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Muon accelerators offer an attractive option for a range of future particle physics experiments. They can enable high energy (TeV+) high energy lepton colliders whilst mitigating the difficulty of synchrotron losses, and can provide intense beams of neutrinos for fundamental physics experiments investigating the physics of flavor. The method of production of muon beams results in high beam emittance which must be reduced for efficient acceleration. Conventional emittance control schemes take too long, given the very short (2.2 microsecond) rest lifetime of the muon. Ionisation cooling offers a much faster approach to reducing particle emittance, and the international MICE collaboration aims to demonstrate this technique for the first time. This paper will present the MICE RF system and its role in the context of the overall experiment., Comment: 2 pp

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 MV/m and in an external magnetic field of three tesla. This eliminates a significant technical risk that has previously been inherent in ionization cooling channel designs., Comment: 7 pages, 7 figures

Microscopic images of the surfaces of metallic electrodes used in high-pressure gas-filled 805 MHz RF cavity experiments1 have been used to investigate the mechanism of RF breakdown.2 The images show evidence for melting and boiling in small regions of ~10 micron diameter on tungsten, molybdenum, and beryllium electrode surfaces. In these experiments, the dense hydrogen gas in the cavity prevents electrons or ions from being accelerated to high enough energy to participate in the breakdown process so that the only important variables are the fields and the metallic surfaces. The distributions of breakdown remnants on the electrode surfaces are compared to the maximum surface gradient E predicted by an ANSYS model of the cavity. The local surface density of spark remnants, proportional to the probability of breakdown, shows a strong exponential dependence on the maximum gradient, which is reminiscent of Fowler-Nordheim behavior of electron emission from a cold cathode. New simulation results have shown good agreement with the breakdown behavior of the hydrogen gas in the Paschen region and have suggested improved behavior with the addition of trace dopants such as SF 6.3 Present efforts are to extend the computer model to include electrode breakdown phenomena and to use scanning tunneling microscopy to search for work function differences between the conditioned and unconditioned parts of the electrodes.

A feasibility study on liquid hydrogen (LH 2 ) absorbers for muon ionization cooling is reported. In muon ionization cooling, an LH 2 absorber is required to have a high cooling power greater than 100 W to cool heat deposited by muons passing through. That heat in LH 2 can be removed at either external or internal heat exchangers, which are cooled by cold helium gas. As one of the internal heat exchanger types, a convection-type absorber is proposed. In the convection-type absorber, heat is taken away by the convection of LH 2 in the absorber. The heat exchanger efficiency for the convection-type absorber is calculated. A possible design is presented.

Measurements of the X-ray flux, electron flux and spectrum are presented with the aim of evaluating the usefulness of ionization sensitive single particle detectors in the immediate environment of an rf cavity. The measured fluxes are found to be roughly consistent with field emission of electrons followed by one generation of bremsstrahlung photon production, with absorption and scattering of the final photons and electrons in the cavity and vacuum chamber structure.

An 800 MHz RF test cell filled with high pressure gaseous hydrogen was used to study RF breakdown phenomena in hydrogen and helium gases as a function of pressure and temperature. The maximum achieved RF surface gradient was 80 MV/m at 1.83 MPa and 77 K, where the breakdown of the molybdenum electrodes of the test cell limited the study of the linear dependence of the breakdown voltage on gas density known as Paschen's Law. The test cell conditioning was also much faster in gas than in vacuum cavities. The high gradient and fast conditioning are encouraging results for the use of high-pressure RF cavities for ionization cooling of muon beams for muon colliders, neutrino factories, and intense sources.

A major technological challenge in building a muon cooling channel is operating rf cavities in multitesla external magnetic fields. We report the first proof-of-principle experiment of a high pressure gas-filled rf cavity for use with intense ionizing beams and strong external magnetic fields. rf power consumption by beam-induced plasma is investigated with hydrogen and deuterium gases with pressures between 20 and 100 atm and peak rf gradients between 5 and $50\text{ }\text{ }\mathrm{MV}/\mathrm{m}$. The low pressure case agrees well with an analytical model based on electron and ion mobilities. Varying concentrations of oxygen gas are investigated to remove free electrons from the cavity and reduce the rf power consumption. Measurements of the electron attachment time to oxygen and rate of ion-ion recombination are also made. Additionally, we demonstrate the operation of the gas-filled rf cavity in a solenoidal field of up to 3 T, finding no major magnetic field dependence. All these results indicate that a high pressure gas-filled cavity is a viable technology for muon ionization cooling.

