Muon Accelerators for Particle Physics (MUON)

Muon beams of low emittance provide the basis for the intense, well-characterised neutrino beams of a neutrino factory and for multi-TeV lepton-antilepton collisions at a muon collider. The international Muon Ionization Cooling Experiment (MICE) has demonstrated the principle of ionization cooling, the technique by which it is proposed to reduce the phase-space volume occupied by the muon beam at such facilities. This paper documents the performance of the detectors used in MICE to measure the muon-beam parameters, and the physical properties of the liquid hydrogen energy absorber during running.

A muon collider represents the ideal machine to reach very high center-of-mass energies and luminosities by colliding elementary particles. This is the result of the low level of beamstrahlung and synchrotron radiation compared to linear or circular electron-positron colliders. In contrast with other lepton machines, the design of a detector for a multi-TeV muon collider requires detailed knowledge of the interaction region due to the significant backgrounds created by muon beam decays in the collider ring. The physics reach can be properly evaluated only when the detector performance in such an environment is determined. In this work, the backgrounds generated by muon beams of 750 GeV are characterized and the performance of the tracking system and the calorimeter detector is illustrated. Solutions to minimize the effect of the beam-induced backgrounds are discussed and applied to obtain track and jet reconstruction performance. The μ⁺μ⁻→ Hν→ b ν process is fully simulated and reconstructed to demonstrate that physics measurements are possible in this harsh environment. The measurement precision for the Higgs boson coupling to b is evaluated for √s=1.5, 3, and 10 TeV and compared to other proposed machines.

Small muon beams increase the luminosity of a muon collider. Reducing the momentum and position spreads of muons reduces emittance and leads to small, cool beams. Ionization cooling has been observed at the Muon Ionization Cooling Experiment. 6D emittance reduction by a factor of 100, 000 has been achieved in simulation. Another factor of 5 in cooling would meet the basic requirements of a high luminosity muon collider. In this paper we compare, for the first time, the amount of RF needed in a cooling channel to previous linacs. We also outline three methods aimed to help achieve a final factor of 5 in 6D cooling.

The Muon Ionization Cooling Experiment (MICE) collaboration has developed the MICE Analysis User Software (MAUS) to simulate and analyze experimental data. It serves as the primary codebase for the experiment, providing for offline batch simulation and reconstruction as well as online data quality checks. The software provides both traditional particle-physics functionalities such as track reconstruction and particle identification, and accelerator physics functions, such as calculating transfer matrices and emittances. The code design is object orientated, but has a top-level structure based on the Map-Reduce model. This allows for parallelization to support live data reconstruction during data-taking operations. MAUS allows users to develop in either Python or C++ and provides APIs for both. Various software engineering practices from industry are also used to ensure correct and maintainable code, including style, unit and integration tests, continuous integration and load testing, code reviews, and distributed version control. The software framework and the simulation and reconstruction capabilities are described.

A Muon Collider poses a number of challenging problems in the lattice design –- low β^*, small circumference, large physical and dynamic aperture—which must be solved in order to realize the unique opportunities it offers for the high-energy physics. This contribution presents basic solutions which make it possible to achieve the goals for both the energy frontier collider and the Higgs factory with Nb₃Sn magnet parameters.

A low-energy medium-luminosity Muon Collider (MC) is being studied as a possible Higgs Factory (HF). Electrons from muon decays will deposit more than 300 kW in superconducting (SC) magnets of the HF collider ring. This imposes significant challenges to SC magnets used in the HF storage ring (SR) and interaction regions (IR). Conceptual designs of SC dipole and quadrupole magnets are described which provide high operating gradient and field in a large aperture to accommodate the large size of muon beams (due to low β*), as well as a cooling system to intercept the large heat deposition from the showers induced by decay electrons. The distribution of heat deposition in the main elements of HF SR lattice requires large-aperture magnets to accommodate thick high-Z absorbers to protect the SC coils. Based on the developed MARS15 model and intensive simulations, a sophisticated protection system from radiation was designed for the collider SR and IR to bring the peak power density in the SC coils well below the quench limit and reduce the dynamic heat deposition in the cold mass of SC magnets by a factor of 100. The radiation protection system consists of tight tungsten masks in the magnet interconnect regions and elliptical tungsten liners in the magnet aperture optimized for each magnet. These elements reduce also the background particle fluxes in the collider detector.

We discuss the technical feasibility, key machine parameters and major challenges of a 14 TeV c.m.e. muon-muon collider in the LHC tunnel. The luminosity of the collider is evaluated for three alternative muon sources—the PS synchrotron, one of a type developed by the US Muon Accelerator Program (MAP) and a low-emittance option based on resonant muon pair production. Project affordability is also discussed.

The Muon Ionization Cooling Experiment (MICE) has been built at the STFC Rutherford Appleton Laboratory to demonstrate the principle of muon beam phase-space reduction via ionization cooling. Muon beam cooling will be required at a future proton-derived neutrino factory or muon collider. Ionization cooling is achieved by passing the beam through an energy-absorbing material, such as liquid hydrogen, and then re-accelerating the beam using RF cavities. This paper describes the hydrogen system constructed for MICE including: the liquid-hydrogen absorber, its associated cryogenic and gas systems, the control and monitoring system, and the necessary safety engineering. The performance of the system in cool-down, liquefaction, and stable operation is also presented.

