[en] The design process of modern high-energy synchrotrons involves the development of the accelerator lattice in pieces, typically an arc made up of repetitive cells interrupted by occasional matched insertions for injection, extraction, acceleration and various other systems required by the facility. The focusing elements of an insertion must be such that the periodic amplitude functions at the ends of the insertion match those of the cells on either side of the insertion. How well this match has to be and its sensitivity to the global betatron tunes of the accelerator as well as the particle momentum are the underlying themes of this report. Many of the relationships also are of use to the designers of beamlines which are used to transport and inject beams into a synchrotron. Most of the content of this paper is not new to the accelerator physics community, but we thought it would be useful to place this important, basic information all in one place. Besides the classic work of Courant and Snyder, our sources include other papers, internal reports, and numerous discussions with our colleagues

[en] The Lattice/Beam Dynamics Working Group was charged with reviewing and identifying technical issues and their potential solutions for (a) a 2 x 2 TeV high luminosity p-pbar collider, and (b) a 30 x 30 TeV high luminosity pp collider. Rather than attempting to solve very specific problems for these devices in the relatively short time scale of a workshop, the group attempted to look at more general questions to try to indicate in which directions future work in these areas should proceed. The emphasis of the group tended toward lattice issues and general accelerator design issues for the above two cases, with more specific questions being addressed as directed by the needs seen by the Workshop Synthesizers

[en] During Tevatron injection, Flying Wires have been used to measure the transverse beam size after each transfer from the Main Injector in order to deduce the transverse emittances of the proton and antiproton beams. This amounts to 36 + 9 = 45 flies of each of 3 wire systems, with an individual wire passing through each beam bunch twice during a single ''fly''. Below they estimate the emittance growth induced by the interaction of the wires with the particles during these measurements. Changes of emittance from Flying Wire measurements conducted during three recent stores are compared with the estimations

[en] Power supply ripple at frequencies of 720 Hz and its harmonies is expected to affect the motion of particles in the collider. These ripple frequencies are nearly resonant with the betatron frequencies. To estimate the tolerable ripple levels, we have tracked particles through the complete nonlinear lattice for 10⁴ turns with ripple fed from 10 different power stations and including up to 7 different ripple frequencies. We presently estimate that relative ripple amplitudes must be below the 10⁸ level for there to be no significant impact on the emittance over the short term

[en] During Tevatron injection, Flying Wires have been used to measure the transverse beam size after each transfer from the Main Injector in order to deduce the transverse emittances of the proton and antiproton beams. This amounts to 36 + 9 = 45 flies of each of 3 wire systems, with an individual wire passing through each beam bunch twice during a single ''fly''. below they estimate the emittance growth induced by the interaction of the wires with the particles during these measurements. Changes of emittance from Flying Wire measurements conducted during three recent stores are compared with the estimations

[en] We present the strategy which has been used recently to optimize the performance of the Fermilab Tevatron proton-antiproton collider. We use a relatively simple heuristic model based on the antiproton production rate, which optimizes the number of antiprotons in a store in order to maximize the integrated luminosity. A store is terminated as soon as the target number of antiprotons is reached and the Tevatron quickly resets to load another store. Since this procedure was implemented, the integrated luminosity has improved by ∼ 35%. Other recent operational improvements include decreasing the shot setup time, and reducing beam-beam effects by making the proton and antiproton brightness more compatible, for example by scraping protons to smaller emittances

[en] Superconducting helical dipole magnets will be used in the Brookhaven Relativistic Heavy Ion Collider (RHIC) to maintain polarization of proton beams and to perform localized spin rotations at the two major experimental detector regions. Requirements for the helical dipole system are discussed, and magnet prototype work is reported

No abstract available

[en] The basic beam dynamics of a next generation 50 x 50 TeV hadron collider based on a high field magnet approach have been outlined over the past several years. Radiation damping not only produces small emittances, but also flat beams, just as in electron machines. Based on open-quotes Snowmass 96close quotes parameters, we investigate the issues associated with flat beams in very high energy hadron colliders

[en] An algorithm has been developed for converting an ''order-by-order symplectic'' Taylor map that is truncated to an arbitrary order (thus not exactly symplectic) into a Courant-Snyder matrix and a symplectic implicit Taylor map for symplectic tracking. This algorithm is implemented using differential algebras, and it is numerically stable and fast. Thus, lifetime charged-particle tracking for large hadron colliders, such as the Superconducting Super Collider, is now made possible