31. |
Invariant manifolds and stability: Some results for 1‐D maps |
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AIP Conference Proceedings,
Volume 292,
Issue 1,
1992,
Page 385-396
M. Giovannozzi,
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摘要:
To give an analytic estimate of the stability domain of nonlinear systems, like large accelerators, has been a subjected of intense theoretical studies for many years. Up to now, even for the simple case of the one‐dimensional He´non map, one could not determine the border of the stability domain using analytic tools. On the other hand this estimate can easily be found by tracking through the map. A promising new attempt is presented here, to estimate the dynamic aperture for the He´non map via following the invariant manifolds of its hyperbolic fixed point. The same technique is then applied to a different map and an attempt to generalize the method presented in this paper to generic 1‐D polynomial maps is briefly discussed.
ISSN:0094-243X
DOI:10.1063/1.45125
出版商:AIP
年代:1992
数据来源: AIP
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32. |
Aperture determination of RHIC92 from randomly generated initial coordinates |
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AIP Conference Proceedings,
Volume 292,
Issue 1,
1992,
Page 397-408
G. F. Dell,
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PDF (344KB)
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摘要:
Results obtained by tracking 100 particles for 1000 turns when initial coordinates are selected randomly, with the requirement that the total emittance be constant, are compared to results from 1000‐turn and 106‐turn runs when initial coordinates satisfy &egr;x(i)=&egr;h(i) andXi’=Yi’=0. For studies of ten distributions of magnetic field errors, the 100‐particle results give apertures equivalent to those from 106‐turn runs, have an aperture distribution of considerably less width, and yet require only one tenth the computer time.
ISSN:0094-243X
DOI:10.1063/1.45126
出版商:AIP
年代:1992
数据来源: AIP
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33. |
The effect of synchrobetatron coupling on the dynamic aperture |
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AIP Conference Proceedings,
Volume 292,
Issue 1,
1992,
Page 409-413
G. Parzen,
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摘要:
The effect of synchrobetatron coupling on the dynamic aperture was studied by comparing the dynamic aperture for a particle with a large fixed &Dgr;p/p, no synchrotron oscillations present, with the dynamic aperture for a particle, with a synchrotron oscillation amplitude of the same &Dgr;p/p. The particle with the synchrotron present was found to have a smaller dynamic aperture than the particle with the fixed &Dgr;p/p. It is suggested that this reduction in dynamic aperture may be due to non‐linear coupling between the longitudinal and transverse motions. (AIP)
ISSN:0094-243X
DOI:10.1063/1.45128
出版商:AIP
年代:1992
数据来源: AIP
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34. |
The modern approach to single‐particle dynamics for circular rings |
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AIP Conference Proceedings,
Volume 292,
Issue 1,
1992,
Page 417-487
Etienne Forest,
Leo Michelotti,
Alex J. Dragt,
J. Scott Berg,
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摘要:
In this paper, we describe the hybrid local/global approach applied to single‐particle ring dynamics. We contrast this modern approach to the traditional methods used in accelerator theory. We describe how this approach unites numerical and analytical aspects. Due to lack of space, we emphasize only the analytical (global) aspect of the modern approach. Work supported in part by DOE.
ISSN:0094-243X
DOI:10.1063/1.45095
出版商:AIP
年代:1992
数据来源: AIP
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35. |
Towards C++ object libraries for accelerator physics |
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AIP Conference Proceedings,
Volume 292,
Issue 1,
1992,
Page 488-491
Leo Michelotti,
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摘要:
This paper concerns creation of libraries of reusable objects in the language C++for doing accelerator design and analysis. The C++language possesses features which lend themselves to writing portable, scientific solftware. The two libraries of C++classes (objects) which have been under development are (1) MXYZPTLK, which implements automatic differentiation and (2) BEAMLINE, which provides objects for modeling beam line and accelerator components. A description of the principle classes in these two libraries is presented. (AIP)
ISSN:0094-243X
DOI:10.1063/1.45096
出版商:AIP
年代:1992
数据来源: AIP
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