A book on Lie Methods for Nonlinear Dynamics with Applications to Accelerator Physics is currently in preparation. The most recent version, described below, is presently available in draft form. It is expected that newer versions will become available approximately every few months. Some figures in the book may not be viewable on the screen because they consist of many very small dots; however, they all should print (with the exception of the stereographic view of the dynamic aperture of the Henon map in Section 1.2, which has yet to be made in digital form). To download either the Table of Contents, or the Full Book, click on one of the links below:
Version of 24 January 2009: This version has some 1,458 pages (18 pages more than the 18 December 2008 version). Section 1.4.3 on Duffing's Equation is now complete. Chapter 13 of the earlier version, which was overly long, has now been reorganized into six smaller, more digestible chapters. Together they describe how to compute Realistic Transfer Maps for Straight Beam-Line elements. In particular, the use of both circular and elliptical cylinder surfaces is now fully documented and numerically benchmarked. The Numerical Benchmarks chapter illustrates that accuracies of a few parts in 10,000 or better can be acheived. These chapters and their planned sequel, Chapter 19 on Realistic Transfer Maps for Curved Beam-Line Elements, describe how, for the first time, it is now possible to compute realistic transfer maps based on 3-dimensional field data on a mesh as provided by various electromagnetic solvers. See Figure 14.1.1. In this approach all fringe-field and higher-order multipole effects are automatically included. All known errors have been corrected.