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.

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.

RHIC nine-magnet spin flipper has been operated successfully during RHIC polarized proton Run 17, with 97% spin flip efficiency achieved. The results show the importance of mirror resonance removal, small spin tune spread, and proper spin flipper driving tune sweep speed. Detailed spin tracking simulations, based on a Lorentz force and Thomas-BMT differential equation numerical solver code for accuracy, have been carried out to understand the experimental results. Agreement within measurement accuracy is obtained at injection energy, 23.8 GeV. It is not as tight at 255 GeV, reasons for that are exposed. These measurements and numerical studies allow to determine the sensitivity of spin-flip efficiency to the dispersion slopes at the two Siberian snakes and to the ac dipole frequency sweep speed. They also provide guidance for future developments at BNL's electron-ion collider.

A novel neutron source concept, in which a deuterium beam (energy of about 100 keV) is to be injected into a tube filled with tritium gas or tritium plasma to generate D-T fusion reactions whose products are 14.06 MeV neutrons and 3.52 MeV alpha particles, is described. At the opposite end of the tube, the energy of deuterium ions that did not interact is recovered. Be walls of proper thickness will absorb 14 MeV neutrons and release 2 – 3 lower energy neutrons. Each ion source and tube forms a module. Larger systems can be formed from multiple units. Beam propagation can be further enhanced with vortex-stabilized discharges, electron beams in opposite direction (with energy recovery) or magnetic fields where possible. Deuterium ions propagating through tritium plasma are slowed down and deposit significant energy in the tritium target. Plasma heating results in high temperature electron, thus reducing deuterium ion energy loss. Equilibrium electron temperature exceeding 200 eV can be achieved. Unlike current methods, where accelerator based neutron sources require large amounts of power for operation, this neutron source is compact and can generate neutrons at higher power efficiency. Being modular, the concept can be tested in tabletop experiments. Concept description and basic calculation will be presented. Among possible applications for this neutron source concept are sub-critical nuclear breeder reactors and accelerator transmutation of radioactive waste.

We discuss the goals, the designs, the state of technical readiness, and the critical R&D needs of the accelerators that are currently under discussion as Higgs and electroweak factories. We also address the respective staging options enabling future energy-frontier colliders. The accelerators covered are based on many different techniques and approaches. They include several circular colliders, various linear colliders, colliders based on energy recovery linacs (ERLs), ERL-ring combinations, as well as gamma-gamma colliders. The linear colliders proposed consist of options for the International Linear Collider (ILC), for the Compact Linear Collider (CLIC), for the Cold Copper Collider (C^3), and for the more recent Higgs-Energy Lepton Collider (HELEN). ERLs are key components of the Recycling Linear e+e- Collider (ReLiC), of the Energy Recovery Linear Collider (ERLC), and of the Circular Energy Recovery Collider (CERC). Among the more conventional ring colliders, the following proposals are featured: the Future Circular Collider (FCC-ee), the Circular Electron Positron Collider (CEPC), the Electron Positron Circular Collider at Fermilab (EPCCF), and the Large Electron Positron collider $\#$3 (LEP-3). In addition, we consider the X-ray FEL based gamma-gamma Collider Higgs Factory (XCC) and the High-Energy High-Luminosity gamma-gamma collider (HE&HL gamma-gamma). Finally, a Higgs factory based on a circular muon collider is mentioned for completeness.

Colliders are essential research tools for particle physics. Numerous future collider proposal were discussed in the course of the US high energy physics community strategic planning exercise Snowmass'21 . The Implementation Task Force (ITF) has been established to evaluate the proposed future accelerator projects for performance, technology readiness, schedule, cost, and environmental impact. Corresponding metrics has been developed for uniform comparison of the proposals ranging from Higgs/EW factories to multi-TeV lepton, hadron and ep collider facilities, based on traditional and advanced acceleration technologies. This article describes the metrics and approaches, and presents evaluations of future colliders performed by the ITF.

We present a Circular Energy Recovery Collider (CERC) as an alternative approach for a high-energy high-luminosity electron-positron collider to current designs for high-energy electron-positron colliders either based on two storage rings with 100 km circumference or two large linear accelerators. Using Energy Recovery Linacs (ERL) located in the same-size 100 km tunnel would allow a large reduction of the beam energy losses, and therefore a reduction of the power consumption, while providing higher luminosity. It also opens a path for extending the center-of-mass (CM) energy to 500 GeV, which would enable double-Higgs production, and even to 600 GeV for production and measurements of the top Yukawa coupling. Furthermore, this approach would allow recycling of not only the energy but also of the particles. This feature opens the possibility for colliding fully polarized electron and positron beams.