The nuSTORM facility has been designed to deliver beams of electron neutrinos and muon neutrinos (and their anti-particles) from the decay of a stored muon beam with a central momentum of 3.8 GeV/c and a momentum acceptance of 10%. The facility is unique in that it will: 1. Allow searches for sterile neutrinos of exquisite sensitivity to be carried out; 2. Serve future long- and short-baseline neutrino-oscillation programs by providing definitive measurements of electron neutrino and muon neutrino scattering cross sections off nuclei with percent-level precision; and 3. Constitutes the crucial first step in the development of muon accelerators as a powerful new technique for particle physics. The document describes the facility in detail and demonstrates its physics capabilities. This document was submitted to the Fermilab Physics Advisory Committee in consideration for Stage I approval. The nuSTORM facility has been designed to deliver beams of electron neutrinos and muon neutrinos (and their anti-particles) from the decay of a stored muon beam with a central momentum of 3.8 GeV/c and a momentum acceptance of 10%. The facility is unique in that it will: 1. Allow searches for sterile neutrinos of exquisite sensitivity to be carried out; 2. Serve future long- and short-baseline neutrino-oscillation programs by providing definitive measurements of electron neutrino and muon neutrino scattering cross sections off nuclei with percent-level precision; and 3. Constitutes the crucial first step in the development of muon accelerators as a powerful new technique for particle physics. The document describes the facility in detail and demonstrates its physics capabilities. This document was submitted to the Fermilab Physics Advisory Committee in consideration for Stage I approval.

An integrated program is described, starting with muon experiments in the Booster era, continuing with a 2 MW target station, a 4 GeV Neutrino Factory and a 3 TeV Muon Collider, all driven by Project X. This idea provides an integrated approach to the Intensity and Energy Frontiers at Fermilab., 3 pp. 11th International Workshop on Neutrino Factories, Superbeams and Betabeams: NuFact 09. 20-25 Jul 2009. Chicago, Illinois

The idea of using a muon storage ring to produce a high-energy ({approx_equal} 50 GeV) neutrino beam for experiments was first discussed by Koshkarev in 1974. A detailed description of a muon storage ring for neutrino oscillation experiments was first produced by Neuffer in 1980. In his paper, Neuffer studied muon decay rings with E{sub {mu}} of 8, 4.5 and 1.5 GeV. With his 4.5 GeV ring design, he achieved a figure of merit of {approx_equal} 6 x 10{sup 9} useful neutrinos per 3 x 10{sup 13} protons on target. The facility we describe here ({nu}STORM) is essentially the same facility proposed in 1980 and would utilize a 3-4 GeV/c muon storage ring to study eV-scale oscillation physics and, in addition, could add significantly to our understanding of {nu}{sub e} and {nu}{sub {mu}} cross sections. In particular the facility can: (1) address the large {Delta}m{sup 2} oscillation regime and make a major contribution to the study of sterile neutrinos, (2) make precision {nu}{sub e} and {bar {nu}}{sub e} cross-section measurements, (3) provide a technology ({mu} decay ring) test demonstration and {mu} beam diagnostics test bed, and (4) provide a precisely understood {nu} beam for detector studies. The facility is the simplest implementation of the Neutrino Factory concept. In our case, 60 GeV/c protons are used to produce pions off a conventional solid target. The pions are collected with a focusing device (horn or lithium lens) and are then transported to, and injected into, a storage ring. The pions that decay in the first straight of the ring can yield a muon that is captured in the ring. The circulating muons then subsequently decay into electrons and neutrinos. We are starting with a storage ring design that is optimized for 3.8 GeV/c muon momentum. This momentum was selected to maximize the physics reach for both oscillation and the cross section physics. See Fig. 1 for a schematic of the facility.

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 the MICE beam-instrumentation system. In this paper, the MICE Muon Beam and beam-line instrumentation are described. The muon rate is presented as a function of the beam loss generated by the MICE target dipping into the ISIS proton beam. For a 1 V signal from the ISIS beam-loss monitors downstream of our target we obtain a 30 KHz muon rate, with a neglible pion contamination in the beam. 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 the MICE beam-instrumentation system. In this paper, the MICE Muon Beam and beam-line instrumentation are described. The muon rate is presented as a function of the beam loss generated by the MICE target dipping into the ISIS proton beam. For a 1 V signal from the ISIS beam-loss monitors downstream of our target we obtain a 30 KHz instantaneous muon rate, with a neglible pion contamination in the beam.

