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 the problem of Muon Cooling.
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.
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.
A muon collider would open new frontiers of investigation in high energy particle physics, allowing precision measurements to be made at the TeV energy frontier. One of the greatest challenges to constructing a muon collider is the preparation of a beam of muons on a timescale comparable to the lifetime of the muon. Frictional cooling is a potential solution to this problem. In this paper, we briefly describe frictional cooling and detail the Frictional Cooling Demonstration (FCD) experiment at the Max Planck Institute for Physics, Munich. The FCD experiment, which aims to verify the working p…
One of the focuses of research and development towards the construction of a muon collider is muon beam preparation. Simulation of frictional cooling shows that it can achieve the desired emittance reduction to produce high-luminosity muon beams. We show that for positively charged particles, charge exchange interactions necessitate significant changes to schemes previously developed for negatively charged particles. We also demonstrate that foil-based schemes are not viable for positive particles.
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.
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.
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…
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 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.
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…
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.
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.
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…
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 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…
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…
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
European Organization for Nuclear Research (CERN)（欧洲核子研究中心）；Northern Illinois University（北伊利诺伊大学）；Argonne National Laboratory（阿贡国家实验室）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
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…
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…
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…
A large admittance sector cyclotron filled with LiH wedges surrounded by helium or hydrogen gas is explored. Muons are cooled as they spiral adiabatically into a central swarm. As momentum approaches zero, the momentum spread also approaches zero. Long bunch trains coalesce. Energy loss is used to inject the muons into the outer rim of the cyclotron. The density of material in the cyclotron decreases adiabatically with radius. The sector cyclotron magnetic fields are transformed into an azimuthally symmetric magnetic bottle in the center. Helium gas is used to inhibit muonium formation by posi…
A complete scheme for production, cooling, acceleration, and ring for a 1.5 TeV center of mass muon collider is presented, together with parameters for two higher energy machines. The schemes starts with the front end of a proposed neutrino factory that yields bunch trains of both muon signs. Six dimensional cooling in long-period 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 helical lattices. Final transverse cooling to the re…
A number of recent developments have led to simulations of an inverse cyclotron for cooling intense muon beams for neutrino factories and muon colliders. Such a device could potentially act as a novel beam cooling mechanism for muons, and it would be significantly smaller and cheaper than other cooling channel designs. Realistic designs are still being explored, but the first simulations of particle tracking in the inverse cyclotron, with accumulation in the cyclotron core, have been done with electrostatic simulations in the particle-in-cell code VORPAL. We present an overview of the muon inv…
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…
I present a scheme to obtain a 2 to 40 GeV low emittance muon beam, not requiring cooling and within today's technological resources, to be used for early commissioning of muon accelerator projects, or alternatively dedicated muon and neutrino parameter measurements. In particular, a muon rate of 5x10^4 mu/s in a normalized transverse emittance of 5 um at 22 GeV, and energy spread of 1 GeV obtained from O(10^11) e+/s on target at 44 GeV. This emittance is below the expected results of advanced emittance cooling techniques for muons produced from protons-on-target, and represents an alternative…
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…
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.
In studies of the dynamics of charged particles in a cyclotron magnetic field, the specified field is generally B_z in the z = 0 midplane where B_r and B_theta are zero. B_r(r, theta, z) and B_theta(r, theta, z) are simple to determine through a linear expansion which assumes that B_z is independent of z. But, an expansion to only first order may not be sufficient for orbit simulations at large z. This paper reviews the expansion of a specified B_z(r, theta, z = 0) out of the z = 0 midplane to arbitrary order, and shows simple examples worked out to 4th order.
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.
Muon ionization cooling is the only practical method for preparing high-brilliance beams needed for a neutrino factory or muon collider. The muon ionization cooling experiment (MICE) under development at the Rutherford Appleton Laboratory comprises a dedicated beamline to generate a range of input emittance and momentum, with time-of-flight and Cherenkov detectors to ensure a pure muon beam. A first measurement of emittance is performed in the upstream magnetic spectrometer with a scintillating-fiber tracker. A cooling cell will then follow, alternating energy loss in liquid hydrogen with RF a…
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.
Transverse ionization cooling of muons is modeled as a Brownian motion of the muon beam as it traverses a Li or Be rod. A Langevin like equation is written for the free particle case (no external transverse magnetic field) and for the case of a harmonically bound beam in the presence of a focusing magnetic field. We demonstrate that the well known muon cooling equations for short-absorbers can be extrapolated to the useful case of a long absorber rod with a focusing magnetic field present.
The Muon Ionization Cooling Experiment (MICE) will demonstrate the feasibility of ionization cooling, the technique by which it is proposed to cool the muon beam at a future neutrino factory or muon collider. The position and momentum reconstruction of individual muons in the MICE trackers allows for the development of alternative figures of merit in addition to beam emittance. Contraction of the phase space volume occupied by a fraction of the sample, or equivalently the increase in phase space density at its core, is an unequivocal cooling signature. Single-particle amplitude and non-paramet…
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…
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.
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.
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.
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.
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…
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.
A new experimental area designed to develop, test and verify muon ionization cooling apparatus using the 400-MeV Fermilab Linac proton beam has been fully installed and is presently being commissioned. Initially, this area was used for cryogenic tests of liquid-hydrogen absorbers for the MUCOOL R&D program and, now, for high-power beam tests of absorbers, high-gradient rf cavities in the presence of magnetic fields (including gas-filled cavities), and other prototype muon-cooling apparatus. The experimental scenarios being developed for muon facilities involve collection, capture, and cooling …
The (International Design Report) IDR neutrino factory scenario for capture, bunching, phase-energy rotation and initial cooling of micro's produced from a proton source target is explored. It requires a drift section from the target, a bunching section and a -E rotation section leading into the cooling channel. The rf frequency changes along the bunching and rotation transport in order to form the 's into a train of equal-energy bunches suitable for cooling and acceleration. Optimization and variations are discussed. An important concern is rf limitations within the focusing magnetic fields, …
We outline a plan for final muon ionization cooling with quadrupole doublets focusing onto short absorbers followed by emittance exchange in vacuum to achieve the small transverse beam sizes needed by a muon collider. A flat muon beam with a series of quadrupole doublet half cells appears to provide the strong focusing required for final cooling. Each quadrupole doublet has a low beta region occupied by a dense, low Z absorber. After final cooling, normalized xyz emittances of (0.071, 0.141, 2.4) mm-rad are exchanged into (0.025, 0.025, 70) mm-rad. Thin electrostatic septa efficiently slice th…
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…
A multi-laboratory collaboration is studying the feasibility of building a muon collider, the first phase of which maybe a neutrino factory. The phase space occupied by the muons is very large and needs to be cooled several orders of magnitude for either machine, 100,000 to 1 million for the collider and ten to 100 for the factory. Ionization cooling is the base line method for muon cooling. This scheme uses hydrogen absorbers and rf re-acceleration in a long series of magnetic focusing channels to cool the muons. At Fermilab two rf cavity types are under study to provide the required cooling …
