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DOE OSTI2025

Reconstruction of beam parameters and betatron radiation spectra measured with a Compton spectrometer

The photon flux resulting from high-energy electron beam interactions with high-field systems, such as those found in the upcoming FACET-II experiments at the SLAC National Accelerator Laboratory, yields deep insight into the electron beam’s underlying dynamics during the interaction. However, extracting this information is an intricate process. To demonstrate how to approach this challenge using modern methods, this paper utilizes simulated data that models plasma wakefield acceleration-derived betatron radiation in experiments to determine reliable methods of reconstructing key beam and beam-plasma interaction properties. For betatron radiation measurements, translating the observed 200⁢ keV to 30⁢ MeV photon double-differential energy-angle spectra obtained from an advanced Compton spectrometer requires testing multiple methods to optimize the pipeline from its response to incident electron beam information. The paper compares maximum likelihood estimation and machine learning to refine the translation of photon spectra into precise electron beam metrics, such as spot size, energy, and emittance, enhancing the understanding of beam behavior within these dense, high-field environments. We also introduce machine learning and the expected maximization algorithm to reconstruct the primary photon spectrum, employing a multilayer neural network for regression analysis of the energy and angle spectra. With appropriate modifications, the advanced methods reproduce relevant incident beam parameters with high accuracy, even for beam sizes in the <10 μ⁢m range. This capacity is critical to understanding intense beam propagation and its optimization in plasma.

Beam code development & simulation techniques↗

DOE OSTI2025

Nonparaxial propagation of an intense relativistic electron beam through dense media

An envelope equation is used to explore the propagation of a focused electron beam through dense conductive media like partially ionized high-pressure gas, metal vapor plumes from beam-target interactions, or low-density solid-phase targets. Envelope equations have been a most useful tool for predicting experimental results of beam propagation in gas, and they are refined for the general problem of propagation through a dense medium. The envelope equation is modified to account for the large beam divergence resulting from multiple scattering. The envelope code results are in qualitative agreement with published experimental data. Published by the American Physical Society 2025

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Latent diffusion can map beam loss to two-dimensional phase-space projections

Beam loss monitors (BLMs) and beam current monitors (BCMs) are ubiquitous at particle accelerators around the world. These simple devices provide noninvasive high-level beam measurements but give no insight into the detailed 6D (𝑥,𝑦,𝑧,𝑝 𝑥 ,𝑝 𝑦 ,𝑝 𝑧 ) beam phase-space distributions or dynamics. We show that generative conditional latent diffusion models can learn intricate patterns to solve the extreme inverse problem of mapping waveforms of tens of BLMs or BCMs along an accelerator to detailed 2D projections of a charged particle beam’s 6D phase-space density. This transformational method can be used at any particle accelerator to transform simple noninvasive devices into detailed beam phase-space diagnostics. We demonstrate this concept via multiparticle simulations of the high-intensity beam in the kilometer-long Los Alamos Neutron Science Center linear proton accelerator.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Physics-constrained superresolution diffusion for six-dimensional phase space diagnostics

Adaptive physics-constrained superresolution diffusion is developed for noninvasive virtual diagnostics of the six-dimensional (6D) phase space density of charged particle beams. An adaptive variational autoencoder embeds initial beam condition images and scalar measurements to a low-dimensional latent space from which a 32 6 pixel 6D tensor representation of the beam's 6D phase space density is generated. Projecting from a 6D tensor generates physically consistent two-dimensional projections. Physics-guided superresolution diffusion transforms low-resolution images of the 6D density to high resolution 256 × 256 pixel images. Unsupervised adaptive latent space tuning enables tracking of time-varying beams without knowledge of time-varying initial conditions. The method is demonstrated with experimental data and multiparticle simulations at the HiRES UED. The general approach is applicable to a wide range of complex dynamic systems evolving in high-dimensional phase space. The method is shown to be robust to distribution shift without retraining. Published by the American Physical Society 2025

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

JuTrack: A Julia package for auto-differentiable accelerator modeling and particle tracking

Efficient accelerator modeling and particle tracking are key for the design and configuration of modern particle accelerators. In this work, we present JuTrack, a nested accelerator modeling package developed in the Julia programming language and enhanced with compiler-level automatic differentiation (AD). With the aid of AD, JuTrack enables rapid derivative calculations in accelerator modeling, facilitating sensitivity analyses and optimization tasks. Here we demonstrate the effectiveness of AD-derived derivatives through several practical applications, including sensitivity analysis of space-charge-induced emittance growth, nonlinear beam dynamics analysis for a synchrotron light source, and lattice parameter tuning of the future Electron-Ion Collider (EIC). Through the incorporation of automatic differentiation, this package opens up new possibilities for accelerator physicists in beam physics studies and accelerator design optimization.