The design of a low-energy (4 GeV) neutrino factory (NF) is described, along with its expected performance. The neutrino factory uses a high-energy proton beam to produce charged pions. The ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ decay to produce muons (${\ensuremath{\mu}}^{\ifmmode\pm\else\textpm\fi{}}$), which are collected, accelerated, and stored in a ring with long straight sections. Muons decaying in the straight sections produce neutrino beams. The scheme is based on previous designs for higher energy neutrino factories, but has an improved bunching and phase rotation system, and new acceleration, storage ring, and detector schemes tailored to the needs of the lower energy facility. Our simulations suggest that the NF scheme we describe can produce neutrino beams generated by $\ensuremath{\sim}1.4\ifmmode\times\else\texttimes\fi{}{10}^{21}$ ${\ensuremath{\mu}}^{+}$ per year decaying in a long straight section of the storage ring, and a similar number of ${\ensuremath{\mu}}^{\ensuremath{-}}$ decays.

This document summarizes the findings of the Accelerator Working Group (AWG) of the International Scoping Study (ISS) of a Future Neutrino Factory and super-beam Facility. The work of the group took place at three plenary meetings along with three workshops, and an oral summary report was presented at the NuFact06 workshop held at UC-Irvine in August, 2006. The goal was to reach consensus on a baseline design for a Neutrino Factory complex. One aspect of this endeavor was to examine critically the advantages and disadvantages of the various Neutrino Factory schemes that have been proposed in recent years., 73 pages, 60 figures

The idea of coalescing multiple muon bunches at high energy to enhance the luminosity of a muon collider provides many advantages. It circumvents space-charge, beam loading, and wakefield problems of intense low- energy bunches while restoring the synergy between muon colliders and neutrino factories based on muon storage rings. A sampling of initial conceptual design work for a coalescing ring is presented here.

The Fermilab proton source is capable of providing 8 GeV protons for both the future long-baseline neutrino program (NuMI), and for a new program of low energy muon experiments. In particular, if the 8 GeV protons are rebunched and then slowly extracted into an external beamline, the resulting proton beam would be suitable for a muon-to-electron conversion experiment designed to improve on the existing sensitivity by three orders of magnitude. We describe a scheme for the required beam manipulations. The scheme uses the Accumulator for momentum stacking, and the Debuncher for bunching and slow extraction. This would permit simultaneous operation of the muon program with the future NuMI program, delivering 10{sup 20} protons per year at 8 GeV for the muon program at the cost of a modest ({approx}10%) reduction in the protons available to the neutrino program.

Most ionization cooling schemes now under consideration are based on using many large flasks of liquid hydrogen energy absorber. One important example is the proposed Muon Ionization Cooling Experiment (MICE), which has recently been approved to run at the Rutherford Appleton Laboratory (RAL). In the work reported here, a potential muon cooling demonstration experiment based on a continuous liquid energy absorber in a helical cooling channel (HCC) is discussed. The original HCC used a gaseous energy absorber for the engineering advantage of combining the energy absorption and RF energy regeneration in hydrogen-filled RF cavities. In the Muon And Neutrino eXperiment (MANX) that is proposed here, a liquid-filled HCC is used without RF energy regeneration to achieve the largest possible cooling rate in six dimensions. In this case, the magnetic fields of the HCC must diminish as the muons lose momentum as they pass through the liquid energy absorber. The length of the MANX device is determined by the maximum momentum of the muon test beam and the maximum practical field that can be sustained at the magnet coils. We have studied a 3 meter-long HCC example that could be inserted between the MICE spectrometers at RAL.

A study of RF breakdown of metals in gases has begun as part of a program to develop RF cavities filled with dense hydrogen gas to be used for muon ionization cooling. A pressurized 805 MHz test cell is being used at Fermilab to compare the conditioning and breakdown behavior of copper, molybdenum, chromium, and beryllium electrodes as functions of hydrogen and helium gas densities. These results will be compared to the predicted or known RF breakdown behavior of these metals in vacuum.

