This report discusses the focusing in the FODO cells along the linear accelerators in a recirculating muon accelerator that is part of the ongoing study of a neutrino factory in Europe. The quadrupoles for the focusing in the FODO cells alternate with RF cavities that accelerate the muon beam. The report derives the parameters of the FODO cells that accommodate the muon beam with the assumed emittance. Two different styles of focus- ing are considered, constant betatron wavelength and constant quadrupole gradient.

Focusing by symmetrical triplets is studied for the linear accelerator lattices in recirculating muon accelerators with several passes where the ratio of final to initial muon energy is about four. Triplet and FODO lattices are compared. At similar acceptance, triplet lattices have straight sections for the RF cavities that are about twice as long as in FODO lattices. For the same energy gain, the total lengths of the linear accelerators with triplet lattices are about the same as of those with FODO lattices.

This guide describes the installation and use of Mathematica notebooks and packages related to neutrino factory studies of recirculating linear accelerators and muon decay rings. The material is available on WWW and on the NICE PC network at CERN.

The design of a muon storage ring for a neutrino factory is described. It operates at 50 GeV and has a bowtie shape. It sends neutrino beams from two long straight sections with a small muon beam divergence to two distant detectors at 1000 and 3000 km distance. It is designed for a normalised emittance of about 1.67 mm and an rms momentum spread of 0.5%. The procedure for arriving at the parameters of the optical modules and of the whole storage ring and their values are given. The verification of the optical design includes tracking many thousands of muons for their lifetime, and demonstrates that the dynamic aperture is larger than the physical one. The parameters of the RF system and of the fast injection kickers are also considered.

Two Fortran programs are described that process MAD tracking output for 104 or more particles, and produce histograms. The loshst program produces histograms of the par- ticle losses by turn and by position along the orbit. The trkhst program computes means and standard deviations of the particle positions in 6D phase space and the emittances in all three directions, and produces histograms of the particle distributions at the end of the MAD tracking run.

The Large Hadron Collider Project LHC was approved by the CERN Council in December 1994. Commissioning with beam will start in the second half of 2005. The paper discusses the most important parameters, the general layout of the LHC octants, and the status of the experiments ALICE, ATLAS, CMS and LHC-B. Also described are some aspects of the beam-beam interactions, the transverse coupled-bunch instability, as well as the technical developments of the cryogenics, the tests of half an are cell, and the new civil engineering needed.

Plans for future hadron colliders are presented, and accelerator physics and engineering aspects common to these machines are discussed. The Tevatron is presented first, starting with a summary of the achievements in Run IB which finished in 1995, followed by performance predictions for Run II which will start in 1999, and the TeV33 project, aiming for a peak luminosity L approximate to I (nbs)(-1). The next machine is the Large Hadron Collider LHC at CERN, planned to come into operation in 2005. The last set of machines are Very Large Hadron Colliders which might be constructed after the LHC. Three variants are presented: Two machines with a beam energy of 50 TeV, and dipole fields of 1.8 and 12.6 T in the arcs, and a machine with 100 TeV and 12 T. The discussion of accelerator physics aspects includes the beam-beam effect, bunch spacing and parasitic collisions, and the crossing angle. The discussion of the engineering aspects covers synchrotron radiation and stored energy in the beams, the power in the debris of the particle collisions, ground motion, and concepts for reducing the cost per TeV of future hadron colliders.

The effect of plane ground waves on the closed orbit in circular storage rings is studied by computer simulation. Selected elements are displaced vertically. The displacements are computed for plane ground motion waves with given wavelength and phase. The closed orbit is computed with MAD. Results for the amplification factors are presented and discussed for simple lattices consisting only of FODO cells, for LEP and LHC. The expectation values of the orbit offsets for realistic spectra of ground motion are calculated. For all machines studied, they are orders of magnitude smaller than the beam radii. Differences in the response to ground motion waves at harmonic numbers much smaller than the tunes between simple FODO lattices, machines with symmetrical low- insertions like LEP, and anti-symmetrical low- insertions like LHC are also discussed.

We study the transverse motion of the barycentres of bunches in two beams that circulate in opposite direction in a storage ring, and are coupled by the beam-beam effect. The motion is described by a linear system of oscillators, and represented by a matrix. We distinguish between perfect machines in which the bunch parameters and the are and interaction point parameters are all equal, and machines with errors in which at least one of these conditions is not satisfied. We determine the regions in tune space where the motion is unstable, analytically for perfect machines, and numerically for machines with errors. We identify these regions as resonances related to the tunes of one of the two beams or to their sum. We establish which resonances are excited under given conditions. We find that more resonances occur in machines with errors than in perfect machines. By multi-particle tracking, we study the instability at finite amplitudes.

The Large Hadron Collider Project LHC was approved by the CERN Council in December 1994. Commissioning with beam will start in the second half of 2005. The paper discusses the most important parameters, the general layout of the LHC oc- tants, the status of the experiments ALICE, ATLAS, CMS and LHC-B, proton injection using the PS Booster, and the proton synchrotrons PS and SPS. Also described are the technical de- velopments of the arc dipoles, the radio-frequency system, the vacuum chamber, cryogenics and the tests of half an arc cell.