicated dense neural network that maps latent representations to RF parameters. For tuning problems, we leverage the trained LEM and RF estimator within a Bayesian optimization framework to determine optimal RF settings that minimize beam loss. This paper summarizes our recent efforts and demonstrates how this unified approach effectively addresses these traditionally separate challenges.

For the PIP-II program, transverse emittance in the Fermilab Booster must remain well controlled at higher bunch intensities. 4-plate beam position monitors (BPMs) have a small but measurable quadrupole moment, making it possible to infer transverse emittance. By compositing many BPMs together, it becomes possible to improve the quality of the quadrupole signal. The Fermilab Booster BPM system has been used to measure these quadrupole moments in the past year and derive emittances from them. Recent benchmarks show that the derived BPM emittances show similar emittance evolution and value to IPM and Multiwire data. This approach can both supplement and complement existing non-intercepting emittance monitors in accelerators.

Optical transition radiation (OTR) beam profile monitors are widely used to measure the transverse profiles of low-charge electron bunches at advanced linear accelerator facilities such as LCLS-II and FACET-II. However, in scenarios involving strong longitudinal compression or microbunching-induced current spikes, the incoherent OTR signal—proportional to the transverse beam density—is often dominated by coherent OTR (COTR). The resulting COTR patterns exhibit complex dependencies on the full spatiotemporal structure of the beam, rendering conventional profile interpretation ineffective. In this work, we present a novel, backwards-differentiable simulation framework for COTR emission, enabling gradient-based inference of beam characteristics directly from COTR images. We further integrate this framework with the generative phase space reconstruction (GPSR) method to recover high-fidelity 4D transverse phase space distributions of strongly compressed beams. Simulation results demonstrate the ability of this approach to accurately reconstruct detailed beam structure from COTR-based diagnostics, offering a new path toward high-resolution characterization of ultrashort electron bunches.

Increasing the performance and capabilities of free electron lasers, such as LCLS-II, hinges on our ability to precisely control and measure the 6-dimensional phase space distribution of the beam. However, conventional tomographic techniques necessitate a substantial number of measurements and computational resources to characterize a single beam distribution, using many hours of valuable beam time. Novel diagnostic techniques are needed to significantly reduce the number of measurements required to reconstruct detailed, 6-dimensional beam features to enable feedback for precision beam shaping for accelerators and characterize unknown physical phenomena. In this work, we present a novel approach to analyzing experimental measurements using differentiable beam dynamics simulations and generative representations of 6-dimensional phase space distributions. We discuss developments in combining this work with advanced accelerator control algorithms and parasitic beam measurements to autonomously monitor the 6-dimensional phase space distribution of the beam at LCLS-II during accelerator operations.

The UC Davis Crocker Nuclear Laboratory (CNL) operates a 76-inch Isochronous Cyclotron dating to the 1960s. Recent experiments have revealed unexplained beam behavior, which cannot be directly measured with the current diagnostics. Direct measurements of the beam in the Cyclotron are challenging due to the harsh environment, including high radiation, strong magnetic fields, RF interference, and spatial constraints. To address this, we are developing a novel beam probe capable of resolving longitudinal bunch structure across 16 positions simultaneously. The fast beam probe consists of a segmented fast plastic scintillator array coupled via fiber optics to external Silicon Photomultipliers (SiPMs), mounted on a radially translating probe. We report on the probe's performance from in-air tests at the general-purpose beamline. The results demonstrate sub-nanosecond resolution, consistent sensitivity across channels, and clear signatures of beam dynamics, establishing the system’s viability for measurements inside the CNL Cyclotron.

Digital twins of particle accelerators are used to plan and control operations and design data collection campaigns. However, a digital twin relies on parameters that are hard to measure directly, e.g., magnet alignments, power supply transfer functions, magnet nonlinearities, and stray fields. These parameters can be constrained by beam position and profile measurements. We use Bayesian statistical inference to estimate the parameters, and their uncertainties, probabilistically by calibrating the Bmad digital twin to beam measurements. The inference is computationally accelerated using a machine learning emulator of the physical accelerator digital twin trained to a perturbed-parameter ensemble of Bmad simulations. The result is a joint posterior distribution over parameters (control currents, individual magnet transfer function coefficients, and beam monitor errors) which is propagated to uncertainties in predicted beam positions and profiles, which we validate against beam responses measured at the AGS booster at Brookhaven National Laboratory.