Eight new ideas are being developed under SBIR/STTR grants to cool muon beams for colliders, neutrino factories, and muon experiments. Analytical and simulation studies have confirmed that a six‐dimensional (6D) cooling channel based on helical magnets surrounding RF cavities filled with dense hydrogen gas can provide effective beam cooling. This helical cooling channel (HCC) has solenoidal, helical dipole, helical quadrupole, and helical sextupole magnetic fields to generate emittance exchange and achieve 6D emittance reduction of over 3 orders of magnitude in a 100 m segment. Four such sequential HCC segments, where the RF frequencies are increased and transverse physical dimensions reduced as the beams become cooler, implies a 6D emittance reduction of almost five orders of magnitude. Two new cooling ideas, Parametric‐resonance Ionization Cooling and Reverse Emittance Exchange, then can be employed to reduce transverse emittances to a few mm‐mr, which allows high luminosity with fewer muons than previously imagined. We describe these new ideas as well as a new precooling idea based on a HCC with z dependent fields that can be used as MANX, an exceptional 6D cooling demonstration experiment.

This report describes a PARMILA simulation of the Fermilab Drift Tube Linac (DTL). Effects on the H{sup -} beam associated with random noise on the DTL quadrupole currents are studied.

Using the PARMILA code running under PC-WINDOWS, the present performance of the Fermilab Drift Tube Linac has been analyzed in the light of new demands on the Linac/Booster complex (the Proton Source). The Fermilab Drift Tube Linac (DTL) was designed in the sixties as a proton linac with a final energy of 200 MeV and a peak current of 100mA. In the seventies, in order to enable multi-turn charge exchange injection into the Booster, the ion source was replaced by an H- source with a peak beam current of 25mA. Since then the peak beam current was steadily increased up to 55mA. In the early nineties, part of the drift tube structure was replaced with a side-coupled cavity structure in order to increase the final energy to 400 MeV. The original and still primary purpose of the linac is to serve as the injector for the Booster. As an added benefit, the Neutron Therapy Facility (NTF) was built in the middle seventies. It uses 66MeV protons from the Linac to produce neutrons for medical purposes. The Linac/Booster complex was designed to run at a fundamental cycling rate of 15Hz, but beam is accelerated on every cycle only when NTF is running. Until recently the demand from the High Energy Physics program resulted in an average linac beam repetition rate of order 1 Hz. With the MiniBoone experiment and the NuMI program, the demands on the Proton Source have changed, with emphasis on higher beam repetition rates up to 7.5Hz. Historically the beam losses in the linac were small, localized at one spot, so activation was not an important issue. With higher beam rate, this has the potential to become the dominant issue. Until today all tuning in the linac and Proton Source was governed by two goals: to maximize the peak beam current out of the linac and to minimize the beam losses in the linac. If maximal peak current from the linac is no longer a primary goal, then the linac quadrupoles can be adjusted differently to achieve different goals.

The MuCool hydrogen-absorber RandD program is summarized. Prototype absorbers featuring thin aluminum windows and 'flow-through' or 'convection' cooling are under development for eventual power-handling tests in a proton beam and a cooling demonstration in a muon beam. Testing these prototypes and their components involves application of novel techniques.

We present measurements of dark currents and x rays in a six cell 805 MHz cavity, taken as part of an rf development program for muon cooling, which requires high power, high stored energy, low frequency cavities operating in a strong magnetic field. We have done the first systematic study of the behavior of high power rf in a strong (2.5-4 T) magnetic field. Our measurements extend over a very large dynamic range in current and provide good fits to the Fowler-Nordheim field emission model assuming mechanical structures produce field enhancements at the surface. The locally enhanced field intensities we derive at the tips of these emitters are very large, (-10 GV/m), and should produce tensile stresses comparable to the tensile strength of the copper cavity walls and should be capable of causing breakdown events. We also compare our data with estimates of tensile stresses from a variety of accelerating structures. Preliminary studies of the internal surface of the cavity and window are presented, which show splashes of copper with many sharp cone shaped protrusions and wires which can explain the experimentally measured field enhancements. We discuss a 'cold copper' breakdown mechanism and briefly review alternatives. We also discuss amore » number of effects due to the 2.5 T solenoidal fields on the cavity such as altered field emission due to mechanical deformation of emitters, and dark current ring beams, which are produced from the irises by ExB drifts during the nonrelativistic part of the acceleration process.« less