43 PARTICLE ACCELERATORS↗

DOE OSTI2026

Dynamic evolution of ultracold electron beams from nanostructured cathodes

Dynamic Coulomb expansion of dense, nonuniform particle beamlets can lead to causticlike formations in the charge density profile of the resultant beam. Such features only occur for cold beams where thermal diffusion of the particles is minimized. These phenomena have been observed experimentally for select cases with ion beams but not yet for electron beams as the electron dynamics occur over far faster timescales. We simulate the interaction of electron bunches while varying the initial transverse temperature and density profiles to determine the thresholds that characterize this pattern formation. Furthermore, we extend the simulations to geometric arrangements that are more pertinent to the nanotip cathode application and consider the effects of asymmetries and the impact of a low-density halo on the overall process. The simulations are conducted using a previously documented high-fidelity algorithm for collisional particle dynamics. These studies identify the temperature and density thresholds required for caustic formation and provide guidance for optimizing the design of nanoscale structured cathodes. We also demonstrate that the correlation between the final density patterns and the underlying beam parameters enables a virtual diagnostic tool for measuring ultralow emittance beams solely based on a transverse charge density profile.

43 PARTICLE ACCELERATORS↗

DOE OSTI2026

Polarization transmission in the Hadron Storage Ring of the Electron-Ion Collider

The successful operation of the future Electron-Ion Collider is contingent on maintaining high hadron beam polarization up to 275 GeV. The Hadron Storage Ring lattice, however, features a symmetry-breaking interaction region that excites strong, nonsystematic spin resonances, posing a significant threat to polarization preservation. This paper systematically investigates two complementary strategies to ensure high polarization transmission. The first method involves optimizing the vertical betatron phase advance between Siberian snakes to orchestrate a cancellation of depolarizing kicks across the ring. We demonstrate through simulations that both dynamic and fixed-optics solutions based on this principle can successfully preserve polarization through the strongest resonances. The second, more powerful approach involves optimizing the snake rotation axes to suppress resonance driving terms at their source. We revisit established symmetric configurations, such as the Lee-Courant schemes, and introduce a novel, highly symmetric “Doubly Lee-Courant” (DLC) scheme, which enforces a local 𝜋 spin phase advance across every consecutive pair of snakes. Our analysis reveals a clear performance hierarchy, with the DLC configuration providing an exceptionally robust and energy-insensitive baseline for polarization preservation. We conclude that a hybrid strategy, using a DLC snake scheme as a symmetric foundation and betatron phase tuning for fine corrections, offers the most effective path forward for the EIC and future high-energy polarized-beam facilities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Tomography of longitudinal phase space linearization for the generation of attosecond electron bunches

The generation of electron bunches on the attosecond timescale is important for a multitude of accelerator-based applications. Here, we report on a tomographic measurement of the (pre)linearized longitudinal phase space of a low charge 3 MeV electron bunch generated with the 1.6 cell Pegasus photoinjector for the generation of attosecond bunches. The nonlinear correlations in the longitudinal phase space induced by space charge at the photocathode, radiofrequency field curvature of the gun, and vacuum dispersion are compensated using a compact X-band linearizer. Then, the initial and compensated phase of the picosecond electron bunch is precisely reconstructed by neural network assisted tomographic reconstruction from momentum spectra at varying buncher linac phase. Finally, we combine the measured phase space shape with particle tracking simulations to show that electron bunches as short as 941 as develop downstream the beamline.

Beam control↗

DOE OSTI2026

A Unified Beam-Dynamics and Hardware Design Framework for Hybrid Nonlinear-Kicker Injection in NSLS-II

Nonlinear kickers (NLKs) enable off-axis injection in ultralow-emittance storage rings by providing a strong kick to the injected beam while remaining nearly transparent to the stored beam. In hybrid schemes, a conventional four-kicker bump defines the injected trajectory, and the NLK reduces the first-turn action under constrained beam offset and optics conditions. Effective operation additionally requires stable and reproducible first-turn injection trajectories. We develop a compact action–angle framework that expresses NLK dynamics in terms of Courant–Snyder invariants and yields an analytical bound on achievable action reduction. This formulation provides direct design rules for NLK placement, phase advance, injected-beam offset, and kicker field profile. Within this framework, we identify the 8-wire NLK as a practical baseline and extend its design by relaxing the square-geometry constraint, enabling inward shifting of the off-axis field peak while preserving on-axis field and gradient cancellation. Application to the NSLS-II lattice shows how aperture, pulsed-power, and mechanical constraints combine to determine a coupled design solution. Multi-turn tracking confirms that candidate NLK locations maintain sufficient stay-clear (aperture-clearance) margin, while the optimized wire geometry reduces the required current and Lorentz force load. The results establish a unified approach for NLK-assisted injection design and provide a practical pathway for upgrades in diffraction-limited storage rings.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Experimental Studies of Nonlinear Integrable Optics with Elliptic Potentials