We present results from online optimization studies of a duoplasmatron ion source designed to produce 50 keV protons for acceleration to 2.5 MeV and subsequent injection into the Integrable Optics Test Accelerator (IOTA) at Fermilab. Using a Bayesian exploration technique, we developed multi-parameter models of the source’s proton current and employed these models to optimize its performance. Depending on the spectrometer configuration used to isolate the proton beam and the chosen optimization objective, we identified three candidate operating points, achieving normalized 50 % emittances between 0.57 μm and 1.3 μm and a maximum proton current of 14.5 ± 0.6 mA.

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

Calculating the effects of Coherent Synchrotron Radiation (CSR) is one of the most computationally expensive tasks in accelerator physics. Here, we use convolutional neural networks (CNN's), along with a latent conditional diffusion (LCD) model, trained on physics-based simulations to speed up calculations. Specifically, we produce the 3D CSR wakefields generated by electron bunches in circular orbit in the steady-state condition. Two datasets are used for training and testing the models: wakefields generated by three-dimensional Gaussian electron distributions and wakefields from a sum of up to 25 three-dimensional Gaussian distributions. The CNN's are able to accurately produce the 3D wakefields ~250-1000 times faster than the numerical calculations, while the LCD has a gain of a factor of ~34. We also test the extrapolation and out-of-distribution generalization ability of the models. They generalize well on distributions with larger spreads than what they were trained on, but struggle with smaller spreads.

The impedance of in-vacuum undulators (IVUs) significantly affect the broadband impedance and, consequently, the beam dynamics in storage rings. During the IVU design phase, numerous iterative discussions between physicists and engineers are required, often involving extensive simulations of the complete 3D geometry, a few meters long, using limited computational resources. In this paper, we propose training a Gaussian process model with limited simulation data to emulate the physical model. We compare the predictions of the trained model to the simulation data and explore its application in optimizing the IVU design.

Laser Assisted Charge Exchange (LACE) technology is being developed to replace foil-based charge exchange injection in high power H- accelerators. The possibility of replacing the foil with field-stripping will greatly reduce injection losses, and therefore is a promising technology for future high-intensity multi-megawatt power H- beams. The technique of LACE has been demonstrated but not in a configuration that allows injection of beam into a ring. This talk will present recent progress on design of a demonstrator at SNS that will allow injection into the SNS ring. The committee also hopes that this talk will review previous experimental results from LACE feasibility studies.

Inferring 4D or 6D phase space distributions from 1D or 2D measurements is a challenging inverse problem encountered in particle accelerators. Entropy maximization (ME) is an established method to incorporate prior information in under-constrained problems but is typically infeasible in high-dimensional spaces. In this talk, I discuss two approaches to high-dimensional ME. The first approach extends the Generative Phase Space Reconstruction (GPSR) algorithm, utilizing a class of generative models called normalizing flows which provide stochastic differentiable entropy estimates. The second approach modifies the classic MENT algorithm, using the method of Lagrange multipliers and Markov Chain Monte Carlo (MCMC) sampling to solve the constrained optimization. After reviewing the theory behind these approaches, I describe numerical tests of their convergence and accuracy, followed by applications to experimental data. I conclude by mentioning possible routes to uncertainty quantification within the ME framework.

This paper presents the application of BeamTracking.jl, a key package in the Julia based SciBmad software ecosystem for differentiable accelerator physics simulations. This study demonstrates the use of phase space tomography to reconstruct the 2D phase space distribution of a particle beam. Using the SciBmad tracking package BeamTracking.jl, the phase space distribution of the beam can be constructed from the beam’s projections after being transported through a quadrupole and a drift. This result showcases the utility of SciBmad and highlights its potential for studying and optimizing injection, transport, and beam acceleration.

