Introduction

This chapter considers the global aspects of the dynamics to be conceptually the more important and warranting the leading role. The description of the local dynamics is geared towards simulation. In contrast with the global theory, it seeks a theory of single particle dynamics where the individual magnets are functionally independent. In the standard treatment of circular ring dynamics, the equations of motion and other details are introduced in parallel with the Courant-Snyder ansatz. In many areas of physics it is often the case that there are two or more equivalent points of view which compete in the mind of the practitioners. One famous case is the Feynman-Schwinger description of quantum-electrodynamics. Traditional treatments try to find descriptions of the entire field which treat together the local and global aspects of the dynamics. This is an honorable goal which is doomed to failure in complex systems. The chapter also presents an overview of the key concepts discussed in this book.