The neutrino beam produced from muons decaying in a storage ring would be an ideal tool for precise neutrino cross section measurements and the search for sterile neutrinos due to its precisely known flavour content and spectrum. In the proposed nuSTORM facility, pions would be directly injected into a racetrack storage ring, where the circulating muon beam would be captured. In this paper we show that a muon decay ring based on a racetrack scaling FFAG (Fixed Field Alternating Gradient) with triplet focusing structures is a very promising option with potential advantages over the FODO based solution. We discuss the ring concept, machine parameters, linear optics design, beam dynamics and the injection system.

The hit response of silicon vertex and tracking detectors to muon collider beam background and results of a study of hit reducing techniques are presented. The background caused by decays of the 750 GeV/c μ⁺ and μ⁻ beams was simulated using the MARS15 program, which included the infrastructure of the beam line elements near the detector and the 10^o nozzles that shield the detector from this background. The ILCRoot framework, along with the Geant4 program, was used to simulate the hit response of the silicon vertex and tracker detectors to the muon decay background remaining after the shielding nozzles. The background hit reducing techniques include timing, energy deposition, and hit location correlation in the double layer geometry.

Helical Six-Dimensional Muon Ionization Cooling Channel (HCC) with High Pressure Hydrogen Gas-Filled RF (HPRF) Cavities is presented. The helical cooling theory is evaluated in a numerical analysis and translated into a conventional cooling scheme. The analysis predicts that the collective forces focus the beam in the HCC with HPRF cavities. The machine development for the HCC is also presented in the paper.

The helical FOFO snake six-dimensional muon ionization cooling channel design is presented which incorporates wedge absorbers in such a way that simultaneous cooling of both signs of muons is possible.

Muon ionization cooling involves passing particles through solid or liquid absorbers. Careful simulations are required to design muon cooling channels. New features have been developed for inclusion in the transfer map code COSY Infinity to follow the distribution of charged particles through matter. To study the passage of muons through material, the transfer map approach alone is not sufficient. The interplay of beam optics and atomic processes must be studied by a hybrid transfer map-Monte-Carlo approach in which transfer map methods describe the deterministic behavior of the particles, and Monte-Carlo methods are used to provide corrections accounting for the stochastic nature of scattering and straggling of particles. The advantage of the new approach is that the vast majority of the dynamics are represented by fast application of the high-order transfer map of an entire element and accumulated stochastic effects. The gains in speed are expected to simplify the optimization of cooling channels which is usually computationally demanding. Progress on the development of the required algorithms and their application to modeling muon ionization cooling channels is reported.

A Neutrino Factory where neutrinos of all species are produced in equal quantities by muon decay is described as a facility at the intensity frontier for exquisite precision providing ideal conditions for ultimate neutrino studies and the ideal complement to Long Baseline Facilities like LBNF at Fermilab. It is foreseen to be built in stages with progressively increasing complexity and performance, taking advantage of existing or proposed facilities at an existing laboratory like Fermilab. A tentative layout based on a recirculating linac providing opportunities for considerable saving is discussed as well as its possible evolution toward a muon collider if and when requested by Physics. Tentative parameters of the various stages are presented as well as the necessary R&D to address the technological issues and demonstrate their feasibility.

We summarize the current state of a concept for muon acceleration aimed at a future Neutrino Factory. The main thrust of these studies was to reduce the overall cost while maintaining performance by exploring the interplay between the complexity of the cooling systems and the acceptance of the accelerator complex. To ensure adequate survival for the short-lived muons, acceleration must occur at high average gradient. The need for large transverse and longitudinal acceptances drives the design of the acceleration system to an initially low RF frequency, e.g., 325 MHz, which is then increased to 650 MHz as the transverse size shrinks with increasing energy. High-gradient normal conducting RF cavities at these frequencies require extremely high peak-power RF sources. Hence superconducting RF (SRF) cavities are chosen. We consider two cost effective schemes for accelerating muon beams for a stageable Neutrino Factory: exploration of the so-called "dual-use" linac concept, where the same linac structure is used for acceleration of both H⁻ and muons and, alternatively, an SRF-efficient design based on a multi-pass (4.5) "dogbone" RLA, extendable to multi-pass FFAG-like arcs.

An intense beam of muons is needed to provide a luminosity on the order of 10³⁴ cm⁻²s⁻¹ for a multi-TeV collider. Because muons produced by colliding a multi-MW proton beam with a target made of carbon or mercury have a large phase space, significant six dimensional cooling is required. Through ionization cooling—the only cooling method that works within the lifetime of the muon—and emittance exchange, the desired emittances for a Higgs Factory or higher energy collider are attainable. A cooling channel utilizing gas filled radio frequency cavities has been designed to deliver the requisite cool muon beam. Technology development of these RF cavities has progressed from breakdown studies, through beam tests, to dielectric loaded and reentrant cavity designs. The results of these experiments are summarized.

