D. M. Kaplan, E. L. Black, M. Boghosian, K. W. Cassel, R. P. Johnson, S. Geer, C. J. Johnstone, M. Popovic, S. Ishimoto, K. Yoshimura, L. Bandura, M. A. Cummings, A. Dyshkant, D. Hedin, D. Kubik, C. Darve, Y. Kuno, D. Errede, M. Haney, S. Majewski, M. Reep, D. Summers
A stored-muon-beam neutrino factory may require transverse ionization cooling of the muon beam. We describe recent progress in research and development on energy absorbers for muon-beam cooling carried out by a collaboration of university and laboratory groups.
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Low energy muon experiments such as mu2e and g-2 have a limited energy spread acceptance. Following techniques developed in muon cooling studies and the MICE experiment, the number of muons within the desired energy spread can be increased by the matched use of wedge absorbers. More generally, the phase space of muon beams can be manipulated by absorbers in beam transport lines. Applications with simulation results are presented.
Emittance exchange mediated by wedge absorbers is required for longitudinal ionization cooling and for final transverse emittance minimization for a muon collider. A wedge absorber within the MICE beam line could serve as a demonstration of the type of emittance exchange needed for 6-D cooling, including the configurations needed for muon colliders. Parameters for this test are explored in simulation and possible experimental configurations with simulated results are presented.
Ionization cooling in a straight beamline reduces the transverse emittance of a beam, and has little effect on the longitudinal emittance (generally, in fact, it increases the longitudinal emittance). Once the beamline bends, the introduction of dispersion creates a coupling between the transverse and longitudinal planes. If this coupling is handled properly, one can achieve cooling in all three phase space planes. This is usually done by placing a wedge-shaped absorber in a region where there is dispersion. I will demonstrate using an eigenvalue analysis that there are other configurations of…
Muon colliders and neutrino factories are attractive options for achieving the highest lepton-antilepton collision energies and the most precise measurements of the parameters of the neutrino mixing matrix. The performance and cost of these future facilities depends sensitively on how well a beam of muons can be cooled. The recent progress of muon-cooling prototype tests and design studies nourishes the hope that such facilities can be built during the next decade.
Muon colliders and neutrino factories are attractive options for future facilities aimed at achieving the highest lepton-antilepton collision energies and precision measurements of parameters of the Higgs boson and the neutrino mixing matrix. The performance and cost of these depend on how well a beam of muons can be cooled. Recent progress in muon cooling design studies and prototype tests nourishes the hope that such facilities can be built during the coming decade. The status of the key technologies and their various demonstration experiments is summarized.
We are considering a RF cavity with Beryllium disk installed in the middle of the cavity as an ionization cooling element for the muon/pion beam. Specially arranged wedge-type shape of the disk together with nonzero dispersion allows 6D cooling of muon beam. Technical aspects of this system and conceptual design are discussed in this paper also. This type of cooler demonstrates advantages if compared with the RF cavity filled with pressurized gas or with the helical cooler.
Muon storage rings have been proposed for use as a source of high-energy neutrino beams (the Neutrino Factory) and as the basis for a high-energy lepton-antilepton collider (the Muon Collider). The Neutrino Factory is widely believed to be the machine of choice for the search for leptonic CP violation while the Muon Collider may prove to be the most practical route to multi-TeV lepton-antilepton collisions. The baseline conceptual designs for each of these facilities requires the phase-space compression (cooling) of the muon beams prior to acceleration. The short muon lifetime makes it impossi…
We show that Compton scattering can be used to cool TeV-scale muon beams, and we derive analytical expressions for the equilibrium transverse angular spread, longitudinal energy spread, and power requirements. We find that a factor of a few thousand reduction in emittance is possible for a 3 TeV muon collider.
Six-dimensional ionization cooling of muons is essential for muon colliders and possibly beneficial for neutrino factories. An experiment to demonstrate six-dimensional ionization cooling using practical apparatus is presented. It exploits recent innovative ideas that may lead to six-dimensional muon-cooling channels with emittance reduction approaching that needed for high-luminosity muon colliders.
We describe the program of research and development being undertaken by a consortium of Illinois university groups to develop liquid-hydrogen energy absorbers for muon-beam cooling for a possible stored-muon-beam neutrino factory.
