[en] Beam stability issues of the VLHC rings in Phase 1 and Phase 2 are reviewed. For accelerator rings of circumference 232 km and beam pipe radius of the order of 1 cm, the impedance of the vacuum chamber is dominated by the resistive wall. The most dangerous instabilities are the single-bunch transverse mode coupling instability and the transverse coupled bunch instability driven by the resistive wall at sub-revolution frequency. Scaling is studied concerning the thresholds of these instabilities and the dominance of the resistive wall impedance as the size of the accelerator increases

[en] During polarized beam experiments, the 50 GeV proton synchrotron, proposed by the Institute of Nuclear Study of Japan, requires zero-dispersion straight sections. This will be implemented by turning on a special excitation of the quadrupoles resulting in a dispersion wave through the arcs of the machine. Aside from the inconvenience of the power supply, this special excitation also brings about unwanted high betatron functions and high dispersion functions, which will eventually limit the performance of the accelerator at high intensities. In this paper, dispersion suppressors are introduced. A new preliminary lattice that contains two straight sections with nonzero dispersion and two straight sections with zero dispersion is presented. The whole ring remains having a reasonable imaginary γ_t. The horizontal and vertical betatron functions have been kept to below 32.4 m and dispersion function between -0.52 and 1.86 m. The number of 6.2 m dipoles is reduced from 96 to 92, and the dipole field at 50 GeV will become slightly above 18 T. Some analysis of the new lattice is discussed. 10 refs., 9 figs., 1 tab

[en] Some issues are presented on the rf system in the future Fermilab prebooster, which accelerates 4 bunches each containing 0.25 x 10₁₄ protons from 1 to 3 GeV kinetic energy. The problem of beam loading is discussed. The proposal of having a non-tunable fixed-frequency rf system is investigated. Robinson's criteria for phase stability are checked and possible Robinson instability growth is computed

[en] Space-charge effects on beam stabilities are studied for the proposed two-ring high-intensity Fermilab booster destined for the muon collider. This includes microwave instabilities and rf potential-well distortions. For the first ring, ferrite insertion is suggested to cancel the space-charge distortion of the rf wave form. To control the inductance of the ferrite during ramping and to minimize resistive loss, perpendicular biasing to saturation is proposed

[en] The lattice design of the 50-50 Gev muon collider is presented. Due to the short lifetime of the 50 GeV muons, the ring needs to be as small as possible. The 4 cm low betas in both planes lead to high betatron functions at the focusing quadrupoles and hence large chromaticities, which must be corrected locally. In order to maintain a low rf voltage of around 10 MV, the momentum-compaction factor must be kept to less than 10^-2 , and therefore the flexible momentum-compaction modules are used in the arcs. The dynamical aperture is larger than 6 to 7 rms beam size for ±5 rms momentum offset. Comments are given and modifications are suggested

[en] The miscellaneous components of an accelerator may contribute a substantial or even dominant part of the interaction between beam and surroundings. We have estimated the beam impedances of a few of these components. When needed, we have added our own conceptions to the descriptions available at the Workshop on the RHIC Performance in order to make definite the calculations of impedance. These assumed parameters, while not unique, hopefully illustrate feasible and typical designs. 8 refs., 4 figs., 2 tabs

[en] During the course of the last decade, traveling wave accelerating structures for a future Linear Collider have been the object of intense R and D efforts. An important problem is the efficient computation of the long range wakefield with the ability to include small alignment and tuning errors. To that end, SLAC has developed an RF circuit model with a demonstrated ability to reproduce experimentally measured wakefields. The wakefield computation involves the repeated solution of a deterministic system of equations over a range of frequencies. By taking maximum advantage of the sparsity of the equations, they have achieved significant performance improvements. These improvements make it practical to consider simulations involving an entire linac (approximately 10³ structures). One might also contemplate assessing, in real time, the impact of fabrication errors on the wakefield as an integral part of quality control

[en] The longitudinal and transverse impedances of an off-centered beam in a rectangular beampipe are solved exactly using conformal mapping. The results are represented in each case by the product of the corresponding impedance due to a circular beampipe with the beam at the center and a form factor that takes into account that the beampipe is rectangular in shape and that the beam is off center. When the width to height ratio of the beampipe is large, the form factor is found to stay flat for a wide range of beam displacement. Both effects due to the resistivity of the beampipe wall and to space charge are considered. (author)

[en] Two barrier RF systems were fabricated, tested and installed in the Fermilab Main Injector. Each can provide 8 kV rectangular pulses (the RF barriers) at 90 kHz. When a stationary barrier is combined with a moving barrier, injected beams from the Booster can be continuously deflected, folded and stacked in the Main Injector, which leads to doubling of the beam intensity. This paper gives a report on the beam experiment using this novel technology

[en] In order to maintain a reasonable r.f. system, it may be necessary for a collider with ultra-short bunches to operate with a small slippage factor, for example, η<1 x 10^-6 for all the particles in the bunches. The buckets dominated by the zeroth order, first order, or second order of η are examined, and the required r.f. voltages are computed. The problem of microwave instability is addressed. The reliability of computing higher-order momentum-compaction factor using lattice codes is examined. (orig.)