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Symplectic Tracking in Circular Accelerators with High Order Maps


Abstract

It is discussed how high order transfer maps generated using differential algebraic methods can be used for symplectic tracking. Contrary to the usual tracking, the map approach makes it possible to study the specific properties of the system with as few approximations as desired without prohibitive extra effort. For example, the full Hamiltonian can be used, and the elements can be treated with finite length and with their fringe fields. Furthermore, tracking through maps is usually significantly faster than element by element tracking.

Different schemes for fast symplectic tracking suited for different degrees of nonlinearity of the original map are presented. The fact that different approaches sometimes produce different long term results shows that symplectification is not the cure of all evil and should be used cautiously. It also suggests to use a symplectification scheme which changes the original map by the least amount possible.


M. Berz, in: "Nonlinear Problems in Future Particle Accelerators" (1991) 288-296, World Scientific


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