A high-energy muon collider scenario requires a final cooling system that reduces transverse emittance to ~25 microns (normalized) while allowing longitudinal emittance increase. Ionization cooling using high-field solenoids (or Li Lens) can reduce transverse emittances to ~100 microns in readily achievable configurations, confirmed by simulation. Passing these muon beams at ~100 MeV/c through cm-sized diamond wedges can reduce transverse emittances to ~25 microns, while increasing longitudinal emittances by a factor of ~25. Implementation will require optical matching of the exiting beam into…
Muon colliders and neutrino factories are attractive options for future facilities aimed at achieving the highest lepton-antilepton collision energies and precision measurements of parameters of the neutrino mixing matrix. The performance and cost of these depend sensitively on how well a beam of muons can be cooled. Recent progress in muon cooling design studies and prototype tests nourishes the hope that such facilities can be built in the decade to come.
The MuCool R&D program is described. The aim of MuCool is to develop all key pieces of hardware required for ionization cooling of a muon beam. This effort will lead to a more detailed understanding of the construction and operating costs of such hardware, as well as to optimized designs that can be used to build a Neutrino Factory or Muon Collider. This work is being undertaken by a broad collaboration including physicists and engineers from many national laboratories and universities in the U.S. and abroad. The intended schedule of work will lead to ionization cooling being well enough estab…
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.
The International Muon Ionization Cooling Experiment (MICE) is devoted to a study of a muon cooling channel capable of giving the desired performance for a Neutrino Factory. One of the goals is achieving an absolute accuracy of measurements of emittance reduction as high as 0.1%. The paper describes results of a Monte Carlo study on allowed density variations of liquid hydrogen corresponding to the desired accuracy of the measurements.
The Muon Ionization Cooling Experiment (MICE) has measured the evolution of emittance due to ionization energy loss. Muons were focused onto an absorber using a large aperture solenoid. Lithium-hydride and liquid hydrogen- absorbers have been studied. Diagnostic devices were placed upstream and downstream of the focus, enabling the phase- space coordinates of individual muons to be reconstructed. By observing the properties of ensembles of muons, the change in beam emittance was measured. Data taken during 2016 and 2017 are currently under study to evaluate the change in emittance due to the a…
Muon Colliders would usher in a new era of scientific investigation in the field of high energy particle physics. The cooling of muon beams is proving to be the greatest obstacle in the realization of a Muon Collider. Monte Carlo simulations of a muon cooling scheme based on Frictional Cooling were performed. Critical issues, which require further study, relating to the technical feasibility of such a scheme are identified. Frictional Cooling, as outlined in this paper, provides sufficient six-dimensional emittance to make luminous collisions possible. It holds exciting potential in solving th…
Ionization cooling of a muon beam is a key technique for a Neutrino Factory or Muon Collider. An international collaboration is mounting an experiment to demonstrate muon ionization cooling at the Rutherford Appleton Laboratory. We aim to complete the experiment by 2010.
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,…
Possible application for muon experiments such as mu2e is discussed of the initial part of the ionization cooling channel originally developed for muon collider. It is shown that with the FNAL Booster as the proton driver the mu2e sensitivity can be increased by two orders of magnitude compared to the presently considered experiment.
The international Muon Ionization Cooling Experiment (MICE) aims to demonstrate muon beam ionization cooling for the first time and constitutes a key part of the R&D towards a future neutrino factory or muon collider. Beam cooling reduces the size of the phase space volume occupied by the beam. Non-parametric density estimation techniques allow very precise calculation of the muon beam phase-space density and its increase as a result of cooling. These density estimation techniques are investigated in this paper and applied in order to estimate the reduction in muon beam size in MICE under vari…
The possibility of the Enhanced Optical Cooling of muon beams in storage rings is investigated.
