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DOE OSTI2021

IOTA Run 2 Beam Dynamics Studies in Nonlinear Integrable Systems

Nonlinear integrable optics is a promising design approach for suppressing fast collective instabilities. To study it experimentally, a new storage ring, the Integrable Optics Test Accelerator (IOTA), was built at Fermilab. IOTA has recently completed its second scientific run, incorporating many hardware and instrumentation improvements. This report presents the results of the two integrable optics experiments - the quasi-integrable Henon-Heiles octupole system and the fully integrable Danilov-Nagaitsev system. We demonstrate tune spread and dynamic aperture in agreement with tracking simulations, and a stable crossing of the integer resonance. Based on recovered single-particle phase space dynamics, we show improved invariant jitter consistent with intended effective Hamiltonian. We conclude by outlining future plans and efforts towards proton studies and larger designs.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Understanding sextupole

In this study, we reassess the dynamics within a simple accelerator lattice featuring a single degree of freedom and incorporating a sextupole magnet. In the initial segment, we revisit the H\'enon quadratic map, a representation of a general transformation with quadratic nonlinearity. In the subsequent section, we unveil that a conventional sextupole is essentially a composite structure, comprising an integrable McMillan sextupole and octupole, along with non-integrable corrections of higher orders. This fresh perspective sheds light on the fundamental nature of the sextupole magnet, providing a more nuanced understanding of its far-from-trivial chaotic dynamics. Importantly, it enables the description of driving terms of the second and third orders and introduces associated nonlinear Courant-Snyder invariant.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Resonance compensation at the CERN PS booster aided by Bayesian optimization and BOBYQA

The CERN Proton Synchrotron Booster (PSB) operation involves the crossing of multiple resonance lines in the tune diagram. Loss maps from dynamic tune scans are a helpful way to visualize and quantify the strength of such resonances. Sextupole and octupole correctors can be used in order to partially or fully compensate multiple resonance lines, i.e., third and fourth order lines. The following work explores the application of advanced optimization algorithms such as Bayesian Optimization and Bound Optimization By Quadratic Approximation (BOBYQA) in order to compensate these resonance lines with available correctors.

43 PARTICLE ACCELERATORS↗

DOE OSTI2020

Experimental Studies of Single Invariant Quasi-Integrable Nonlinear Optics at IOTA

The Integrable Optics Test Accelerator is a research electron and proton storage ring recently commissioned at the Fermilab Accelerator Science and Technology facility. Its research program is focused on testing novel techniques for improving beam stability and quality, notably the concept of non-linear integrable optics. In this paper, we report on run 1 results of experimental studies of a quasi-integrable transverse focusing system with one invariant of motion, a Henon-Heiles type system implemented with octupole magnets. Good agreement with simulations is demonstrated on key parameters of achievable tune spread, dynamic aperture, and invariant conservation. We also outline current simulation and hardware improvement efforts for run 2, planned for fall of 2019.

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

Nonlinear Optics Measurements in IOTA

Nonlinear integrable optics is a recently proposed accelerator lattice design approach which allows to generate an amplitude dependent tune shift which is needed in high brightness accelerators to mitigate fast coherent instabilities. Whereas usually octupoles are used to achieve this task, this concept allows doing so without exciting any resonances, in turn preventing any particle loss. The concept is based around a special magnet design, together with specific constraints on the optics of the accelerator. To study such a system, the Integrable Optics Test Accelerator (IOTA) was recently constructed and commissioned at Fermilab. For the assessment of the performance of this concept, good knowledge of the optics and the (non-)linear dynamics without the special magnet is of key importance. As such, measurements were conducted in the IOTA ring, using the captured turn-by-turn data by the beam position monitors after excitation to infer quantities such as amplitude detuning and resonance driving terms. In this note, first results of these measurements are presented.

