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DOE OSTI2021

Estimates of Damped Energy Spread and Emittance in a Two Energy Storage Ring Cooler

In this paper we provide estimates of the damped energy spread and emittance in a two-energy storage ring cooler. Two energy storage rings have two loops at markedly different energies, one at low energy and the other at high energy. In a cooling application the low energy ring has a cooling section to cool the ion beam and the high energy ring may have a wiggler section to enhance the damping effect on electron beam. The linear optics in the cooling section is designed to attain the maximum cooling of ion beams. Similarly, the linear optics in the wiggler section is designed to attained the required equilibrium emittance and energy spread. Hence, the radiation events in these two rings are different and independent. Since the values of damped energy spread and emittance depend on a range of parameters related to lattice design and rings energies, we present analytical calculations along with simulation results to estimate the values of damped energy spread and emittance in a two energy storage ring cooler.

Dhital, B.↗

DOE OSTI2021

ANALYSIS OF MULTIBUNCH SPECTRUM FOR AN UNEVEN BUNCH DISTRIBUTION IN A STORAGE RING

Modern storage-ring designs often require an uneven bunch distribution pattern. An uneven bunch fill pattern can result in complex structures for the beam current spectra. Particularly at high average beam currents, these complex current spectra need to be taken into account in concern of beam-dynamical effects. In this study, we analyze a beam current spectrum for various filling patterns with bunch trains and gaps. The characteristics of the resulting beam current spectra are illustrated and discussed.

Li, Rui↗

DOE OSTI2021

Transverse Beam Tails and Beam Lifetime in the EIC Electron Storage Ring

For most storage ring design purposes it is sufficient to assume a Gaussian distribution of the electrons in a bunch. However, a more detailed knowledge of the population in the transverse tails beyond a few sigma is necessary to predict the beam lifetime and the synchrotron radiation load in the interaction region due to beam-gas scattering and the beam-beam interaction. This report presents simulations to determine the required vacuum level as well as to serve as input data for detailed synchrotron radiation simulations.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Dual-energy electron storage ring

A dual-energy electron storage ring is a novel concept initially proposed to cool hadron beams at high energies. The design consists of two closed rings operating at significantly different energies: the low-energy ring and the high-energy ring. These two rings are connected by an energy recovery linac (ERL) that provides the necessary energy difference. The ERL features superconducting radio-frequency (SRF) cavities that first accelerate the beam from the low energy E L to the high energy E H and then decelerate the beam from E H to E L in the next pass. The different SRF cavities in the ERL section can be adjusted based on the applications. In this paper, we present a possible layout of a dual-energy electron storage ring. The preliminary optics of the ring is designed to optimize chromaticity correction, dynamic aperture, momentum aperture, beam lifetime, radiation damping, and intrabeam scattering effects. The primary focus of this paper is on the stability conditions and beam dynamics studies associated with this storage ring. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

The Concept and Applications of a Dual Energy Storage Ring

A dual energy electron storage ring configuration is initially proposed as an electron cooler to cool the ion beam in a collider. It consists of two energy loops, the electron beam in the high energy loop undergoes the synchrotron radiation damping to obtain the desired beam property and the beam in the low energy loop is for cooling of the ion beam. The two different energy loops are connected by an energy recovery linac. A lattice design of such a dual energy storage ring has been completed and beam stability conditions are established. We performed numerical simulations to demonstrate the beam qualities and evaluated the cooling performance. In this paper, we present the study results and discuss possible applications of such a concept in many physics research and medical fields.

Dhital, B.↗

DOE OSTI2025

Half-life determination of heavy ions in a storage ring considering feeding and depleting background processes

Heavy-ion storage rings have relatively large momentum acceptance which allows for multiple ion species to circulate at the same time. This needs to be considered in radioactive decay measurements of highly charged ions, where atomic charge exchange reactions can significantly alter the intensities of parent and daughter ions. In this study, we investigate this effect using the decay curves of ion numbers in the recent 205 Tl 81+ bound-state beta decay experiment conducted using the Experimental Storage Ring at GSI Darmstadt. To understand the intricate dynamics of ion numbers, we present a set of differential equations that account for various atomic and nuclear reaction processes—bound state beta decay, atomic electron recombination and capture, and electron ionization. By incorporating appropriate boundary conditions, we develop a set of differential equations that accurately simulate the decay curves of various simultaneously stored ions in the storage ring: 205 Tl 81+ , 205 Pb 81+ , 205 Pb 82+ , 200 Hg 79+ , and 200 Hg 80+ . Through a quantitative comparison between simulations and experimental data, we provide insights into the detailed reaction mechanisms governing stored heavy ions within the storage ring. Our approach effectively models charge-changing processes, reduces the complexity of the experimental setup, and provides a simpler method for measuring the decay half-lives of highly charged ions in storage rings.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Numerical modeling of a proof-of-principle experiment on optical stochastic cooling at an electron storage ring