Beam halo refers to the low-density distribution of particles extending beyond the beam core, and its generation and mitigation are important topics in particle accelerator design. Effective mitigation of beam halo is essential for the cooler design based on Energy Recovery Linac (ERL), which must deliver an electron beam with average beam current of 100 mA and a charge 1 nC per bunch. In the ERL injector and booster linacs, space charge effects are stronger due to relatively low beam energy (6 MeV). Additionally, the longer bunch length of approximately 100 ps in this regime vs the RF period of 5.08 ns makes the formation of beam halos more likely. Therefore, effective collimation of beam halo is critical to maintaining the required beam parameters. To design an effective collimation scheme, several halo distributions were generated at the cathode and used to study halo formation within the injector-merger. This paper presents different halo distributions and halo formation, providing insights on halo collimation strategy.

The microwave instability is typically driven by perturbations whose characteristic wavelength is much shorter than the bunch. In this case, Boussard argued that the microwave instability threshold can be found using the predictions of an infinite (coasting) beam, with the average current replaced by the peak current. We revisit this problem, and theoretically show that if the variation of the synchrotron tune with energy can be neglected then Boussard's hypothesis holds provided 1) the longitudinal ring impedance is dominated by frequencies much shorter that the inverse bunch length; 2) the single-particle wakefield is much shorter than the bunch length, or, equivalently, the impedance is slowly varying over frequencies longer than the inverse bunch length; 3) the resulting instability has a sudden onset with growth rate of the order of the synchrotron frequency. The first two conditions imply that perturbations are localized within distances much less than the bunch length, while the last condition means that the instability experiences significant growth before the particles can make one synchrotron oscillation. While these conditions may be ``obvious'' in retrospect, we believe that the last two have not been clearly stated or widely appreciated.

Optimizing accelerator lattices requires evaluating phase space densities through extended or repeated particle-in-cell simulations. These are computationally expensive due to the need to solve the equations of motion for large numbers of charged particles in prescribed and self-consistent fields. We introduce a method that significantly reduces the computational burden by constructing approximate invariant densities via a two-step transfer operator approach. The method gives practical approximations to phase-space level curves, capturing essential dynamics without extensive particle pushing. Prior work has shown how to find such curves via kernel-based level set learning. Our method is fast, avoids kernel tuning, and integrates with existing codes, enabling rapid assessment of figures of merit in constrained optimization algorithms such as Adjoint with a Chaser, AWC. AWC efficiently computes gradients with respect to lattice parameters while preserving moment periodicity and accounting for self-fields and collective effects. We present results demonstrating accuracy, speed-up, and trade-offs between precision and computational cost in lattice design.

The Spallation Neutron Source uses charge exchange injection of 1.3 GeV, H- ions to accumulate roughly 2x10E protons per pulse in the accumulator ring. This is achieved using a flexible painting system capable of controlling all four transverse coordinates of injected beam over the 1ms injection cycle. Recently we demonstrated injection of an ~800 MeV beam into a single non-planar mode in the SNS ring, which we call eigenpainting. This poster will outline future plans for exploring the space charge dynamics of beams prepared by eigenpainting in the SNS ring, including comparison of hollow, gaussian, and uniformly painted beams.

Nonlinear focusing elements enhance the stability of particle beams in high-energy colliders via Landau Damping, a phenomenon that acts through the tune spread these elements introduce. This experiment at Fermilab's Integrable Optics Test Accelerator (IOTA) aims to investigate the influence of nonlinear focusing elements on transverse beam stability by employing a novel method to directly measure the strength of Landau Damping. This method employs an active transverse feedback system as a controlled source of impedance to induce a coherent beam instability. The beam’s resulting growth rate and transverse feedback parameters can then be used to directly measure the stability diagram, a threshold which maps the system's stability conditions. A proof-of-principle experiment of this measurement method was first explored at the LHC, where the experiment at IOTA aims to map out the entirety of the stability diagram and to obtain the beam distribution function from the stability diagram, a procedure never done before that would enable one to obtain the beam distribution tails. Here we present the initial results of stability diagram data analysis, simulation results, and plans for further investigation.

The Strong Hadron Cooler (SHC) proposed for the Electron-Ion Collider (EIC) requires high-current, low-emittance electron bunches with minimal energy spread. The Energy Recovery Linac (ERL) injector plays a critical role in shaping the beam before acceleration. We present a multi-objective optimization study of the SHC ERL injector and merger using space charge tracking in Bmad and parallel genetic algorithm. The optimized configuration reduces the normalized transverse emittance by 62% and energy spread by 85% from the original configuration.