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

Modeling Transverse Space Charge effects in IOTA with pyORBIT

The role and mitigation of space charge effects are important aspects of the beam physics research to be performed at the Integrable Optics Test Accelerator (IOTA) at Fermilab. The impact of nonlinear integrability (partial and complete) on space charge driven incoherent and coherent resonances will be a new feature of this accelerator and has the potential to influence the design of future low energy proton synchrotrons. In this report we model transverse space charge effects using the PIC code pyORBIT. First we benchmark the single particle tracking results against MADX with checks on symplecticity, tune footprints, and dynamic aperture in a partially integrable lattice realized with a special octupole string insert. Our space charge calculations begin with an examination of the 4D symplecticity. Short term tracking is done first with the initial bare lattice and then with a matching of the rms values with space charge. Next, we explore slow initialization of charge as a technique to establish steady state and reduce emittance growth and beam loss following injection into a mismatched lattice. We establish values of space charge simulation parameters so as to ensure numerical convergence. Finally, we compare the simulated space charge induced tune shifts and footprints against theory.

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

Design of double- and multi-bend achromat lattices with large dynamic aperture and approximate invariants

A numerical method to design nonlinear double- and multi-bend achromat (DBA and MBA) lattices with approximate invariants of motion is investigated. The search for such nonlinear lattices is motivated by Fermilab’s Integrable Optics Test Accelerator (IOTA), whose design is based on an integrable Hamiltonian system with two invariants of motion. While it may not be possible to design an achromatic lattice for a dedicated synchrotron light source storage ring with one or more exact invariants of motion, it is possible to tune the sextupoles and octupoles in existing DBA and MBA lattices to produce approximate invariants. In our procedure, the lattice is tuned while minimizing the turn-by-turn fluctuations of the Courant-Snyder actions J x and J y at several distinct amplitudes, while simultaneously minimizing diffusion of the on-energy betatron tunes. The resulting lattices share some important features with integrable ones, such as a large dynamic aperture, trajectories confined to invariant tori, robustness to resonances and errors, and a large amplitude-dependent tune-spread. Compared to the nominal NSLS-II lattice, the single- and multi-bunch instability thresholds are increased and the bunch-by-bunch feedback gain can be reduced.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Beam Scattering Through Foil at NSRL

In this note, we describe the foil structure that is used in the NASA Space Radiation Laboratory (NSRL) transport line just before D6 septum magnet. Foils of different materials and thickness are used through which different ion species at different energies pass. Foil removes the electrons from the incoming ions and make it fully stripped (or partially stripped is also possible). Further, when charged particles pass through a foil, the outgoing particles form a Gaussian like angular distribution. This Gaussian like distribution passes through a set of octupole magnets creates a uniform beam distribution at the NSRL target which is required for various beam experiments. We utilize the Bmad and SRIM packages to calculate the energy loss through the foils for various ion species at different energies and charge states. Finally, we provide a summary of the energy loss calculations through the foils using these two different methods.

43 PARTICLE ACCELERATORS↗

DOE OSTI2022

Heating, DPA, and He production in the Proton Beam Window Assembly for the Second Target Station

This report details the analysis of the heating rates, dpa values, and He production in the Proton Beam Window (PBW), the assembly around the PBW, and the shielding above it. Neutronics calculations use a detailed Unstructured Mesh (UM) converted from the solid CAD model of the PBW design of June 2022. The rest of the geometry is taken from the CSG master model (as of June 2022). For this analysis, a proton beam profile with a footprint of ≈90 cm 2 has been used. This proton profile was created by a Ring to Second Target magnet array configuration using octupole magnets. Maximum values in the PBW (aluminum) are 5.4 J/cc/pulse heating rate, 1.1 dpa per year, and 660 appm He-production per year. These results within ~ 10% with the previous calculations from June 2020. Average heating and dpa rates have been calculated for each component in the PBW assembly and will be used to evaluate and design the cooling needs and make decisions on removable components for the PBW. It is desirable to optimize and simplify the PBW design by only replacing components that are at the end of their lifetime. Additional analysis for the energy deposition in the PBW is performed for two super-Gaussian beam profiles with a footprint of 60 cm 2 and 30 cm 2 respectively. Also, an estimate of the PBW lifetime is performed for two realistic quadrupole beam profiles.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Understanding Sextupole

