Within the context of a design study of a LINAC for ionization cooling, this paper presents the result of incorporating a scattering model in RF-Track (v2.1) for charged particles heavier than electrons. This inclusion enables simulations for applications like ionization cooling channels for muon colliders. Within RF-Track, a novel semi-Gaussian mixture model has been introduced to describe the deflection of charged particles in material. This innovative model comprises a Gaussian core and a non-Gaussian tail function to account for the effects of single hard scattering. To validate the accuracy of our results, we conducted a benchmarking comparison against other particle tracking codes, with the outcomes demonstrating a high level of agreement.

Ionization cooling stands as the only cooling technique capable of efficiently reducing the phase space of a muon beam within a short time frame. The optimal cooling parameters of a muon collider aim to minimize transverse emittance while simultaneously limiting longitudinal emittance growth, resulting in optimal luminosities within the collider ring. This study shows that achieving efficient cooling performance requires selecting the best initial muon beam parameters. Because for every transvere emittance there exist an optimal beam energy for ionization cooling. We present a technique that enables the determination of these optimal initial parameters through simulations and compare them with an improved analytical scattering model.

The proton complex is the first piece in the Muon Collider, it comprises a high power acceleration section, a compressor and a target delivery system. For the International Muon Collider Collaboration we are investigating the possibility of having a full energy 5-GeV linac followed by an accumulator and a compressor ring and finally a target delivery system. In this paper we present the initial studies for the complex and derived initial beam parameters at each interface.

The Muon Cooling Complex is a crucial component of the future high-energy Muon Collider, where the ionization cooling technique is employed to reduce muon beam emittance by several orders of magnitude. This cooling technique necessitates the utilization of normal conducting, RF-accelerating cavities operating within a multi-Tesla magnetic field. This study illustrates the conceptual RF design of a 704 MHz copper cavity equipped with beryllium windows for the muon cooling demonstrator. Based on the specifications from the beam dynamics, frequency-domain eigenmode simulations have been conducted to calculate the primary RF figure of merits for the cavity. Subsequently, the cavity geometry has been optimized based on the results obtained from the eigenmode simulations. In a selected case, more advanced engineering analyses, including thermo-mechanical and Lorentz Force Detuning (LFD) simulations, have been performed to enable operation at gradients of up to 44 MV/m within strong solenoidal magnetic fields of up to 7.2 T.

Circular muon colliders provide the potential to explore center-of-mass energies at the multi-TeV scale within a relatively compact footprint. Because of the short muon lifetime, only a small fraction of stored beam particles will contribute to the physics output, while most of the muons will decay in the collider ring. The resulting power carried by decay electrons and positrons can amount to hundreds of Watt per meter. Dedicated shielding configurations are needed for protecting the superconducting magnets against the decay-induced heat and radiation damage. In this paper, we present generic shielding studies for two different collider options (3 TeV and 10 TeV), which are presently being explored by the International Muon Collider Collaboration. We show that the key parameter for the shielding design is the heat deposition in the magnet cold mass, which will be an important cost factor for facility operation due to the associated power consumption.

During the operation of a muon collider in an underground tunnel, most circulating muons decay into an electron (or positron) and a neutrino-antineutrino pair, resulting in a narrow disk of high-energy neutrinos emitted radially in the collider plane and emerging on the Earth’s surface at distances of several km. Thus, dedicated studies are required to assess any potential radiation protection risks to the public due to the interaction of such neutrinos near the surface. This work presents a set of FLUKA Monte Carlo simulations aimed at characterizing the radiation showers generated by the interactions of high-energy neutrinos from TeV-scale muon decays in a reference sample of soil. The results are expressed in terms of effective dose in soil at different distances from the muon decay, quantifying the peak dose and the width of the radiation cone, for beam energies of 1.5 TeV and 5 TeV. The implications of these results for realistic muon collider scenarios are discussed, along with possible methods to mitigate the local neutrino flux.

Muon production in the multi-TeV muon collider studied by the International Muon Collider Collaboration is planned to be performed with a high-power proton beam interacting with a fixed target. The design of the target area comes with a set of challenges related to the radiation load to front-end equipment. The confinement of the emerging pions and muons requires very strong magnetic fields achievable only by superconducting solenoids, which are sensitive to heat load and long-term radiation damage. The latter concerns the ionizing dose in insulation, as well as the displacement damage in the superconductor. The magnet shielding design has to limit the heat deposition and ensure that the induced radiation damage is compatible with the operational lifetime of the muon production complex. Finally, the fraction of the primary beam passing through the target unimpeded poses a need for an extraction channel. In this study, we use the FLUKA Monte Carlo code to assess the radiation load to the solenoids, and we explore the possible spent proton beam extraction scenarios taking into account the constraints stemming from the beam characteristics and the required magnetic field strength.

Ionization cooling stands as the only cooling technique capable of efficiently reducing the phase space of a muon beam within a short time frame. The optimal cooling parameters of a muon collider aim to minimize transverse emittance while simultaneously limiting longitudinal emittance growth, resulting in optimal luminosities within the collider ring. This study shows that achieving efficient cooling performance requires selecting the best initial muon beam parameters. Because for every transvere emittance there exist an optimal beam energy for ionization cooling. We present a technique that enables the determination of these optimal initial parameters through simulations and compare them with an improved analytical scattering model.

Within the context of a design study of a LINAC for ionization cooling, this paper presents the result of incorporating a scattering model in RF-Track (v2.1) for charged particles heavier than electrons. This inclusion enables simulations for applications like ionization cooling channels for muon colliders. Within RF-Track, a novel semi-Gaussian mixture model has been introduced to describe the deflection of charged particles in material. This innovative model comprises a Gaussian core and a non-Gaussian tail function to account for the effects of single hard scattering. To validate the accuracy of our results, we conducted a benchmarking comparison against other particle tracking codes, with the outcomes demonstrating a high level of agreement.