Muon colliders have been proposed for the next generation of particle accelerators that study high-energy physics at the energy and intensity frontiers. In this paper we study a possible implementation of muon ionization cooling, Parametric-resonance Ionization Cooling (PIC), in the twin helix channel. The resonant cooling method of PIC offers the potential to reduce emittance beyond that achievable with ionization cooling with ordinary magnetic focusing. We examine optimization of a variety of parameters, study the nonlinear dynamics in the twin helix channel and consider possible methods of …
Emittance exchange mediated by wedge absorbers can be used for longitudinal ionization cooling and for final transverse emittance minimization for a muon collider. A wedge absorber within the Muon Ionization Cooling Experiment (MICE) could serve as a demonstration of the type of emittance exchange needed for six-dimensional (6D) cooling, including the configurations needed for muon colliders. Parameters for this test have been explored in simulation and applied to experimental configurations using a wedge-shaped absorber. A polyethylene wedge absorber has been fabricated and placed in MICE and…
The Muon Ionization Cooling Experiment (MICE) at Rutherford Appleton Laboratory has studied ionization cooling of muons. Several million individual muon tracks have been recorded passing through a series of focusing magnets and a liquid hydrogen or lithium hydride absorber in a variety of magnetic configurations. Identification and measurement of muon tracks upstream and downstream of the absorber are used to study the evolution of the 4D emittance. This paper presents and discusses these results.
A program is underway to develop liquid-hydrogen energy absorbers for ionization cooling of muon-beam transverse emittance. Minimization of multiple-scattering-induced beam heating requires thin windows. The first window prototype has been destructively tested, validating the finite-element-analysis model and the design approach.
A complete scheme for production and cooling a muon beam for three specified muon colliders is presented. Parameters for these muon colliders are given. The scheme starts with the front end of a proposed neutrino factory that yields bunch trains of both muon signs. Emittance exchange cooling in slow helical lattices reduces the longitudinal emittance until it becomes possible to merge the trains into single bunches, one of each sign. Further cooling in all dimensions is applied to the single bunches in further slow helical lattices. Final transverse cooling to the required parameters is achiev…
A six-dimensional muon ionization cooling in a helical magnet channel has been studied. The cooling performance which is analytically evaluated by solving the exact Hamiltonian is reproduced in numerical simulation. One of the key beam elements for the helical channel is a dense-hydrogen gas-filled RF cavity which realizes a compact cooling channel. Besides, a beam-induced gas plasma in the cavity can generate a plasma-focusing effect. This will generate extremely small betatron function, which realizes extremely low emittance beam.
An intense beam of muons is needed to provide a luminosity on the order of 10$^{34}$ cm$^{-2}$s$^{-1}$ 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 deliv…
Performance and tolerance study of the rectilinear cooling channel for a muon collider
本文针对μ子对撞机初始六维冷却需求，提出含附加偶极磁铁的直线冷却通道概念设计，给出通用设计方法，并研究π模射频腔及场误差对冷却性能的影响。
New computational tools are essential for accurate modeling and simulation of the next generation of muon-based accelerators. One of the crucial physics processes specific to muon accelerators that has not yet been simulated in detail is beam-induced plasma effect in liquid, solid, and gaseous absorbers. We report here on the progress of developing the required simulation tools and applying them to study the properties of plasma and its effects on the beam in muon ionization cooling channels.
Muon Transverse Ionization Cooling: Stochastic Approach
μ子的横向电离冷却被建模为μ子束在穿过Li或Be棒时的布朗运动。一个朗之万方程写的自由粒子的情况下（没有外部横向磁场）和一个谐波约束光束的情况下，在存在一个聚焦磁场。我们证明了众所周知的短吸收体的μ子冷却方程可以外推到一个长的吸收体棒与聚焦磁场存在的有用的情况下。
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 facto…
Novel magnetic helical channel designs for capture and cooling of bright muon beams are being developed using numerical simulations based on new inventions such as helical solenoid (HS) magnets and hydrogen-pressurized RF (HPRF) cavities. We are close to the factor of a million six-dimensional phase space (6D) reduction needed for muon colliders. Recent experimental and simulation results are presented.
After summarizing the important commonalities between neutrino factories and muon colliders, the key differences are discussed. These include a much larger needed cooling factor (~10^6 in six-dimensional emittance), a smaller number of muon bunches (perhaps only one of each charge), and acceleration to much higher energy, implying significantly different technical choices for some of the cooling and acceleration subsystems. The final storage rings are also quite different. Nevertheless, a neutrino factory could serve as a key stepping stone on the path to a muon collider.
