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The general concept of radiation therapy used in conventional cancer treatment is to increase the therapeutic index by creating a physical dose differential between tumors and normal tissues through precision dose targeting, image guidance, and radiation beams that deliver a radiation dose with high conformality, e.g., protons and ions. However, the treatment and cure are still limited by normal tissue radiation toxicity, with the corresponding side effects. A fundamentally different paradigm for increasing the therapeutic index of radiation therapy has emerged recently, supported by preclinical research, and based on the FLASH radiation effect. FLASH radiation therapy (FLASH-RT) is an ultra-high-dose-rate delivery of a therapeutic radiation dose within a fraction of a second. Experimental studies have shown that normal tissues seem to be universally spared at these high dose rates, whereas tumors are not. While dose delivery conditions to achieve a FLASH effect are not yet fully characterized, it is currently estimated that doses delivered in less than 200 ms produce normal-tissue-sparing effects, yet effectively kill tumor cells. Despite a great opportunity, there are many technical challenges for the accelerator community to create the required dose rates with novel compact accelerators to ensure the safe delivery of FLASH radiation beams.

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.

In this paper, we investigate the stability of the particle trajectories in fixed field alternating gradient accelerators (FFAs) in the presence of field errors. The emphasis is on the scaling radial sector FFA type: A collaboration work is ongoing in view of better understanding the properties of the 150 MeV scaling FFA at Kyoto University Institute for Integrated Radiation and Nuclear Science in Japan and progress toward high-intensity operation. Analysis of certain types of field imperfections revealed some interesting features that required the development of an analytical model based on the scalloping angle of the orbits. This helped explain some of the experimental results as well as generalize the concept of a scaling FFA to a nonscaling one for which the tune variations obey a well-defined law. Based on this, a compensation scheme of tune variations in imperfect scaling FFAs is presented. This is the cornerstone of a novel concept of a fixed tune FFA in which the scaling is not achieved at every azimuthal position of the ring but rather in an average sense.

The Proton EDM Experiment (pEDM) is the first direct search for the proton electric dipole moment (EDM) with the aim of being the first experiment to probe the Standard Model (SM) prediction of any particle EDM. Phase-I of pEDM will achieve \\(10^{-29} e\\cdot\\)cm, improving current indirect limits by four orders of magnitude. This will establish a new standard of precision in nucleon EDM searches and offer a unique sensitivity to better understand the Strong CP problem. The experiment is ideally positioned to explore physics beyond the Standard Model (BSM), with sensitivity to axionic dark matter via the signal of an oscillating proton EDM and across a wide mass range of BSM models from \\(\\mathcal{O}(1\\text{GeV})\\) to \\(\\mathcal{O}(10^3\\text{TeV})\\). Utilizing the frozen-spin technique in a highly symmetric storage ring that leverages existing infrastructure at Brookhaven National Laboratory (BNL), pEDM builds upon the technological foundation and experimental expertise of the highly successful Muon $g$$-$$2$ Experiments. With significant R\\&D and prototyping already underway, pEDM is preparing a conceptual design report (CDR) to offer a cost-effective, high-impact path to discovering new sources of CP violation and advancing our understanding of fundamental physics. It will play a vital role in complementing the physics goals of the next-generation collider while simultaneously contributing to sustaining particle physics research and training early-career researchers during gaps between major collider operations.

We describe a proposal to search for an intrinsic electric dipole moment (EDM) of the proton with a sensitivity of \\targetsens, based on the vertical rotation of the polarization of a stored proton beam. The New Physics reach is of order \\(10^~3\\)TeV mass scale. Observation of the proton EDM provides the best probe of CP-violation in the Higgs sector, at a level of sensitivity that may be inaccessible to electron-EDM experiments. The improvement in the sensitivity to \\(\\theta_{QCD}\\), a parameter crucial in axion and axion dark matter physics, is about three orders of magnitude.

