摘要:

The results of measurements of seismic vibrations in the Exploratory Shaft (at the tunnel depth) and in the ASST building (on the surface) of the Superconducting Super Collider (SSC) site are presented. Spectral and correlation analysis of the data obtained in the frequency band 0.05–1500 Hz is performed. It is found that amplitudes of ambient ground motion are lower than collider requirements, but cultural vibrations are unacceptably large and will cause fast growth of transverse emittance of the SSC beams. The issues of uncorrelated slow ground motion governed by the ‘‘ATL law’’ are also discussed on the example of the SSC collider. © 1995American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.47321

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

This paper introduces the method of averaging and applies it to several beam dynamics problems. Averaging is an important tool in the rigorous study of ODEs with a small parameter, and it leads to a systematic perturbation expansion complete with error bounds. First‐ and second‐order averaging theorems are presented and applied; in addition, proofs are included for the interested reader. Resonance at first and second order is treated. © 1995American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.47308

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

We use the method of normal forms (NF) to explore perturbative solutions to a broad class of nonlinear differential equations and to symplectic planar maps. The method employs introduction of a transformation from the original variables to a new set that yields equations that are more amenable to analysis. The transformation is not unique and ‘‘freedom’’ is thereby introduced, which is exploited to tailor the structure of the expansion to match various constraints that one might impose. Kahn and Zarmi, and Kahn, Murray, and Zarmi have introduced and used the method of minimal normal forms (MNF) and variations thereof that exploit the lack of uniqueness and consequent freedom of choice in the normal form expansion to realize ‘‘compact’’ expansions that have a simple structure, are easy to use, and have significant computational advantages over other schemes. © 1995American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.47309

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Tracking a full Superconducting Super Collider (SSC) lattice to determine the long‐term dynamic aperture is very computer‐intensive. The author argues that low‐order maps (≤9) may have enough information to determine long‐term apertures. However, evaluating such maps is not trivial and can consume more time than tracking the original lattice. The author describes a way to construct an ‘‘equivalent’’ one‐turn map consisting of a small number of kicks, which to any specific order has the same generator as the original map, and minimizes spurious high‐order terms. For a ninth‐order map, the number of kicks is 36, and can be evaluated 50 times faster than SSC element‐by‐element tracking. Perhaps more importantly, the conjecture that low‐order terms of the map determine long‐term behavior can be tested. An affirmative result would allow simulation of the SSC in the Tevatron by adding a suitable set of nonlinear lenses. © 1995American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.47310

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Given a symplectic map for an accelerator lattice or sequence of elements, we show how to generate a nonlinearly stable symplectic map that has the same linear terms and the same lowest‐order nonlinear terms as the given map. Techniques are presented for producing stable maps both for the case in which the map is given by a generating function and in the case in which the map is given by a Lie map. © 1995American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.47322

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

It was found that any homogeneous polynomial can be written as a sum of integrable polynomials of the same degree, with which each associated Lie transformation can be evaluated exactly. An integrable polynomial factorization has thus been developed to convert an analytic symplectic map into a product of exactly evaluable Lie transformations associated with integrable polynomials. © 1995American Institute of Physics

ISSN:0094-243X    

DOI:10.1063/1.47319

出版商:AIP    

年代:1995

数据来源: AIP