We present a study of intra-beam scattering (IBS) in high-brightness electron beams, incorporating a recent theory that accounts for enhanced temporal correlations of electric field fluctuations. These correlations, absent in conventional binary-collision models, arise from the periodic betatron motion of particles within the beam. To enable direct verification of the theoretical calculations, we perform simulations in a computer code specifically written for that purpose. In the code, the particle distribution is preserved over time, ensuring conditions compatible with theoretical assumptions, and the IBS is neatly separated from the conventional Space Charge (SC) effect. The simulations, benchmarked against an exactly solvable case of an infinite isotropic uniform plasma, show good agreement with both uncorrelated models, such as Piwinski’s, and the new correlation-based theory, across various bunch distributions and dynamical regimes. This validates the simulation approach and highlights the role of time-correlated fields in accurate IBS modeling.

RF breakdown is the major limitation to achieving higher accelerating gradients. Recent experimental evidence shows that this limitation can be mitigated by reducing the RF pulse length to a few nanoseconds. One key challenge in designing an accelerator operating in the short-pulse regime is achieving the required short filling time. In this work, we designed a novel waveguide power splitter to independently feed an array of accelerating cells. A prototype X-band waveguide array for a one-to-four power splitter has been developed to drive standing-wave cavities operating in the short-pulse regime. The power is designed to be equally split and fed into four cavities, with the desired phase advance per cavity. A 3D-printed prototype has been used for low-power microwave measurements ("cold" tests). The results, including measurements with a vector network analyzer and time-domain measurements, show good agreement with simulations. Ongoing work includes designing a multi-cell accelerator based on this concept for two-beam acceleration with few-nanosecond RF pulses.

An advanced charge selector is currently under development at the Facility for Rare Isotope Beams (FRIB) to intercept unwanted charge states of stripped heavy ion beams. Rotating graphite wheels are employed to absorb beams with a power up to 5 kW and a size as small as an rms width of 0.7 mm × 1.25 mm. The implantation of beam ions and accumulated radiation damage affect the material properties, potentially leading to its structural failure. Determining the foreign ion accumulation behavior is one critical aspect for predicting the operational lifetime of the graphite wheels. In this study, ion implantation distribution was first characterized using SRIM simulations, then coupled with Monte Carlo analysis to account for wheel geometry and rotational dynamics. The evolution of the ion concentration profiles was subsequently determined considering the diffusion effects. The analysis reveals that strategic beam positioning optimization, combined with diffusion effects, substantially reduces peak ion concentrations and implantation rates, providing essential data for graphite wheel lifetime assessment.

New 0.5m long SCU prototypes were designed based on lessons learned from the previous full length (1.5 m) core experiences. The original monolithic cores have all steel poles. The new cores have plastic back poles to avoid electrical shorts of superconducting wires to cores. Magnetostatic calculation was made for one period model for each of two designs under consideration. Then, magnetostatic, and mechanical analysis was also conducted for the prototype SCUs with the lengths of 29.5 and 23.5 periods. The software used for this simulation is ANSYS Maxwell and Mechanical. Both the magnetostatic and the mechanical analyses confirm the validity of the new design.

Design of radio frequency (RF) couplers and diagnostics require a good understanding of the electromagnetic mode patterns of RF cavities. This study investigates the adiabatic transformation of transverse magnetic (TM) modes in a cylindrical cavity into transverse electromagnetic (TEM) modes of a coaxial cavity by gradually introducing an inner conductor. Using CST Studio Suite, we simulate the eigenmode evolution as the geometry transforms from a pure cylindrical to a coaxial configuration. We track the behavior of TM010 through TM014 modes to observe the continuous evolution into the corresponding TEM0 through TEM4 modes of the coaxial cavity. The process is governed by the evolution of the electric field orientation as the geometry shifts, enabling the axial TM fields to reorient into the radial electric field configuration of TEM modes. Field patterns, eigen-frequencies, and mode indentities are analyzed throughtout the transition. The results provide simulation-based evidence that TM to TEM conversion occurs without generation of newer eigenmodes, offering a valuable insight into the design of transition regions in superconducting RF (SRF) systems and provides a foundation for experimental validation.

