Polarized ion beams at the Electron Ion Collider (EIC) are essential to address some of the most important open questions at the twenty-first century frontiers of understanding of the fundamental structure of matter. Here, we summarize the science case and identify polarized H-2, He-3, Li-6, and Li-7 ion beams as critical technology that will enable experiments which address the most important science. Furthermore, we discuss the required ion polarimetry and spin manipulation at the EIC. The current EIC accelerator design is presented. We identify a significant research and development effort across national and international laboratories and universities that is required over about a decade to realize the polarized ion beams and estimate (based on previous experience) that it will require about 20 full-time equivalent (FTE) over 10 years (or a total of about 200 FTE-years) of personnel, including graduate students, postdoctoral researchers, technicians, and engineers. Attracting, educating, and training a new generation of physicists in experimental spin techniques will be essential for the successful realization. Artificial intelligence and machine learning are seen as having significant potential for both acceleration of research and development and amplification of discovery in the optimal realization of this unique quantum technology on a cutting-edge collider. The research and development effort is synergistic with research in atomic physics and fusion energy science.

Precision measurements in storage rings are increasingly limited by the ability to monitor collective spin dynamics coherently over long time scales. Existing polarimetry techniques rely on destructive scattering processes that preclude continuous, non-intercepting tracking of spin evolution and constrain both statistical sensitivity and systematic control. Here we introduce a non-destructive, phase-coherent polarimetry method in which the stored beam polarization is treated as a continuous dynamical observable rather than a quantity inferred from scattering events. Spin-dependent electromagnetic fields generated by a polarized relativistic beam establish a symmetry-selected differential signal on pickup electrodes. This signal is transduced into a narrowband phase modulation of a high-Q resonator interrogated with a coherent probe, while dominant charge-induced backgrounds are rejected through geometric symmetry, helicity reversal, and synchronous demodulation. Controlled spin precession (spin-wheel operation) provides a stable phase reference enabling phase-coherent detection of slow spin evolution. Combined with optimized lattice symmetry and beam cooling, this approach can substantially extend the usable spin coherence time, with values approaching 10^5 s appearing realistic within existing accelerator technology. The resulting readout supports optimal slope-based estimation with T^-3/2 statistical scaling while eliminating the efficiency penalties inherent to scattering-based polarimetry. For storage-ring EDM experiments, this combination enables sensitivity approaching the level expected within the Standard Model. More broadly, the method establishes a general phase-coherent architecture for collective spin measurements in storage rings, adapting resonant sensing concepts from axion dark-matter searches to charged-particle precision experiments.

Polarized ion beams at the Electron Ion Collider are essential to address some of the most important open questions at the twenty-first century frontiers of understanding of the fundamental structure of matter. Here, we summarize the science case and identify polarized $^2$H, $^3$He, $^6$Li and $^7$Li ion beams as critical technology that will enable experiments which address the most important science. Further, we discuss the required ion polarimetry and spin manipulation in EIC. The current EIC accelerator design is presented. We identify a significant R\&D effort involving both national laboratories and universities that is required over about a decade to realize the polarized ion beams and estimate (based on previous experience) that it will require about 20 FTE over 10 years (or a total of about 200 FTE-years) of personnel, including graduate students, postdoctoral researchers, technicians and engineers. Attracting, educating and training a new generation of physicists in experimental spin techniques will be essential for successful realization. AI/ML is seen as having significant potential for both acceleration of R\&D and amplification of discovery in optimal realization of this unique quantum technology on a cutting-edge collider. The R\&D effort is synergistic with research in atomic physics and fusion energy science.

The Relativistic Heavy Ion Collider (RHIC) Run 24 was 27 cryo weeks, operating with collisions at the STAR and sPHENIX detectors. The primary mode was polarized protons at 100 GeV, where there was 22 weeks of physics production. sPHENIX continued commissioning, becoming fully operational after 13 weeks and the addition of isobutane to their TPC gas mixture. STAR had a low luminosity run followed by twenty weeks of high luminosity and radially polarized beams. To reduce the beam-beam parameter and maximize the number of collisions within a small vertex region at sPHENIX, sPHENIX planned to operate with a crossing angle. For 8 weeks, collisions were only at sPHENIX until the beam-beam parameter was sufficiently low to support the additional collisions at STAR. A significant number of power dips earlier in the run greatly affected machine performance and reliability. At the maximum achieved performance, the luminosity was limited by four factors simultaneously: accelerating RF cavity intensity limit, intensity from the injectors, losses at rebucketing, and dynamic aperture. Despite these difficulties, sPHENIX and STAR were able to collect sufficient data commensurate with their goals.

