Symplectic Tracking through Circular Accelerators with High Order Maps

It is discussed how high order transfer map8 generated using dift'erential 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 ..desired without prohibitive extra eft'ort. For example, the full Hamiltonian can be used. and the elementa can be treated with finite length and with their fringe field.. Furthermore, track ins through maps ia usually significantly faster than element by elemen~ tracking. Dift'eren~ schemes for fas~ symplec~ic tracking suited for dift'eren~ degree8 of nonlinearity of the original map are presented. The fact tha~ different approaches sometimes produce differeD~ long term reaulta showl that symplectification is no~ the cure of all evil and should be used cautiously. I~ al8O sugesta to use a symplectification scheme which chanses the original map by the le..~ amouD~ p~ible.