Throughout its operation, the RHIC triplet magnets have been subject to a mechanical vibration around 10 Hz. These mechanical vibrations were found to produce a beam orbit jitter that was detrimental to the collider luminosity. During RHIC operation, this has been effectively mitigated by the implementation of a fast feedback orbit control system. For the Electron Ion Collider (EIC) Hadron Storage Ring (HSR), the RHIC triplet package will be modified, magnets will be removed, and the cryogenic lines will be rearranged inside the cryostat. A comprehensive analysis of the RHIC triplet vibration has been undertaken to ensure that the planned triplet piping modifications would not increase the current triplet magnet vibrations and overwhelm the existing fast feedback control system. This paper aims to describe the current understanding of the root cause and kinematic of the RHIC triplet vibrations and offer mitigation options for EIC.

Intra-Beam Stripping (IBS) is a critical beam loss mechanism in high-intensity H- linacs and presents a significant limitation to increasing beam power. This work presents a computational framework to evaluate and mitigate IBS-induced beam loss along the Spallation Neutron Source (SNS) LINAC. Our calculation is based on an analytic theory and involves evaluation of a 9D integral using the Monte-Carlo technique. We first benchmarked our calculations against simplified, analytically solvable cases. We then applied our algorithm to Gaussian bunches with a known probability density function (PDF). We next expanded our algorithm to arbitrary bunch distributions using the Neural Spline Flow (NSF) models trained on PyORBIT tracking data. In the future, we plan to validate our algorithm experimentally and apply it to design IBS mitigation strategies.

The Coherent Electron Cooling (CeC) technique is a breakthrough in accelerator science, enhancing ion beam brightness in facilities like the Electron-Ion Collider (EIC). The success of CeC relies on high-performance photocathodes (PCs) for photoinjectors, where ideal PCs exhibit high QE, low emittance, long lifetimes, and minimal dark current. Alkali antimonide PCs meet these requirements. Among these, Na-K-Sb shows enhanced robustness, particularly under high-temperature conditions from high-power laser illumination, which generates high current electron beams. It also demonstrates improved vacuum stability and long-term QE consistency compared to other alkali antimonides like K2CsSb and Cs3Sb. These attributes make Na-K-Sb an effective choice for applications requiring both thermal and vacuum stability. This work presents the growth of Na-K-Sb PCs using the CeC cathode deposition system, alongside detailed QE measurements and spatially resolved QE maps. These findings highlight the potential of Na-K-Sb PCs to advance CeC performance significantly and foster the development of high current, high-brightness electron sources for broader applications

We describe the development of a MADX-to-Xsuite simulation framework for the Fermilab Main Injector (MI) along with the subsequent evaluation of transition-crossing behaviors in the accelerator. In particular, we studied the introduction of quadrupole magnets into the lattice as part of a transition-jump system that will be implemented in the machine through the Second Proton Improvement Plan (PIP-II). Simulated beam losses spurred by transition-induced instabilities were assessed under several systematic effects, including MI quad errors, magnet-to-magnet variability in the jump magnets, emulated power supply errors, and timing jitter.

The LANSCE Modernization Project (LAMP) aims at upgrading the front end of the LANSCE accelerator, involving one single radio-frequency quadrupole (RFQ) at 201.25 MHz for simultaneously accelerating both proton (H+) and negative hydrogen ion (H-) beams from 100 keV to 3 MeV. To meet the diverse set of beam requirements at various user stations, the RFQ must be capable of accelerating a continuous-wave beam as well as a pulsed input beam. For example, with H- beam production, the RFQ accelerates a continuous-wave-like beam for the Lujan Center, and a pulsed beam for the Weapons Neutron Research (WNR) facility. The WNR operational mode is the highlight of the LANSCE accelerator and of the LAMP upgrade. We introduce the design optimization of the RFQ for ensuring that all associated requirements of the LAMP key performance parameters are satisfied. The optimization of the overall configuration of the low energy beam transport (LEBT) beamline for shaping the phase spaces of the WNR beam pulse at the entrance to the RFQ is also addressed.