Ionization cooling, a method for shrinking the size of a particle beam, is an essential technique for future particle accelerators that use muons. In this technique, muons lose energy in all three directions by passing through an absorber while only the longitudinal energy is regenerated by RF cavities. Thus the beam phase space area decreases down to the limit of multiple scattering in the energy absorber. Hydrogen is the material of choice for ionization cooling because of its long radiation length relative to its energy loss. In the application discussed here, dense gaseous hydrogen also suppresses RF breakdown by virtue of the Paschen effect, thereby allowing higher accelerating gradients and a shorter and less‐expensive cooling channel. As described in this paper, a channel of RF cavities pressurized with about 3 tons of cold hydrogen gas could provide transverse muon cooling for a Muon Collider or Neutrino Factory. The present status of this research effort and several issues related to the use of hydrogen in this application are described.

The future Muon Collider will have a luminosity of the order of 10/sup 35/ cm/sup -2-1/ during 1000 turns when the muons decay. This requires 10/sup 12/ muons per bunch. The muon source is a 30 GeV proton driver with 2.5 10/sup 13/ protons per pulse. The proton bunch length should be of the order of 1 ns. Short bunches could be created by a tunable momentum compaction lattice which would bring the momentum compaction to zero in a short time. This isochronous condition would allow bunches to shear and become very short in time. We present a lattice where the momentum compaction is a tunable parameter at fixed horizontal and vertical betatron tunes. The values of the maxima of the dispersion function are kept small. We examine two kinds of lattices, with combined function as well as normal dipole and quadrupole magnets.

The proton driver for the /spl mu//spl mu/ collider might operate at about 15 Hz and produce four bunches of 2.5.10/sup 13/ protons/bunch at about 10 GeV (or half that number at 20-30 GeV) with an RMS bunch length of about 1 nsec. A number of options have been considered to produce these bunches using: (a) simple bunch rotation, (b) energy slewing near /spl gamma//sub t/ followed by a fast increase of /spl gamma//sub t/ which facilitates bunching, and (c) change of RF frequency in a ring-to-ring transfer. Flexible momentum compaction (FMC), or similar, lattices seem to offer control of /spl gamma//sub t/ even on short time scales. The large momentum spread, space charge tune shift and rapid bunching would tend to stabilize short, intense bunches, although I/sub pk//spl sim/1600 A. Both active (harmonic cavities) and passive (inductive wall) solutions have been considered to minimize high current beam effects. Magnet and vacuum systems would be similar to other high current designs.

We describe the status of our effort to realize a first neutrino factory and the progress made in understanding the problems associated with the collection and cooling of muons towards that end. We summarize the physics that can be done with neutrino factories as well as with intense cold beams of muons. The physics potential of muon colliders is reviewed, both as Higgs Factories and compact high energy lepton colliders. The status and timescale of our research and development effort is reviewed as well as the latest designs in cooling channels including the promise of ring coolers in achieving longitudinal and transverse cooling simultaneously. We detail the efforts being made to mount an international cooling experiment to demonstrate the ionization cooling of muons., Comment: 112 pages, Large report

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., Comment: 7 pages, 1 figure, presented at the 3rd International Workshop on Neutrino Factory Based on Muon Storage Rings (NuFACT'01), May 24-30, 2001, Tsukuba, Japan

The proton driver for a muon collider must be capable of producing 2.5/spl times/10 13 p/bunch on target (in 4 bunches) in order to reach the design luminosity in the collider ring. Additionally, the bunches are very short, with an RMS of only /spl sim/1 ns, to match the longitudinal emittance requirements of downstream capture, cooling, and acceleration systems. This criterion along with the high intensity places constraints on the proton driver design which will require both theoretical and experimental verification. This paper will discuss the bunch shortening techniques to be tested experimentally, the impact of longitudinal space charge, and potential instabilities in such an accelerator.

The proton driver for the muon collider must produce short pulses of protons in order to facilitate muon cooling and operation with polarized beams. In order to test methods of producing these bunches they have operated the AGS near transition and studied procedures which involved moving the transition energy {gamma} to the beam energy. They were able to produce stable bunches with RMS widths of {sigma} = 2.2-2.7 ns for longitudinal bunch areas of {minus}1.5 V-s, in addition to making measurements of the lowest two orders of the momentum compaction factor.