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).

In this white paper we describe concept of $e^+e^-$ linear collider recycling both the used particles and the used beam energy.

AbstractThe acceleration and storage of high energy polarized proton beams has made tremendous progress over the last 40 years challenging along the way the technologies, precision and the understanding of the beam dynamics of accelerators. This progress is most evident in that one can now contemplate high energy colliders with polarized beams and high luminosity at the same time. After a brief summary of the development and history of polarized proton beam acceleration this chapter will focus on the acceleration of polarized proton beams from MeV to the 100s of GeVs and the possibility of accelerating polarized beams to even higher energies in the future. Elements of the history of polarized electron beams, subject to the effects of synchrotron radiation, will be found in the electron beam polarization dedicated chapters in these lectures.

The Snowmass 2021 Implementation Task Force has been established to evaluate the proposed future accelerator projects for performance, technology readiness, schedule, cost, and environmental impact. Corresponding metrics has been developed for uniform comparison of the proposals ranging from Higgs/EW factories to multi-TeV lepton, hadron and ep collider facilities, based on traditional and advanced acceleration technologies. This report documents the metrics and processes, and presents evaluations of future colliders performed by Implementation Task Force.

As the next generation of large accelerator-based facilities are being considered at the Snowmass 2021 study high priority has to be given to environmental sustainability including energy consumption, natural resource use and the environmental impact of effluents. Typically, increased performance - higher beam energies and intensities - of proposed new facilities have come with increased electric power consumption. In the following we discuss the most important areas of development for the sustainability of accelerator-based research infrastructures in three categories - technologies, concepts and general aspects. To achieve the goal of increased performance with reduced energy consumption a focused R&D effort is required with the same or even higher priority as the traditional performance-related R&D. Such a recommendation was included in the recent European Strategy for Particle Physics Accelerator R&D Roadmap.

We present a new 'green energy' approach to the Energy Recovery Linac (ERL) and Recirculating Linac Accelerators (RLA) for the future Electron Ion Colliders (EIC) using single beam line made of very strong focusing combined function permanent magnets and the Fixed Field Alternating Linear Gradient (FFA-LG) principle. We are basing our design on recent very successful commissioning results of the Cornell University and Brookhaven National Laboratory ERL Test Accelerator.

This report is a summary of two preparatory workshops, documenting the community vision for the national accelerator and beam physics research program. It identifies the Grand Challenges of accelerator and beam physics (ABP) field and documents research opportunities to address these Grand Challenges. This report will be used to develop a strategic research roadmap for the field of accelerator science.

The Cornell-BNL ERL Test Accelerator (CBETA) developed several energy-saving measures: multi-turn energy recovery, low-loss superconducting radiofrequency (SRF) cavities, and permanent magnets. With green technology becoming imperative for new high-power accelerators, the lessons learned will be important for projects like the FCCee or new light sources, where spinoffs and lessons learned from CBETA are already considered for modern designs.

The physics program in the EIC calls for polarized neutron beam at high energies. The best neutron carriers are 3He nuclei and deuterons. Both neutron carriers are expected to be used by spin physics program in the EIC. Due to the small magnetic moment anomaly of deuteron particles, much higher magnetic fields are required for spin rotation, so full Siberian snake is not feasible. However, the resonance strength is in general weak and the number of resonances is also small. It is possible to deal with individual resonances with conventional methods, such as betatron tune jump for intrinsic depolarizing resonances; and a weak partial snake for imperfection resonances. The study shows that accelerating polarized deuteron beyond 100 GeV is possible in the EIC.

We present the top-notch design of the proton therapy gantry made of permanent magnets with very strong focusing. This is a superb solution fulfilling all cancer treatment requirements for all energies without changing any parameters. The proton energy range is between 60-250 MeV. The beam arrives to the patient focused on each required treatment energy. The scanning system is place between the end of the gantry and the patient. There are multiple advantages of this design: easy operation, no significant electrical power just for the correction system, low weight, low cost. The design is based on the recent very successful commissioning of the permanent magnet ‘Cornell University and Brookhaven National Laboratory Energy Recovery Linac Test Accelerator ‘CBETA’ project [1-3].