As part of the International Muon Collider study, a beam vacuum window is being developed at CERN. It is required for the final cooling, where the charged particles travel from the vacuum chamber to the absorber; here, the beam loses momentum to cross a second window entering in a RF cavity that increases the longitudinal momentum. The best absorber for the final cooling is hydrogen. As the absorber should be installed inside a high field focusing solenoid, the hydrogen density should be as high as possible, ideally liquid or high pressure gas, to have a reasonable solenoid length. To evaluate the performance of the window, it is necessary to study the tightness at cryogenic temperatures, resistance to burst, high temperature and beam-induced damage. The main objective of the proposed work is to design and validate a versatile bulge test setup for the mechanical characterization of thin windows at different pressures and temperatures to cover all operating conditions, from 77 K to 293.15 K and ideally above. Due to the low thicknesses, a non-contact measuring technique based on a confocal chromatic sensor is proposed.

Achieving the low emittances necessary for a muon collider requires ionization cooling. Much of that cooling occurs in compact cooling cells where superconducting coils and conventional RF cavities are closely interleaved [1]. The real challenges for these cooling cells reside in their engineering challenges: high field solenoids, RF cavities, and absorbers, often designed near technological limits, placed in close proximity to each other. We thus propose to build a prototype ionization cooling cell to demonstrate the capability of constructing an ionization cooling channel reaching the lowest emittances and to provide engineering input for the design of such beamlines. The magnets and cavities will be powered at their design values, and an absorber will be included along with a mechanism for heating the absorber similarly to how a beam would.

We describe a high-efficiency source of muonium that can be transported as a beam in vacuum provides opportunities for fundamental muon and precision physics measurements such as sensitive searches for symmetry violation. Although PSI is currently the world leader, the intense 800-MeV PIP-II linac beam at Fermilab could provide world-class low-energy muon and muonium beams, with unparalleled intensity, driving the next generation of precision muon-based physics experiments at the intensity frontier. However, it is critical to initiate the prerequisite R&D now to prepare for the PIP-II era. A low-energy secondary muon line recently installed in an operating facility (the MeV Test Area, which utilizes the intense 400-MeV Fermilab Linac beam) could support the required R&D, and potentially compete for new physics in the immediate term, if approved. This beamline was developed for μ– and will need to be re-optimized for surface μ+ production and transport, making it also suitable for muon spin rotation physics––a unique research and industrial application for which no U.S. facility exists, and whose facilities are oversubscribed worldwide.

The discovery of neutrino Charge-Parity Violation (CPV) became an important candidate to explain the matter dominance in the Universe. The goal of the ESSnuSB project is to discover and measure neutrino CPV with unprecedented sensitivity*. The construction of the European Spallation Source, ESS, the world’s most intense proton source, represents an outstanding opportunity for such project to take place. ESSnuSB has been granted from EU in the framework of H2020 (2018-2022) and Horizon Europe (2023-2026) to make Design Studies. The aim of the first Design Study was to demonstrate that the ESS linac can be used to generate an intense neutrino beam by doubling its average beam power and that a megaton water Cherenkov detector can be constructed in a mine 360 km from ESS providing detection of neutrinos at the 2nd neutrino oscillation maximum. A CDR** has been published in which it is shown the high physics performance to discover CPV and precisely measure the violating parameter δCP. For this, the modification for neutrino generation to compress the proton pulse length from 2.86 ms, to 1.3 μs has been studied. The second, ongoing, Design Study, ESSnuSB+, is devoted to neutrino cross-section measurements relevant to the CPV discovery. Two facilities are proposed, a low energy nuSTORM (muons decaying to neutrinos in a race-track storage ring) and low energy ENUBET (pions decaying to a muon and a neutrino, allowing the neutrino beam to be monitored by detection of the decay muon).

The cooling section of the Muon Collider requires a number of solenoidal coils of various diameters (0.05-2 m) and fields (2-60 T). An unusual feature of the cooling section is that the RF cavities operates under the large magnetic fields and field gradients generated by the focusing elements. Here we present the design of a test facility based on split coils, wound with HTS, to study the performance of RF cavities under magnetic field. The main characteristics are: 330 mm free room temperature bore, uniform 7 T field along 300 mm on axis, coils energized with parallel or antiparallel field: this last configuration provides a gradient field of about 40 T/m. The use of HTS in form of REBCO tape enables magnet operation at 20 K and cooling via solid conduction by cryocoolers. This facility will be a first prototype of the cooling cell magnets that are being designed in cryogen-free layout at 20 K for energy saving and will allow to anticipate system integration concepts. The conceptual design of the facility is almost frozen and the engineering design is well under way. If we get financial support by 2025 we can commission the facility in 2027.

Generation of a muon beam at a Muon Collider requires relatively short, high-charge proton bunches. They are produced in a high-average-power proton driver by first accumulating a proton beam from a super-conducting linac, then bunching the beam and finally compressing and combining the bunches into a single high-intensity proton pulse. All of these beam formation stages involve handling of unprecedentedly high beam charges. Validation of these intricate beam manipulations requires better understanding of extreme space-charge effects and experimental demonstration. A facility perhaps most closely resembling the proton driver configuration and beam parameters is the Spallation Neutron Source (SNS) accelerator complex at Oak Ridge National Laboratory (ORNL). Considering the energy scaling of the space-charge parameters, many of the beam formation steps planned for the proton driver can be experimentally checked at the SNS at the relevant space-charge interaction levels. This paper discusses potential proton driver and other muon-collider-related R\&D at the SNS.