High-Order Computation and Normal Form Analysis of Repetitive Systems
AbstractBesides the mere tracking of individual particles through an accelerator
lattice, it is often helpful to study the corresponding phase space map
relating initial and final coordinates. Recent years have seen an advance in
the ability to compute high-order maps for rather complex systems including
accelerator lattices. Besides providing insight, the maps allow treatment of
the lattice without approximations, allowing thick elements, fringe-field
effects and even radiation, which is often prohibitive in the case of pure
tracking. At the core of the computation of maps for realistic systems are
the differential algebraic (DA) techniques.
Besides the computation of maps, the DA methods have recently proven useful
for the computation of many properties of the maps in a rather direct way.
In particular, these properties include parameter tune shifts, amplitude
tune shifts, and pseudo invariants. The methods presented here do not rely
on Lie algebraic methods and are noticeably more direct and in many cases
more efficient. Not relying on canonical techniques, they are also
applicable to non-symplectic systems and allow a study of damping phenomena
in repetitive systems.
M. Berz, Chapter in: "Physics of Particle Accelerators", Melvin Month (Ed.)
(1992) 456-489, AIP Publishing
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