Ion profile monitors (IPMs) provide a non-destructive means of measuring the transverse beam size of a passing ion beam in a particle accelerator. The Alternating Gradient Synchrotron (AGS) at Brookhaven National Lab is equipped with two types of IPMs: ion-collecting and electron-collecting. While ion-collecting IPMs are susceptible to significant distortions in the measured beam size due to the space charge of the passing beam, electron-collecting IPMs are much less affected. However, in the AGS, electron-collecting IPMs can only be operated periodically to preserve sensor lifespan, leaving ion IPMs as the sole source of consistent, real-time beam size feedback during operation. In this work, WarpX simulations of IPM operation are used to characterize the measured beam size as a function of beam parameters and IPM operating conditions. These simulations are then compared against experimental data collected from both ion and electron IPMs in the AGS. The findings aim to refine correction factors, enabling more accurate beam size estimations from ion IPM measurements, ultimately improving beam diagnostics and operational efficiency.

Particle accelerators are composed of various components, and their properties are finely tuned to optimize certain particle beam qualities as they accelerate. In particular, particle colliders like the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Lab (BNL) are interested in maximizing luminosity, a measure of the collision rate primarily determined by the beam intensity (number of particles) and its beam size. However, finding and maintaining optimum settings is a time-consuming expert operator activity. This work proposes the use of the Recurrent Proximal Policy Optimization (RPPO), a reinforcement learning algorithm, to find parameters of quadrupole magnet strengths optimizing the beam qualities in the Booster to AGS (Alternating Gradient Synchrotron) section of the RHIC complex.

An AC dipole has been installed in the AGS booster as part of polarized beam developments for the future Electron Ion Collider (EIC). This will allow preserving helion beam polarization through two intrinsic resonances during acceleration to an energy corresponding to |Gγ| = 10.5. AC dipoles can preserve polarization by forcing the beam to undergo large amplitude vertical betatron oscillations. These coherent oscillations cause all particles to sample the strong horizontal fields of quadrupoles, and result in a full spin flip. In preparation for the AC dipole being used for polarized helions, it was first commissioned with polarized protons. The proton extraction energy was raised to allow protons to cross Gγ=0+νy = 4.8087. As an artifact of the experiment using polarized protons, the booster settings for bunch extraction interfered with the coherent oscillations and limited the maximum coherent amplitude. This interference will be well separated in the case of polarized helions. Polarized protons crossed the Gγ=0+νy intrinsic resonance with a full spin flip through use of the AC dipole. Simulations of the resonance crossing using Zgoubi accurately predict the polarization relative to the coherent amplitude.

The RHIC Cold QCD program has produced a remarkable breadth of physics results and experimental techniques in the exploration of the fundamental structure of strongly interacting matter over the years. In this document, we present highlights of longitudinal and transverse spin physics to date and the 25 years of innovation in accelerator science from the RHIC Spin program. These measurements and techniques will be essential to fully realize the scientific missions of the Electron-Ion Collider (EIC) by providing a comprehensive set of measurements in hadronic collisions and laying the foundation for the design of the future EIC.

The Beam Energy Scan phase II (BES-II), performed in the Relativistic Heavy Ion Collider (RHIC) from 2019 to 2021, explored the phase transition between quark-gluon plasma and hadronic gas. BES-II exceeded the goal of a fourfold increase in the average luminosity over that achieved during Beam Energy Scan phase I (BES-I), at five gold beam energies: 9.8, 7.3, 5.75, 4.59, and 3.85 GeV/nucleon. This was accomplished by addressing several beam dynamics effects, including intrabeam scattering, beam-beam, space charge, beam instability, and field errors induced by superconducting magnet persistent currents. Some of these effects are especially detrimental at low energies. BES-II achievements are presented, and the measures taken to improve RHIC performance are described. These measures span the whole RHIC complex, including ion beam sources, injectors, beam lifetime improvements in RHIC, and operation with the world's first bunched beam Low Energy RHIC electron Cooler (LEReC).

7 The partial helices installed in the Alternating Gradient Synchrotron (AGS) 8 [1] eliminate both, the imperfection and the vertical intrinsic spin resonances 9 thus yielding a 70% polarized proton beam with rigidity 79.4 [Tm] with 10 2x10 protons/bunch at the end of the AGS acceleration cycle. 11 The initial beam polarization at the exit of the 200 MeV Linac is measured to 12 be 80%. The 10% loss of the polarization at the end of the AGS acceleration 13 cycle is due to the horizontal spin resonances which are caused by the beta14 tron oscillations of the beam in the presence of the partial helices. To reduce 15 the effect of these horizontal spin resonances on the beam polarization, the 16 “jump Quads method” is applied in the AGS [2] which eliminates, almost 17 all, the horizontal spin resonances and increases the final polarization of the 18 proton beam to the value of 70%. A study [3] shows that these horizontal 19 spin resonances can be totally eliminated by introducing into the AGS ring, 20 skew quadrupoles which linearly couple the beam motions to excite new hori21 zontal spin resonances which minimize the horizontal-spin-resonances caused 22 by the partial-helices. 23 These skew quadrupoles are excited during the time the polarized beam 24 crosses these horizontal spin resonances. The time interval of the spin25 resonance-crossing is of the order of a milliisecond and this requires that the 26 material of the skew quadrupoles is made of ferrite or of laminated iron to 27 minimizes the eddy currents in the conductive parts of the skew quadrupoles. 28 In this technical note we provide results from the electromagnetic design 29 [4] of the Skew Quadrupole. This study includes the calculation of the mag30 netic multipoles of the quadrupole and the Ohmic losses in the coils and all 31 the conductive parts of the quadrupoles including the 0.025” thick lamina32 ∗Work supported by the US Department of Energy †tsoupas@bnl.gov tions of the quadrupole. This study presents also results of the pesence of 33 the beam pipe on the magnetic field at the region of the circulating beam. 34 The information provided in this technical note should be sufficient for the 35 reader to reproduce a 3D model of the skew quadrupole and introduce it in 36 the OPERA computer code [4] to obtain the results presented in this paper. 37 This quadrupole will be used in the AGS ring as a skew quadrupole and will 38 be refered in this paper as either skew quadrupole of simply quadrupole. 39