The international Muon Ionization Cooling Experiment (MICE), which is under construction at the Rutherford Appleton Laboratory (RAL), will demonstrate the principle of ionization cooling as a technique for the reduction of the phase-space volume occupied by a muon beam. Ionization cooling channels are required for the Neutrino Factory and the Muon Collider. MICE will evaluate in detail the performance of a single lattice cell of the Feasibility Study 2 cooling channel. The MICE Muon Beam has been constructed at the ISIS synchrotron at RAL, and in MICE Step I, it has been characterized using th…
Progress in Muon Cooling and Moderation Techniques
本文综述了μ子束冷却与慢化技术，包括电离冷却、慢化、摩擦冷却及激光电离等方法，旨在克服μ子寿命短导致的束流质量限制，为下一代μ子设施和精密实验提供途径。
Low-energy muon beams are useful for a range of physics experiments. We consider the production of low-energy muon beams with small energy spreads using frictional cooling. As the input beam, we take a surface muon source such as that at the Paul Scherrer Institute. Simulations show that the efficiency of low energy muon production can potentially be raised to 1%, which is significantly higher than that of current schemes.
The Muon Ionization Cooling Experiment (MICE) at the Rutherford Appleton Laboratory aims to demonstrate $\approx$ 10% ionization cooling of a muon beam by its interaction with low-Z absorber materials followed by restoration of longitudinal momentum in RF linacs. MICE Step IV, including the first LH2 or LiH absorber cell sandwiched between two particle tracking spectrometers, is the collaboration's near-term goal. Two large superconducting spectrometer solenoids and one focus coil solenoid will provide a magnetic field of $\approx$4 T in the tracker and absorber-cell volumes. The status of the…
Starting from elementary concepts, muon-beam cooling is defined, and the techniques by which it can be accomplished introduced and briefly discussed.
The MuCool R&D program is described. The aim of MuCool is to develop all key pieces of hardware required for ionization cooling of a muon beam. This effort will lead to a more detailed understanding of the construction and operating costs of such hardware, as well as to optimized designs that can be used to build a Neutrino Factory or Muon Collider. This work is being undertaken by a broad collaboration including physicists and engineers from many national laboratories and universities in the U.S. and abroad. The intended schedule of work will lead to ionization cooling being well enough estab…
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, an…
Pressure Spike in The LBNF Absorber Core s Gun Drilled Cooling Channel from an Accident Beam Pulse
本研究模拟了LBNF Absorber在事故束流脉冲下冷却通道内的压力尖峰，通过瞬态结构分析评估了压力上升对铝管道及焊缝强度的影响，并验证其是否超过允许极限。
This paper investigates the feasibility of re-purposing the MuCool Test Area (MTA) beamline and experimental hall to support a Muon Spin Resonance (MuSR) facility, which would make it the only such facility in the US. This report reviews the basic muon production concepts studied and operationally implemented at TRIUMF, PSI, and RAL and their application in the context of the MTA facility. Two scenarios were determined feasible. One, an initial minimal-shielding and capital-cost investment stage with a single secondary muon beamline that utilizes an existing high-intensity beam absorber and, a…
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, for neutrino factory and muon collider scenarios. They require a drift section from the target, a bunching section and a ϕ-δE rotation section leading into the cooling channel. 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 vari…
The goal of the international Muon Ionization Cooling Experiment (MICE) is to demonstrate muon beam ionization cooling for the first time. It constitutes a key part of the R&D towards a future neutrino factory or muon collider. The intended MICE precision requires the development of analysis tools that can account for any effects (e.g., optical aberrations) which may lead to inaccurate cooling measurements. Non-parametric density estimation techniques, in particular, kernel density estimation (KDE), allow very precise calculations of the muon beam phase-space density and its increase as a resu…
Fast muon beam six dimensional (6D) phase space cooling is essential for muon colliders. The Helical Cooling Channel (HCC) uses hydrogen-pressurized RF cavities imbedded in a magnet system with solenoid, helical dipole, and helical quadrupole components that provide the continuous dispersion needed for emittance exchange and effective 6D beam cooling. A series of HCC segments, each with sequentially smaller aperture, higher magnetic field, and higher RF frequency to match the beam size as it is cooled, has been optimized by numerical simulation to achieve a factor of 105 emittance reduction in…
Final Cooling With Thick Wedges for a Muon Collider
针对μ子对撞机最终冷却阶段，本研究开发并优化了基于致密楔块吸收体的4D冷却通道概念设计，通过G4Beamline和Python模拟优化，在x和y方向实现约3.5倍横向冷却，获得了优于以往设计的横向与纵向发射度。
A 10 MeV/c $μ^+$ beam was stopped in helium gas of a few mbar in a magnetic field of 5 T. The muon 'swarm' has been efficiently compressed from a length of 16 cm down to a few mm along the magnetic field axis (longitudinal compression) using electrostatic fields. The simulation reproduces the low energy interactions of slow muons in helium gas. Phase space compression occurs on the order of microseconds, compatible with the muon lifetime of 2 $μ$s. This paves the way for preparation of a high quality muon beam.
