Search Results (5 total)

A second order analytical and an arbitrary order numerical procedure is developed for the computation of transfer maps of energy degraders. The incorporation of the wedges into the optics of fragment separators for next-generation exotic beam facilities, their optical effects, and the optimization of their performance is studied in detail. It is shown how to place and shape the degraders in the system such that aberrations are minimized and resolving powers are maximized.

Next-generation high-intensity large acceptance fragment separators require a careful design due to the large high order aberrations induced by the large aperture superconducting magnets needed to collect rare isotopes obtained from a high energy primary heavy-ion beam hitting a target. In this paper we propose a fragment separator layout based on various symmetries that satisfies the baseline requirements. Analytical calculations based on symmetry theories simplify the design to numerical optimization of a basic cell with only a few magnetic elements. The insight provided by these calculations resulted in the specification of a simple layout with large acceptance, transmission, and resolution. The design method may be easily adapted to project-specific needs. The important effects of energy degraders necessary for full fragment separator design will be addressed in a future publication.

The Tevatron in Run II is operating with three trains of 12 bunches each. Long-range beam-beam interactions have been significant sources of beam loss and lifetime limitations of antiprotons. The dynamics due to the long-range beam-beam interactions depends on several beam parameters such as tunes, coupling, chromaticities, beam separations, intensities, and emittances. We have developed analytical tools to calculate, for example, amplitude dependent tune shifts and chromaticities, beam-beam induced coupling, and resonance driving terms. We report on these calculations and estimates of dynamic aperture and diffusion coefficients with long-term tracking. These theoretical results are compared with observations and used to predict performance at design values of beam parameters.

Long term simulations of Hamiltonian dynamical systems benefit from enforcing the symplectic symmetry. One of the several available methods to perform this symplectification is provided by the recently developed theory of extended generating functions. The theory offers an infinite supply of generator types that can be used for symplectification. Using Hofer's metric, a condition for optimal symplectification is given. In the weakly nonlinear case, the condition provides a generator type that, based on the limited information available on the system, in general gives optimal results.

Recently there has been renewed interest in the influence of fringe fields on particle dynamics, due to studies that revealed their importance in some cases, as, for example, the proposed Neutrino Factory and muon colliders. In this paper, we present a systematic study of generic fringe field effects. Using as an example a lattice of the proposed Neutrino Factory, we show that fringe fields influence the dynamics of particles at all orders, starting with the linear motion. It is found that the widely used sharp cutoff approximation leads to divergences regardless of the specific fall-off shape of the fields. The results suggest that a careful consideration of fringe field effects in the design stage of small machines for large emittances is always recommended.