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Measuring Magnets Transfer Functions in the NSRL Transport Line

The beamline at the NASA Space Radiation Laboratory (NSRL) is equipped with a range of magnets, including dipole magnets, dipole corrector magnets, quadrupole magnets, sextupole magnets, and octupole magnets. The magnet transfer function defines the relationship between the power supply currents and the corresponding magnet strengths. This note presents the measurements of the transfer functions for the dipole correctors and quadrupole magnet in the NSRL beamline.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Coupling between collective modes in the deformed 98 Zr nucleus: Insights from consistent HFB+QRPA calculations with the Gogny interaction

The Zirconium isotopes exhibit structural properties that present multiple challenges to nuclear theory. Investigations of the coupling present within isoscalar modes and within isovector modes are scarce but important for advancing our understanding of the microscopic picture of nuclei. To explore some of these underlying coupling features, and to test the predictive power of a state-of the-art nuclear structure approach, we provide a detailed analysis of the properties of 90,96,98Zr. This region includes a benchmarking case and offers insights into nuclear deformation phenomena. To investigate the coupling between collective modes in deformed nuclei, we focused our analysis on the ground and excited-state properties of these isotopes, employing a consistent approach with the axially-symmetric deformed Hartree-Fock-Bogoliubov (HFB) and the Quasiparticle Random Phase Approximation (QRPA) framework, both using the Gogny D1M force. This approach effectively describes both low-lying and giant-resonance states. We devoted special attention to the deformed 98Zr nucleus, where we confirm the existence of coupling between monopole and quadrupole excitations through the K π = 0 + QRPA components and demonstrate an analogous dipole-octupole coupling through the K π = 0 − and K π = 1 − components. Intrinsic transition densities and associ ated radial projections illustrate the coupling. Our work complements and extends earlier studies carried out using density-functional-based methods and notably, we included the complete Coulomb interaction also in the pairing fields, i.e. we treat terms exactly that are approximated in typical calculations that use the Gogny D1 and D2 interaction families.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Single-Bunch Instabilities Driven by Space Charge During Low-Energy Cooling at Injection in the EIC Hadron Storage Ring

This paper presents a simulation-based study of single-bunch dynamics at the injection energy of 23.8 GeV for protons in the EIC hadron storage ring, focusing on the impact of space-charge–driven instabilities. The analysis demonstrates that at this energy, the proton bunch experiences significant transverse space-charge forces, which can reduce the stability margin in the presence of the geometric and resistive wall impedance. Various collective effects were considered, with particular attention to the nonlinear nature of the transverse space charge. To stabilize the beam, high chromaticity and octupoles were introduced and their effects analyzed using the ELEGANT code. The results provide a quantitative assessment of the stability thresholds and offer guidance for the machine design and operational strategy at injection.

43 PARTICLE ACCELERATORS↗

DOE OSTI2026

Nuclear Structure Studies for Schiff Moment Enhancement

One of the major open questions in modern physics is the origin of the matter-antimatter asymmetry observed in the universe. While the Standard Model contains sources of charge-parity (CP) violation, they appear insufficient to explain the observed dominance of matter over antimatter. As a result, searches for additional sources of CP violation are an important area of contemporary nuclear and particle physics. Atomic electric dipole moments (EDMs) provide sensitive probes of CP-violating interactions. In heavy nuclei, the observable atomic EDM can be enhanced through the presence of a nuclear Schiff moment, which arises from CP-violating nuclear forces and nuclear structure effects. The review paper Nuclear Schiff Moments and CP Violation by Jonathan Engel provides an overview of the theoretical framework connecting CP violation, nuclear structure, and Schiff moments. The long-term goal of this project is to contribute to the identification and characterization of nuclei that may exhibit enhanced Schiff moments. Such nuclei are often associated with strong octupole correlations or low-energy parity-doublet structures that can amplify CP-violating effects. This report summarizes progress made during the initial phase of the project, including a survey of candidate isotopes and preparation for nuclear-structure calculations using the HFODD code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Analytical Dynamic Aperture Calculation Compared to Tracking Results