Experimental and theoretical activities are underway at CERN with the aim of examining the feasibility of a very-high-flux neutrino source. In the present scheme, a high-power proton beam (some 4 MW) bombards a target where pions are produced. The pions are collected and decay to muons under controlled optical condition. The muons are cooled and accelerated to a final energy of 50 GeV before being injected into a decay ring where they decay under well-defined conditions of energy and emittance. We present the most challenging parts of the whole scenario, the muon capture, the ionisation-coolin…
This paper presents new theoretical results on the passage of muons through liquid hydrogen which have been confirmed in a recent experiment. These are used to demonstrate that muon bunches may be compressed by ionisation cooling more effectively than suggested by previous calculations. Muon cooling depends on the differential cross section for energy loss and scattering of muons. We have calculated this cross section for liquid H2 from first principles and atomic data, avoiding traditional assumptions. Thence, 2-D probability maps of energy loss and scattering in mm-scale thicknesses are deri…
Limits of applicability of the Robinson's damping criterion and the problem of enhanced cooling of particle beams in storage rings beyond the criterion are discussed.
Muon cooling is the main technological obstacle in the building of a muon collider. A muon cooling scheme based on Frictional Cooling holds promise in overcoming this obstacle. An experiment designed to demonstrate the Frictional Cooling concept using protons was undertaken. Although the results were inconclusive in the observation of cooling, the data allowed for the qualification of detailed simulations which are used to simulate the performance of a muon collider.
Muon-based accelerators have the potential to enable facilities at both the Intensity and the Energy Frontiers. Muon storage rings can serve as high precision neutrino sources, and a muon collider is an ideal technology for a TeV or multi-TeV collider. Progress in muon accelerator designs has advanced steadily in recent years. In regard to 6D muon cooling, detailed and realistic designs now exist that provide more than 5 order-of-magnitude emittance reduction. Furthermore, detector performance studies indicate that with suitable pixelation and timing resolution, backgrounds in the collider det…
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-sp…
RF cavity design and beam loading effects in the rectilinear cooling channel for a muon collider
本文针对缪子对撞机直线冷却通道的束流负载问题，开展带束窗铜腔的RF设计与效应分析，提出考虑束流横向分布的新型数值补偿方法，为实现高亮度缪子对撞机提供关键技术支撑。
Muon ionization cooling provides the only practical solution to prepare high-brilliance beams necessary for a neutrino factory or muon collider. The Muon Ionization Cooling Experiment (MICE), under development at the Rutherford Appleton Laboratory, is installing the first set of particle detectors ever built to measure to 0.1% the emittance of a 200 MeV/c or so muon beam in and out of a cooling cell, and thus measure the cooling cell's performance. Two identical "emittometers" (a precise scintillating-fiber tracker in solenoidal magnetic field and a 50 ps time-of-flight station) measure the si…
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-δE 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…
Ionization cooling is the preferred method for producing bright muon beams. This cooling technique requires the operation of normal conducting, radio-frequency (RF) accelerating cavities within the multi-tesla fields of DC solenoid magnets. Under these conditions, cavities exhibit increased susceptibility to RF breakdown, which can damage channel components and imposes limits on channel length and transmission efficiency. We present a solution to the problem of breakdown in strong magnetic fields. We report, for the first time, stable high-vacuum, copper cavity operation at gradients above 50 …
Ultra-fast stochastic cooling would be desirable in certain applications, for example, in order to boost final luminosity in a muon collider or neutrino factory, where short particle lifetimes severely limit the total time available to reduce beam phase space. But fast cooling requires very high-bandwidth amplifiers so as to limit the incoherent heating effects from neighboring particles. A method of transit-time optical stochastic cooling has been proposed which would employ high-gain, high-bandwidth, solid-state lasers to amplify the spontaneous radiation from the charged particle bunch in a…
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