The stable transport of charged particle beams is the core challenge in designing and operating accelerators. The current paradigm for transverse focusing is based on quadrupole and dipole elements, described as a linear integrable Hamiltonian by Courant and Snyder. The operational limits of high intensity accelerators are often determined by collective instabilities within the beam. Nonlinear elements may be added to suppress certain forms of these collective effects, but restrict the range of stable trajectories. These shortcomings motivate extending to a nonlinear integrable system which can offer the benefits of suppressing collective instabilities without limiting the stable trajectories. Danilov and Nagaitsev proposed a novel nonlinear integrable system with elliptical potentials, which could be implemented as magnetic elements in an accelerator. Such a system has been implemented for practical verification in the integrable optics test accelerator (IOTA), a small storage ring constructed for beam dynamics studies. Electron beam studies in IOTA treat the low-emittance beam as a macroparticle for detailed probing of the expected single particle dynamics. This dissertation details new measurements of the nonlinear integrable system relevant for practical implementation. Turn-by-turn measurements of the kicked beam responses are used for phase space reconstruction and analysis of the predicted nonlinear dynamics. The stability and aperture for various nonlinear configurations are measured with beam losses. Amplitude dependent detuning, a core figure of merit for suppressing instabilities, is measured and compared with high fidelity particle tracking simulations. The synchrotron radiation images of circulating beam allow direct measurements of the topology and lifetime in configurations where nonlinear focusing terms dominate.

Wieland, John [Michigan U.] (ORCID:000000028971852↗

DOE OSTI2026

Analysis of the elliptic integrable non-linear system in IOTA using tracking of a single electron

Integrable nonlinear lattices that can be realized in practical accelerators are of great interest, as they offer the potential to support high-intensity beams via Landau damping of collective instabilities. One such system, based on an elliptic potential, has been extensively studied at the IOTA storage ring at Fermilab. The analysis of strongly nonlinear dynamics with multi-particle bunches is challenging due to the rapid decoherence of kicked beams. IOTA has the capability to track single electrons using linear multi-anode photomultiplier tubes for simultaneously measuring transverse coordinates and arrival times of synchrotron-radiation pulses. This technology enables the full reconstruction of turn-by-turn positions and momenta in all three planes for a single particle. Using this apparatus, we measured the dependence of small-amplitude tunes on the strength of the nonlinear magnet, as well as tunes dependence on oscillations amplitudes.

Romanov, A. [Fermilab]↗

DOE OSTI2025

Analysis of the Elliptic Integrable Non-Linear System in IOTA Using Tracking of a Single Electron

Romanov, Aleksandr Leonidovich [Fermilab] (ORCID:0↗

DOE OSTI2025

Fully plasma-based electron injector for a linear collider or XFEL

We demonstrate through high-fidelity particle-in-cell (PIC) simulations a simple approach for efficiently generating 20 + GeV electron beams with the necessary charge, energy spread, and emittance for use as an injector in a future linear collider or a next generation XFEL. A high quality injected bunch is generated by self-focusing an unmatched electron driver in a nonlinear plasma wakefield. Over pump depletion distances, the drive beam dynamics and self-loading effects lead to high energy, low-energy spread output beams. For plasma densities of 10 18 c⁢m −3 , PIC simulation results indicate that self-injected beams with 0.52 n⁢C charge can be accelerated to 20 GeV with projected core energy spreads of ≲ 1%, normalized slice emittances of 110n⁢m, peak normalized brightness of ≳ 10 19 A/m 2 /rad 2 , and transfer efficiencies of ≳ 44%.

Particle acceleration in plasmas↗

DOE OSTI2026

Searching for the Most Harmful Field Errors in the HSR IR Superconducting Magnets

In this project, we improve beam stability for the Electron-Ion Collider. Magnetic field errors can reduce beam stability, making it essential to identify the field errors that have the greatest impact on accelerator performance. However, this is particularly challenging because beam stability depends on the complex interactions of many magnetic field errors, resulting in a high-dimensional and nonlinear optimization problem. We determine which field errors are the most influential for the large physical aperture superconducting magnet B2PF, a critical magnet in the Interaction Region (IR) in the Hadron Storage Ring (HSR). We complete and analyze nearly 30,000 simulations on the Brookhaven National Laboratory Linux Cluster by varying 18 nonlinear magnetic field errors. We evaluate beam stability using the dynamic aperture and the tune diffusion. We identify the field errors that most strongly influence beam stability and establish quantitative field error tolerances that improve accelerator performance.