to promptly figure various necessary measures for swift recovery using the 9 o’clock Blue snake coils which survived the dip. Reference reports in particular that, in this 2003 incident, “[it was] decided to run the [failed] snake as a 88% partial snake while keeping the angles between the two snakes as 90° [...]. In general, the polarization level was not as good as Blue ring”. By contrast in this Run 22 incident, thorough simulations using the snake OPERA field maps helped determine new settings of the handicapped, 2-coil, Blue ring 9 o’clock snake currents and local closed orbit bump, and concurrently determine slight adjustment of the 3 o’clock snake currents, which allowed recovering full polarization at store, as good as could be expected from normal operation - even better over extended periods than in the Yellow ring.

The operation of RHIC collider rings in polarized proton runs includes helical snakes, which allow for preserving polarization during acceleration to store energies. The RHIC lattice also includes spin rotators, operated when nonvertical polarization or corrections to the orientation of polarization at the interaction points are required. Utilization of OPERA field maps of snakes and rotators has been systematized in the past decade, in order to assess in detail the effects of these spin devices on beam polarization, and their perturbative effects on beam optics. The method is also used in ongoing studies regarding the future Electron Ion Collider, to permit increasing average store polarization to at least 70% at 275 GeV and the acceleration of polarized helion with low polarization losses. This paper reviews various applications and outcomes of these field map methods. It is thereby also a review of studies undertaken as part of beam polarization research activities at RHIC in recent years.

The electron-ion luminosity in the EIC has a number of limits, including the ion intensity available from the injectors, the total ion beam current, the electron bunch intensity, the total electron current, the synchrotron radiation power, the beam-beam effect, the achievable beta functions at the Interaction Point, the maximum angular spreads at the Interaction Point, the ion emittances reachable with Strong Hadron Cooling, the ratio of horizontal to vertical emittance, and space charge effects. We map the e-A luminosity over the center-of-mass energy range for some ions ranging from deuterons to uranium ions. For e-Au collisions the present design provides for electron-nucleon (e-Au) peak luminosities of up to 4.8×1033 cm−2s−1 with Strong Hadron Cooling.

In recent years, Relativistic Heavy Ion Collider (RHIC) physics program calls for gold beam collisions with energies at and lower than the nominal RHIC injection energy. To get shorter bunches at the three higher energies (9.8 GeV, 7.3 GeV and 5.75 GeV), RHIC 28MHz cavities were used. The longitudinal emittance out of injectors needs to fit in the 28 MHz cavities in RHIC. At two lower energies (4.59 GeV and 3.85 GeV), the 9 MHz RF cavities were used, which set different requirements from injectors. Extensive beam studies were carried out to establish needed beam parameters, such as bunch intensities and longitudinal emittances. In general, enough intensity can be provided for all energies within the longitudinal emittance constraint. This paper summarizes the recent injector operation experiences for various energies.

For RHIC to operate at its top energy (100 GeV/n) while protecting the future sPHENIX detector [1], spontaneous and asynchronous firing of abort kicker modules (pre-fires) have to be avoided [2]. A new triggering circuit for the abort kickers was implemented with relatively slow mechanical relays in series with the standard fast thyratron tubes [3]. The relays prevent unwanted pre-fires during operation, but come at the expense of a long latency about 7 milliseconds between the removal of the beam permit and the actual firing of the abort kickers. Protection considerations of RHIC’s superconducting magnets forbid delaying energy extraction from the main dipoles and quadrupoles for too long after a quench. The beam has thus to circulate in both RHIC rings for a few milliseconds as the current in dipole and quadrupole circuit is being extracted. We present the results of delayed abort experiments conducted in July 2018 with the analysis of fast orbit and tune measurements and discuss the safety implications of this implementation for future RHIC operation.

Two electron lenses are installed in Relativistic Heavy Ion Collider (RHIC). They were used as operational head-on beam-beam compensators in proton-proton collisions, with Gaussian transverse electron beam profiles. One of the lenses was also used with a hollow transverse profile to test hadron beam halo removal under various conditions. Although presently not in the design, the lenses may find applications in the Electron-ion Collider (EIC) for either collimation or beam-beam mitigation.