Cooling of beams circulating in storage rings is critical for many applications including particle colliders and synchrotron light sources. A method enabling unprecedented beam-cooling rates, optical stochastic cooling (OSC), was recently demonstrated in the Integrable Optics Test Accelerator (IOTA) electron storage ring at Fermilab [J. Jarvis , ]. This paper describes the numerical implementation of the OSC process in the particle-tracking program and discusses the validation of the developed model with available experimental data. The model is also employed to highlight some features associated with different modes of operation of OSC. The developed simulation tool should be valuable in guiding future configurations of optical stochastic cooling and, more broadly, modeling self-field-based beam manipulations. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗

DOE OSTI2022

Autoresonant excitation of nonlinear beam motion in storage rings

Understanding and controlling of nonlinear beam dynamics are essential to the performance of storage ring light sources. In order to measure and correct limitations due to nonlinear beam dynamics, an effective method is needed to excite the beam oscillation to large amplitudes. Autoresonance is a method that enables the control of the amplitude of a driven nonlinear oscillator by sweeping the frequency of the driver. In this study, autoresonant excitation of beam transverse oscillations in storage rings is studied. The threshold of the drive amplitude for autoresonance is theoretically obtained, for cases with or without damping. The results are in good agreement with simulations for a simple storage ring model, as well as for models of actual storage rings. Application of the theory to experimental data on the SPEAR3 storage ring also validates the results

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

Beam Dynamics Study in a Dual Energy Storage Ring for Ion Beam Cooling

A dual energy storage ring designed for beam cooling consists of two closed rings with significantly different energies: the cooling and damping rings. These two rings are connected by an energy recovering superconducting RF structure that provides the necessary energy difference. In our design, the RF acceleration has a main linac and harmonic cavities both running at crest that at first accelerates the beam from low energy E_{L} to high energy E_{H} and then decelerates the beam from E_{H} to E_{L} in the next pass. The purpose of the harmonic cavities is to extend the bunch length in a dual energy storage ring as such a longer bunch length may be very useful in a cooling application. Besides these cavities, a bunching cavity running on zero-crossing phase is used outside of the common beamline to provide the necessary longitudinal focusing for the system. In this paper, we present a preliminary lattice design along with the fundamental beam dynamics study in such a dual energy storage ring.

Dhital, B.↗

DOE OSTI2026

A Dedicated Muon EDM Experiment in the `g-2 Storage Ring

Spin precession experiments offer exciting motivations to search for new physics. We propose here an idea of using a modified version of the Muon g-2 storage ring for a potential new scientific program to search for a non-zero muon electric dipole moment (EDM). Using both electric and magnetic dipole fields to produce a "frozen spin" condition for the MDM (all the while enhancing the EDM spin precession), the storage ring would operate at a lower central muon momentum than for the present Muon g-2 measurement. The incident proton beam on target for the muon production can be obtained from the PIP-II high intensity proton beam. Preliminary calculations and simulation results of muon production at 800 MeV PoT, along with the determination of the closed orbit inside the hybrid 'g-2' storage ring configuration, shall be presented. Possibilities of using the 'g-2' storage ring as a test bench to demonstrate the freezing of the MDM spin precession shall be discussed. The operational range of the muon's momentum and energy, and their respective window of electric and magnetic field values to establish the frozen spin condition, shall be presented. We shall also briefly discuss the physics prospects and improvements in muon EDM bounds upon using Fermilab's PIP-II beam.

Narayanan, Aakaash [Fermilab] (ORCID:0000000157944↗

DOE OSTI2026

A Dedicated Muon EDM Experiment in the `g-2 Storage Ring

Narayanan, Aakaash [Fermilab] (ORCID:0000000157944↗

DOE OSTI2024

Formalism for Local Correction of Vertical Crabbing in Hadron Storage Ring

The Electron-Ion Collider (EIC) incorporates crab cavities in both the Electron Storage Ring (ESR) and the Hadron Storage Ring (HSR) to achieve unprecedented luminosity goals. This technical note presents a formalism for the local correction of vertical crabbing in the HSR, addressing the complexities introduced by the integration of crab cavities and the interplay between betatron coupling and crabbing dispersion. Various strategies, including the use of skew quadrupoles and adjustments of Twiss functions, are explored to compensate vertical crabbing to achieve optimal beam-beam performance. The derived theoretical formulas offer practical guidance for minimizing the required vertical crabbing corrections, and will be implemented in the HSR lattice design.