Static electric dipole moments of nondegenerate systems probe mass scales for physics beyond the Standard Model well beyond those reached directly at high energy colliders. Discrimination between different physics models, however, requires complementary searches in atomic-molecular-and-optical, nuclear and particle physics. In this report, we discuss the current status and prospects in the near future for a compelling suite of such experiments, along with developments needed in the encompassing theoretical framework.

Conventional cancer therapies include surgery, radiation therapy, chemotherapy, and, more recently, immunotherapy. These modalities are often combined to improve the therapeutic index. The general concept of radiation therapy is to increase the therapeutic index by creating a physical dose differential between tumors and normal tissues through precision dose targeting, image guidance, and high radiation beams that deliver radiation dose with high conformality, e.g., protons and ions. However, treatment and cure are still limited by normal tissue radiation toxicity, with many patients experiencing acute and long-term side effects. Recently, however, a fundamentally different paradigm for increasing the therapeutic index of radiation therapy has emerged, supported by preclinical research, and based on the FLASH radiation effect. FLASH radiation therapy (FLASH-RT) is an ultra-high dose-rate delivery of a therapeutic radiation dose within a fraction of a second. Experimental studies have shown that normal tissues seem to be universally spared at these high dose rates, whereas tumors are not. The dose delivery conditions are not yet fully characterized. Still, it is currently estimated that large doses of 10 Gy or more delivered in 200 ms or less produce normal tissue sparing effects yet effectively kill tumor cells. There is a great opportunity, but also many technical challenges, for the accelerator community to create the required dose rates with novel and compact accelerators to ensure the safe delivery of FLASH radiation beams.

In this paper, we investigate the stability of the particle trajectories in Fixed Field alternating gradient Accelerators (FFA) in the presence of field errors: The emphasis is on the scaling radial sector FFA type: a collaboration work is on-going in view of better understanding the properties of the 150 MeV scaling FFA at KURRI in Japan, and progress towards high intensity operation. Analysis of certain types of field imperfections revealed some interesting features about this machine that explain some of the experimental results and generalize the concept of a scaling FFA to a non-scaling one for which the tune variations obey a well defined law. A compensation scheme of tune variations in imperfect scaling FFAs is presented. This is the cornerstone of a novel concept of a non-linear non-scaling radial sector fixed tune FFA that we present and discuss in details in the last part of this paper.

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

The Cornell-BNL FFAG-ERL Test Accelerator (C\\(\\beta\\)) will comprise the first ever Energy Recovery Linac (ERL) based on a Fixed Field Alternating Gradient (FFAG) lattice. In particular, we plan to use a Non Scaling FFAG (NS-FFAG) lattice that is very compact and thus space- and cost- effective, enabling multiple passes of the electron beam in a single recirculation beam line, using the superconducting RF (SRF) linac multiple times. The FFAG-ERL moves the cost optimized linac and recirculation lattice to a dramatically better optimum. The prime accelerator science motivation for C\\(\\beta\\) is proving that the FFAG-ERL concept works. This is an important milestone for the Brookhaven National Laboratory (BNL) plans to build a major Nuclear Physics facility, eRHIC, based on producing 21 GeV electron beams to collide with the RHIC ion beams. A consequence of the C\\(\\beta\\) work would be the availability of significantly better, cost-effective, compact CW high-brightness electron beams for a plethora of scientific investigations and applications, such as X-ray sources, dark-matter and dark-energy searches, and industrial high-power Free-Electron Laser (FEL) applications. C\\(\\beta\\) brings together the resources and expertise of a large DOE National Laboratory, BNL, and a leading research university, Cornell. C\\(\\beta\\) will be built in an existing building at Cornell, for the most part using components that have been developed under previous R&D programs, including a fully commissioned world-leading photoemission electron injector, a large SRF accelerator module, and a high-power beam stop. The only elements that require design and construction from scratch is the FFAG magnet transport lattice. This white paper describes a project that promises to propel high-power, high-brightness electron beam science and applications to an exciting new level.