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One dimensional motion in a thick sextupole-a comparison of tracking methods with the exact solution

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2 Author(s)
Hagel, J. ; CERN, Geneva, Switzerland ; Zotter, B.

It is shown that the comparison of Taylor-series mappings with the exact solution of the one-dimensional equations of motion for a charged particle in a sextupole permits the derivation of explicit expressions for the convergence. The existence of a limiting step size is found. It depends in general on the initial conditions (x0, u0) but not on the order of the mapping. These results are similar for all multipolar elements, and they restrict tracking of accelerator lattices by Taylor mappings to a maximum step size. Hence, concatenation of too many nonlinear elements will become divergent even for arbitrary high orders in the expansion of a map. This restriction of concatenation applies also to kick codes, although the zero length of a single element guarantees that the mapping does not diverge element by element. In practice, the convergence of a concatenated map can be tested by comparing results for different step sizes

Published in:

Particle Accelerator Conference, 1989. Accelerator Science and Technology., Proceedings of the 1989 IEEE

Date of Conference:

20-23 Mar 1989

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