43 PARTICLE ACCELERATORS↗

DOE OSTI2022

Beam-Based Diagnostics of Electric Guide Fields and Lattice Parameters for Run-1 of the Muon g-2 Storage Ring at Fermilab

A portion of the Muon g-2 Storage Ring electric system, which provides vertical beam focusing, exhibited an unexpected time dependence that produced a characteristic evolution of the stored beam during Run-1 of the Muon g-2 Experiment at Fermilab (E989). A method to reconstruct the Run-1 electric guide fields has been developed, which is based on a numerical model of the muon storage ring and optimization algorithms supported by COSY INFINITY. This method takes beam profile measurements from the Muon g-2 straw tracking detectors as input, and it produces a full reconstruction of the time-dependent fields. The fields can then be used for the reproduction of detailed beam tracking simulations and the calculation of ring lattice parameters for acceptance studies and systematic error evaluations.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Theories derived from Haissinski equation and their applications to electron storage rings

As a stationary solution of the Vlasov–Fokker–Planck equation, the Haissinski equation predicts the equilibrium line density of a bunch that circulates in a storage ring for a given wake function. The research in this paper shows that some equations regarding the centroid shift of the bunch, the peak position of the bunch profile, bunch length, and the impedance from the bunch profile can be derived from the Haissinski equation in a self-consistent manner. Specifically, a generalized quadratic equation for potential-well bunch lengthening is derived to accommodate any arbitrary impedance model (that is, the impedance spectrum under consideration can take any form). This expands upon Zotter's cubic equation, which is primarily applicable to inductive impedance. The equations derived in this paper are tested using computed impedance models for some electron storage rings, showing machine-dependent properties of impedance effects. We conclude that these equations can be employed in electron storage rings to effectively bridge the gap between impedance computations and beam-based measurements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

Perspective of a Dual Energy Electron Storage Ring Cooler for a Hadron Beam Cooling

A dual energy electron storage ring cooler was proposed and explored to maintain a good hadron beam quality against intra-beam scattering and all heating sources in a collider. The unique configuration of this concept is that electron beam in the low energy section extracts heat away from the hadron beam through Coulomb interaction while electron beam in the high energy section releases heat through its intrinsic synchrotron radiation damping. The early design employs a magnetized electron beam for achieving a high cooling efficiency. Recently, a non-magnetized cooling electron beam was explored in this dual energy cooler. It could meet the same cooling requirements while lowering the risks. This paper presents study results on design and optimization of a dual energy storage ring cooler and describes the trade-offs between using magnetized and non-magnetized cooling for this approach.

Lin, Fanglei↗

DOE OSTI2021

A New Magnetic Measurement System for the Future Low Emittance NSLS-II Storage Ring

A new magnetic measurement system is under construc-tion at BNL for accurate field harmonic measurements and fiducialization of magnets for a future upgrade of the NSLS- II storage ring. The entire storage ring is envi-sioned to be replaced with a new lattice concept, known as Complex Bend, which superimposes dipole and high-gradient quadrupole fields. The magnetic measurement system will use rotating wire and a PCB rotating coil specifically designed for small-aperture (< 15 mm) high gradient magnets. In this paper we describe in detail the mechanical design and the data acquisition hardware and software.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

BAGELS for simultaneous polarization, orbit, and optics control in electron storage rings

We present a new method for minimizing the effects of radiative depolarization in electron storage rings by use of a minimal number of special vertical orbit bumps. The bumps can be used to minimize the effects of radiative depolarization while simultaneously maintaining other common benefits of vertical orbits, e.g., transverse coupling and vertical dispersion control. Because simultaneously optimizing the large number of vertical correctors in a ring is operationally infeasible, we use dimensionality reduction to define a minimal number of the most effective groups of vertical correctors that can be optimized during operation, motivating the name “Best Adjustment Groups for ELectron Spin” (BAGELS). The method is streamlined by using suitable “basis bumps” instead of all individual vertical correctors. We define three types of basis bumps for different purposes: (i) generates no delocalized transverse coupling nor delocalized vertical dispersion, (ii) generates no delocalized vertical dispersion, and (iii) generates no delocalized transverse coupling. BAGELS has been essential in the design of the Electron Storage Ring (ESR) of the Electron-Ion Collider (EIC) and will be beneficial for any polarized electron ring, including FCC-ee. HERA and LEP would have likely benefitted as well. We use BAGELS to significantly increase polarization in the 18 GeV EIC-ESR, beyond what is achievable with conventional methods; in the 1-IP lattice, we nearly double the asymptotic polarization, and in the 2-IP lattice, we more than triple the asymptotic polarization. We also use BAGELS to construct knobs that can be used for global coupling correction, and knobs that generate vertical emittance for beam size matching, all while having minimal impacts on the polarization and orbit/optics. Published by the American Physical Society 2025

43 PARTICLE ACCELERATORS↗

DOE OSTI2022

Single-shot measurement of longitudinal phase space beam profile in an electron storage ring

A novel scheme to measure the longitudinal emittance and phase space profile in an electron storage ring by using correlations between time and the vertical coordinate, and between energy and the horizontal coordinate, is proposed. This longitudinal profile measurement scheme will help to demonstrate recent results of advanced studies for manipulating the longitudinal beam profile and for investigating beam instability in an electron storage ring.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