In studying dynamic aperture in the storage rings, it is becoming increasing beneficial to understand the growth of the fractal boundary of the dynamic aperture without tracking for millions of turns in a hadron ring. This note describes the J. Gao theory applied to the Electron Ion Collider (EIC) Hadron Storage Ring (HSR) and compares simulation results to theoretical predictions to show that the analytical method may prove useful in quick determinations of improved dynamic aperture based on sextupole and octupole configurations.

43 PARTICLE ACCELERATORS↗

DOE OSTI2020

RECENT RESULTS AND OPPORTUNITIES AT THE IOTA FACILITY

The Integrable Optics Test Accelerator (IOTA) was recently commissioned as part of the Fermilab Accelerator Science and Technology (FAST) facility. The IOTA ring was briefly operated with electrons at 47 MeV followed by a 6-months run with 100 MeV electrons. The main goal of the first runwas to study beam dynamics in the integrable lattices with elliptical nonlinear magnets and in the quasi-integrable case with profiled octupole channel. The flexibility of the IOTA ring allowed a wide range of complementary studies, such as experiments with a single electron; studies of fluctuations in undulator radiation and operation with low emittance beams. Over the next year the proton injector will be installed and two runs carried out. One run will be dedicated to the refinement of nonlinear experiments and another will be dedicated to the proof-of-principle demonstration of Optical Stochastic Cooling.

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

EXPERIMENTAL STUDIES OF NONLINEAR INTEGRABLE OPTICS

State-of-the-art accelerators at energy and intensity frontiers require increasingly bright and powerful particle beams. In conventional linear lattices, intense beams suffer from collective instabilities, resulting in beam losses and maximum beam intensity limits. This thesis presents experimental studies of a novel lattice design concept, the nonlinear integrable optics (NIO), aimed at enhancing beam stability limits with little to no beam dynamics degradation. Single-particle beam dynamics measurements of two NIO devices, the quasi-integrable octupole system and the fully integrable Danilov-Nagaitsev system, were carried out at the purpose-built Integrable Optics Test Accelerator (IOTA) at Fermilab. Their simulation, hardware design, and commissioning process are presented. Extensive model and analysis algorithm development and benchmarking is described. Electron beam data from two scientific runs is analyzed, yielding frequency and phase space dynamics consisten t with m odels. These results demonstrate viability and advantages of the NIO design, providing the groundwork for proton studies in the strong space-charge regime and future integrable accelerators.

Kuklev, Nikita↗

DOE OSTI2026

Lifetimes of low-lying levels in 158 Gd

The low-lying structure of the well-deformed nucleus 158 Gd has been revisited to elucidate the nature of the low-lying states in 158 Gd. Earlier (p, t) studies identified numerous 0 + states below 4.3 MeV, prompting questions about whether these states correspond to collective vibrations or shape coexistence. New and previously reported (n, n' γ) measurements are combined, including γ-γ coincidences, excitation functions, and angular distributions, to extract lifetimes and transition probabilities for 44 excited states up to 2.7 MeV, including 32 previously unmeasured levels. Our results confirm or revise γ-ray placements and provide detailed transition strengths, revealing both weakly collective and strongly enhanced B(E2) and B(E1) transition probabilities. In particular, a tentative 0 + state at 2437.8 keV exhibits a strong interband B(E2) transition, which may be a candidate for a possible two-phonon (ββ) excitation. Systematic comparisons with neighboring Gd isotopes, Hartree–Fock–Bogoliubov, and interacting-boson model predictions suggest that the first excited 0 + state in 158 Gd is predicted to be a β-vibration, although it is weakly collective.

158Gd↗