Reprint Server

High-Order Computation and Normal Form Analysis of Repetitive Systems


Besides 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


Click on the icon to download the corresponding file.

Download Postscript version (429389 Bytes).
Download Adobe PDF version (289707 Bytes).

Go Back to the reprint server.
Go Back to the home page.

This page is maintained by Kyoko Makino. Please contact her if there are any problems with it.