Muon beam-induced plasma loading of radio-frequency (RF) cavities filled with high pressure hydrogen gas with 1% dry air dopant has been studied via numerical simulations. The electromagnetic code SPACE, that resolves relevant atomic physics processes, including ionization by the muon beam, electron attachment to dopant molecules, and electron-ion and ion-ion recombination, has been used. Simulations studies have been performed in the range of parameters typical for practical muon cooling channels.

A neutrino factory or muon collider requires the capture and cooling of a large number of muons. Scenarios for capture, bunching, phase-energy rotation and initial cooling of μ 's produced from a proton source target have been developed, initially for neutrino factory scenarios. They require a drift section from the target, a bunching section and a φ -δ E rotation section leading into the cooling channel. Important concerns are rf limitations within the focusing magnetic fields and large losses in the transport. The currently preferred cooling channel design is an "HFOFO Snake" configuration that cools both μ⁺ and μ⁻ transversely and longitudinally. The status of the design is presented and variations are discussed.

Ionization cooling channels with a wide variety of characteristics and cooling properties are being developed. These channels can produce cooling performances that are largely consistent with the linear ionization cooling theory developed previously. In this paper we review ionization cooling theory, discuss its application to presently developing cooling channels, and discuss criteria for optimizing cooling.

An alternative cooling approach to prevent rf breakdown in magnetic fields is described that simultaneously reduces all six phase-space dimensions of a muon beam. In this process, cooling is accomplished by reducing the beam momentum through ionization energy loss in discrete absorbers and replenishing the momentum loss only in the longitudinal direction through gas-filled rf cavities. The advantage of gas filled cavities is that they can run at high gradients in magnetic fields without breakdown. With this approach, we show that our channel can achieve a decrease of the 6-dimensional phase-space volume by several orders of magnitude. With the aid of numerical simulations, we demonstrate that the transmission of our proposed channel is comparable to that of an equivalent channel with vacuum rf cavities. Finally, we discuss the sensitivity of the channel performance to the choice of gas and operating pressure.

Neutrino beams produced from the decay of muons in a racetrack-like decay ring (the so called Neutrino Factory) provide a powerful way to study neutrino oscillation physics and, in addition, provide unique beams for neutrino interaction studies. The Neutrinos from STORed Muons (nuSTORM) facility uses a neutrino factory-like design. Due to the particular nature of nuSTORM, it can also provide an intense, very pure, muon neutrino beam from pion decay. This so-called "Neo-conventional" muon-neutrino beam from nuSTORM makes nuSTORM a hybrid neutrino factory. In this paper we describe the facility and give a detailed description of the neutrino beams that are available and the precision to which they can be characterized. We then show its potential for a neutrino interaction physics program and present sensitivity plots that indicate how well the facility can perform for short-baseline oscillation searches. Finally, we comment on the performance potential of a "Neo-conventional" muon neutrino beam optimized for long-baseline neutrino-oscillation physics.

The goal of nuSTORM is to provide well-defined neutrino beams for precise measurements of neutrino cross-sections and oscillations. The nuSTORM decay ring is a compact racetrack storage ring with a circumference of ∼ 480 m that incorporates large aperture (60 cm diameter) magnets. There are many challenges in the design. In order to incorporate the Orbit Combination section (OCS), used for injecting the pion beam into the ring, a dispersion suppressor is needed adjacent to the OCS . Concurrently, in order to maximize the number of useful muon decays, strong bending dipoles are needed in the arcs to minimize the arc length. These dipoles create strong chromatic effects, which need to be corrected by nonlinear sextupole elements in the ring. In this paper, a FODO racetrack ring design and its optimization using sextupolar fields via both a Genetic Algorithm (GA) and a Simulated Annealing (SA) algorithm will be discussed.

A high-energy muon collider requires a "final cooling" system that reduces transverse emittance by a factor of ∼ 10, while allowing the longitudinal emittance to increase. The baseline approach has low-energy transverse cooling within high-field solenoids, with strong longitudinal heating. This approach and its recent simulation are discussed. Alternative approaches, which more explicitly include emittance exchange are also presented. Round-to-flat beam transform, transverse slicing, and longitudinal bunch coalescence are possible components of an alternative approach. Wedge-based emittance exchange could provide much of the required transverse cooling with longitudinal heating. Li-lens and quadrupole focusing systems could also provide much of the required final cooling.

A preliminary lattice design of a muon collider ring with the center-of-mass (CM) energy of 6 TeV is presented. The ring circumference is 6.3 km, and the beta function at collision point is β^* = 1 cm in each plane. The ring linear optics, a local non-linear chromaticity compensation in the Interaction Region (IR), additional IR non-linear correction knobs, and the effects of non-linear fringe field are discussed. Magnet specifications are based on the maximum pole-tip field of 20 T in dipoles and 15 T in quadrupoles. Careful compensation of the non-linear chromatic and amplitude dependent effects provides a sufficiently large dynamic aperture for the momentum range of up to ± 0.5% without considering magnet errors.