25 September 1997 Arbitrary order maps, remainder terms, and long-term stability in particle accelerators
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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.
© (1997) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Martin Berz, Martin Berz, Kyoko Makino, Kyoko Makino, "Arbitrary order maps, remainder terms, and long-term stability in particle accelerators", Proc. SPIE 3155, Charged Particle Optics III, (25 September 1997); doi: 10.1117/12.279396; https://doi.org/10.1117/12.279396
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