This note describes how a future Fermilab proton driver [1] based on TESLA superconducting linac modules can perform as both the source of protons to produce the muons and as the accelerator of the muons to be used for a neutrino factory or muon collider. Recent advances in muon cooling [2] have the promise of muon emittances that are compatible with the 1300 MHz accelerating structures that are the basis for the ILC design. In the design described here, H{sup -} ions are accelerated to 8 GeV in the superconducting Linac, then stripped, stored and bunched in a ring while the Linac cavities are rephased for muon acceleration. Then the protons are extracted from the ring to produce pions and muons which are cooled in a few hundred meters, accelerated to a few GeV and injected into the Linac at the {beta} = 1 point for acceleration to add 7 GeV. By recirculating the muons in the constant frequency section of such a proton driver Linac, even higher energies can be achieved quickly so that losses from muon decay are minimized. By adding additional refrigeration and RF power, the repetition rate of the Linac can be increased to make largemore » increases in the average flux of a neutrino factory and the average luminosity of a muon collider. driver linac to be able to accelerate muons, including the costs to produce and cool the muons, will be considerably less than the costs estimated in previous neutrino factory design studies. We also believe that such an approach can produce a much higher neutrino flux and, because of the necessity for effective muon cooling, also be on the path to an energy frontier muon collider.« less

Muon Colliders have unique technical and physics advantages and disadvantages when compared with both hadron and electron machines. They should thus be regarded as complementary. Parameters are given of 4 TeV and 0.5 TeV high luminosity \mu^+ \mu^- colliders, and of a 0.5 TeV lower luminosity demonstration machine. We discuss the various systems in such muon colliders, starting from the proton accelerator needed to generate the muons and proceeding through muon cooling, acceleration and storage in a collider ring. Detector background, polarization, and nonstandard operating conditions are discussed., Comment: 42 pages TeX file (aipproc style), 25 postscript figures. Submitted to the Proceedings of the Symposium on Physics Potential and Development of $\mu^+ \mu^-$ Colliders, San Francisco, CA Dec 13-15, 1995. Edited by D. Cline and D. Sanders

The status of the research on muon colliders is discussed and plans are outlined for future theoretical and experimental studies. Besides continued work on the parameters of a 3-4 and 0.5 TeV center-of-mass (CoM) energy collider, many studies are now concentrating on a machine near 0.1 TeV (CoM) that could be a factory for the s-channel production of Higgs particles. We discuss the research on the various components in such muon colliders, starting from the proton accelerator needed to generate pions from a heavy-Z target and proceeding through the phase rotation and decay ($��\to ����_��$) channel, muon cooling, acceleration, storage in a collider ring and the collider detector. We also present theoretical and experimental R & D plans for the next several years that should lead to a better understanding of the design and feasibility issues for all of the components. This report is an update of the progress on the R & D since the Feasibility Study of Muon Colliders presented at the Snowmass'96 Workshop [R. B. Palmer, A. Sessler and A. Tollestrup, Proceedings of the 1996 DPF/DPB Summer Study on High-Energy Physics (Stanford Linear Accelerator Center, Menlo Park, CA, 1997)]., 95 pages, 75 figures. Submitted to Physical Review Special Topics, Accelerators and Beams

New ideas are being developed to cool muon beams for colliders, neutrino factories, and muon experiments. Analytical and simulation studies have confirmed that a six-dimensional (6D) cooling channel based on helical magnets surrounding RF cavities filled with dense hydrogen gas can be used to achieve very small emittances. This helical cooling channel (HCC) has solenoidal, helical dipole, and helical quadrupole magnetic fields to generate emittance exchange and achieve 6D emittance reduction of over 3 orders of magnitude in a 100 m segment. Three such sequential HCC segments, where the RF frequencies are increased and transverse dimensions reduced as the beams become cooler, implies a 6D emittance reduction of almost six orders of magnitude. Two new post-cooling ideas then can be employed to reduce transverse emittances to one or two mm-mr, which allows high luminosity with fewer muons than previously imagined. We describe the new post-cooling ideas as well as a new precooling idea based on a HCC with z -dependent fields that can be used as an exceptional 6D cooling demonstration experiment.