Muon collider is a promising candidate for the next energy frontier machine. However, in order to obtain peak luminosity in the 1035/cm2/s range the collider lattice design must satisfy a number of stringent requirements, such as low beta at IP ([beta]*

The last component of a muon collider facility, as presently envisioned, is a colliding-beam storage ring. Design studies on various problems for this ring have been in progress over the past year. In this paper we discuss the current status of the design. The projected muon currents require very low beta values at the IP, [beta]*= 3 mm, in order to achieve the design luminosity of L= 10[sup 35] cm[sup -2] s[sup -1]. The beta values in the final-focus quadrupoles are roughly 400 km. To cancel the corresponding chromaticities, sextupole schemes for local correction have been included in the optics of the experimental insertion. The hour-glass effect constraints the bunch length to be comparable too. To obtain such short bunches with reasonable rf voltage requires a very small value of the momentum compaction a, which can be obtained by using flexible momentum compaction (FMC) modules in the arcs. A preliminary design of a complete collider ring has now been made; it uses an experimental insertion and arc modules as well as a utility insertion. The layout of this ring is shown schematically, and its parameters are summarized. Though some engineering features are unrealistic, and the beam performance needs some improvement, we believe that this study can serve as the basis for a workable collider design. The remaining sections of the paper will describe the lattice, show beam behaviour, and discuss future design studies.

The muon collider would ex-tend limitations of the e[sup+] e- colliders and provide new physics potentials with a possible discovery of the heavy Higgs bosons. At the maximum energy of 2 TeV the projected luminosity is of the order of 10[sup 35] cm[sup[minus]2]s[sup[minus]1]. The colliding[mu][sup+][mu][sup[minus]] bunches have to be focused to a very small transverse size of few tenths of[mu]m which is accomplished by the betatron functions at the crossing point of[beta]*= 3mm. This requires the longitudinal space of the same length 3 mm. These very short bunches at 2 TeV could circulate only in a quasi-isochronous storage ring where the momentum compaction is very dose to zero. We report on a design of the muon collider isochronous lattice. The momentum compaction is brought to zero by having the average value of the dispersion function through dipoles equal to zero. This has been accomplished by a combination of the FODO cells together with a low beta insertion. The dispersion function oscillates between negative and positive values.

Two modes are being considered for a 50 on 50-GeV muon collider: one being a high-luminosity ring with broad momentum acceptance (dp/p of (approximately) 0.12%, rms) and the other lower luminosity with narrow momentum acceptance (dp/p of (approximately) 0.003%, rms). To reach the design luminosities, the value of beta at collision in the two rings must be 4 cm and 14 cm, respectively. In addition, the bunch length must be held comparable to the value of the collision beta to avoid luminosity dilution due to the hour-glass effect. To assist the rf system in preventing the bunch from spreading in time, the constraint of isochronicity is also imposed on the lattice. Finally, the circumference must be kept as small as possible to minimize luminosity degradation due to muon decay. Two lattice designs will be presented which meet all of these conditions. Furthermore, the lattice designs have been successfully merged into one physical ring with mutual components; the only difference being a short chicane required to match dispersion and floor coordinates from one lattice into the other.

The future??− Muon Collider should have a luminosity of the order of 1035 cm−2 s−1, and the energy of 2 x 2 TeV. The authors present here a demonstration machine at a lower energy to test the feasibility of all components involved, which could be placed inside the existing Relativistic Heavy Ion Collider (RHIC) tunnel. The maximum energy of the muons in the RHIC tunnel depends on the maximum attainable field in the dipoles. The maximum energy in the existing RHIC rings for protons is 250 GeV, where the strength of the magnetic field in the dipoles is 3.5 T.A design of the storage ring lattice for a 50 GeV muon demonstration machine is also presented.

A new lattice for 3 TeV c.o.m. energy with?* = 5mm was developed which follows the basic concept of the earlier 1.5 TeV design but uses quad triplets for the final focus in order to keep the maximum magnet strength and aperture close to those in 1.5 TeV case. Another difference is employment of combined-function magnets with the goal to lower heat deposition in magnet cold mass and to eliminate bending field free regions which produce 'hot spots' of neutrino radiation that can be an issue at higher energy. The proposed lattice is shown to satisfy the requirements on luminosity, dynamic aperture and momentum acceptance.

The ninth Advanced Study Institute (AS!) on Techniques and Concepts of High Energy Physics was almost canceled before ifbegan! A certain visitor to the area (Hurricane Bertha) arrived unexpectedly early in 1996. It was the first hur ricane in memory to menace the Caribbean in early July! Fortunately, it passed St. Croix several days before our meeting, and left very little damage. (The Altar ellis survived the eye of the storm in the in the British West Islands!) The meeting was held once again at the hotel on the Cay, on that spec of land in the harbor ofChrirtiansted, St. Croix, U. S. Virgin Islands. After the first two days of, at times, outrageous downpour, the 71 participants from 26 coun tries began to relax and enjoy the lectures and the lovely surroundings of the In stitute. The primary support for the meeting was provided by the ~cientific Affairs Division of the North Atlantic Treaty Organization (NATO). The ASI was cosponsored by the U. S. department of Energy, by the Fermi National Accelera tor Laboratory (Fermi-lab), by the U. S. National Science Foundation, and by the University of Rochester. In addition, the International Science Foundation con tributed to the support of a participant from Russia. As in the case of the previous ASIs, the scientific program was designed for advanced graduate students and recent Ph. D. recipients in experimental parti cle physics.