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Arbitrary Order Maps, Remainder Terms, and Long Term Stability in Particle Accelerators

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.

M. Berz, K. Makino, Proc. SPIE Charged Particle Optics III 3155 (1997) 186-192

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