43 PARTICLE ACCELERATORS↗

DOE OSTI2026

Analytic Chromaticity Formulas for the Muon g -2 experiment at fermilab

The Muon g-2 Experiment (E989) at Fermilab measured the muon anomalous magnetic moment aμ with unprecedented precision of 127 ppb using a storage ring. The experiment pushed the limits in terms of accuracy and systematic errors. Achieving the 78-ppb total systematic uncertainty required precise beam dynamics modeling and corrections for effects on the measured muon precession frequency. Here, we derived the first analytic aberration formulas up to the second order for the muon g-2 storage ring’s combined-function electrostatic quadrupoles (superimposed magnetic dipole and electric quadrupole fields) using an order-by-order perturbation method. From these, we obtained the exact chromaticity formulas for three ring models of different granularity and validated them against numerical calculations using COSY INFINITY, achieving analytic-numerical agreement to ⁠$\mathscr{O}(10^{-10})$. This work resolved discrepancies between previous approximate derivations and provided essential beam dynamics results for Runs 4-6 analyses. We also calculated nonlinear chromaticities up to ninth order. The experiment completed its final Run 6 in July 2023, collecting 21 times more data than the previous muon g-2 experiment at Brookhaven National Laboratory, with the final result announced in June 2025.

aberrations↗

DOE OSTI2026

Adaptive nonlinear wavefront shaping in layered TMDs

Two-dimensional transition metal dichalcogenides are promising candidates for nonlinear photonics applications, offering strong nonlinear susceptibility and compatibility with integrated platforms. Although considerable effort has been devoted to manipulating second harmonic generation in these materials, the dynamic control of nonlinear wavefronts remains largely unexplored. Metasurfaces have enabled significant progress in nonlinear beam engineering, yet their practical implementation is limited by low conversion efficiencies and restricted design flexibility. In this work, we employ feedback-based wavefront shaping using spatial light modulators to enhance SHG from pyramid-like WS 2 multilayer structures by over three orders of magnitude in selected spatial regions. This approach allows us to program nonlinear holograms and dynamically shape the SHG signal through phase-only modulation, opening new possibilities for nonlinear imaging, optical information processing, and data communication.

Mavian, Alex [Rensselaer Polytechnic Inst., Troy, ↗

DOE OSTI2025

Digital Twin Framework for PIP-II Linac: AI-Driven Multi-Scale Modeling from Ion Source to 800 MeV

The PIP-II linac will enable >1.2 MW beam power for DUNE, requiring unprecedented operational reliability across its warm front-end (RFQ, MEBT) and five distinct SRF sections operating at 162.5/325/650 MHz. We present a comprehensive digital twin framework uniquely combining a fully differentiable fast beam transport code with neural network surrogates trained on high-fidelity PIC simulations, capturing space charge and nonlinear dynamics beyond traditional envelope codes while achieving 10⁴ speedup at <1% accuracy. End-to-end differentiability enables gradient-based optimization across 500+ parameters simultaneously previously impossible with conventional tools while the model incorporates static/dynamic errors and serves as a virtual commissioning platform for diverse hardware integration. The framework facilitates reinforcement learning for pulsed/CW mode transitions, predictive maintenance through anomaly detection, and autonomous tuning algorithm development with real-time execution capability. Validation against physics simulations shows excellent agreement for the front-end, with initial results demonstrating potential for 30% commissioning time reduction and proactive fault mitigation, providing a scalable blueprint for operating next-generation high-intensity accelerators.

Pathak, Abhishek [Fermilab] (ORCID:000000021704208↗

DOE OSTI2025

Digital Twin Framework for PIP-II Linac: AI-Driven Multi-Scale Modeling from Ion Source to 800 MeV

The PIP-II linac will enable >1.2 MW beam power for DUNE, requiring unprecedented operational reliability across its warm front-end (RFQ, MEBT) and five distinct SRF sections operating at 162.5/325/650 MHz. We present a comprehensive digital twin framework uniquely combining a fully differentiable fast beam transport code with neural network surrogates trained on high-fidelity PIC simulations, capturing space charge and nonlinear dynamics beyond traditional envelope codes while achieving 10⁴× speedup at <1% accuracy. End-to-end differentiability enables gradient-based optimization across 500+ parameters simultaneously—previously impossible with conventional tools—while the model incorporates static/dynamic errors and serves as a virtual commissioning platform for diverse hardware integration. The framework facilitates reinforcement learning for pulsed/CW mode transitions, predictive maintenance through anomaly detection, and autonomous tuning algorithm development with real-time execution capability. Validation against physics simulations shows excellent agreement for the front-end, with initial results demonstrating potential for 30% commissioning time reduction and proactive fault mitigation, providing a scalable blueprint for operating next-generation high-intensity accelerators.

Pathak, Abhishek [Fermilab] (ORCID:000000021704208↗