Symplectic Tracking in Circular Accelerators with High Order Maps
AbstractIt 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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