Arbitrary order maps, remainder terms, and long-term stability in particle accelerators

Martin Berz; Kyoko Makino

doi:10.1117/12.279396

25 September 1997 Arbitrary order maps, remainder terms, and long-term stability in particle accelerators

Martin Berz, Kyoko Makino

Proceedings Volume 3155, Charged Particle Optics III; (1997) https://doi.org/10.1117/12.279396
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

It is reviewed how transfer maps of arbitrary order can be calculated in a convenient way using differential algebraic (DA) techniques. Such high-order maps are of use for high- precision optical systems, as well as for the case of repetitive particle accelerators, where nonlinear effects often have a tendency to build up over many turns. It is shown how the methods can be extended to also allow a rigorous treatment of the Lagrange remainder term of the Taylor expansion. The methods can be applied for the estimation of the effects going beyond the aberration order; it is also for the study of the repetitive motion where, leaning on ideas of Lyapunov, Nekhoroshev and others, it for the first time allows a rigorous determination of guaranteed particle survival times.

Citation Download Citation

Martin Berz and Kyoko Makino "Arbitrary order maps, remainder terms, and long-term stability in particle accelerators", Proc. SPIE 3155, Charged Particle Optics III, (25 September 1997); https://doi.org/10.1117/12.279396

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