A summary of different techniques and systems to scrape beam halo in a 50 x 50 GeV??− collider is presented. Such systems are installed in a special utility section with optics specifically designed to meet both the requirements of the scraping system and of injection. Results froma realistic Monte Carlo simulation (STRUCT-MARS) show that a system consisting of steel absorbers several meters in length suppresses halo-induced backgrounds in the collider detector by more than three orders of magnitude. The heat load in superconducting magnets near the scraper system can be reduced to tolerable levels by appropriate collimator design and location. This reduction applies to both injection and collider mode of operation. Also discussed is extraction of halo particles using electrostatic deflectors and bent crys-tals, although neither appears to be effective for a muon collider at this energy.

A recent progress report on the lattice design of the 50-50 GeV muon collider is presented. The ring circumference needs to be as small as possible due to the short lifetime of the 50 GeV muons. The background at the detector is affected by the continuous decay of muons into electrons which requires a dipole between the high focusing quadrupoles and the detector. To obtain a luminosity on the order of 1 x 1033 cm−2 s−1 it is required to have beam intensities on the order of 1 x 1012 particles per bunch. The rms momentum spread of the beam is equal to 0.12% and the beta functions at the interaction point are equal to 4 cm. The maxima of the betatron functions at these quadrupoles are 1,300 m, resulting in large chromaticities which must be corrected by local chromatic correction. Pairs of horizontal and vertical chromatic sextupoles are located at locations where the corresponding betatron functions are 100 m and the values of the horizontal dispersion functions are 3 and 2 m, respectively. They are carefully placed so that most of their nonlinear effects are canceled. The dynamic aperture is larger than 7 times the mean size of the beam for the momentum offsets larger than -6 and +10 sigmas.

Single bunch instabilities for the 50-50 GeV muon collider are discussed. An impedance budget for the collider is estimated. An {vert_bar}[eta]{vert_bar} = 1 x 10−6 is desired to avoid excessive rf systems. Potential-well distortion can be compensated by rf cavities. Longitudinal microwave growth can be reduced by smoothing the bunch distribution before injection. Transverse microwave instability can be damped by chromaticities and octupoles. Beam breakup can be cured by BNS damping in principle, but is nontrivial in practice. More detailed discussions are given in Ref. 1.

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.