A contemporary guide to beam dynamics

A methodological discussion is given for single particle beam dynamics in circular machines. The discussions are introductory, but (or, even therefore) we avoid to rely on too much simplified concepts. We treat things from a very general and fundamental point of view, because this is the easiest and rightest way to teach how to simulate particle motion and how to analyze its results. We give some principles of particle tracking free from theoretical prejudices. We also introduce some transparent methods to deduce the necessary information from the tracking: many of the traditional beam-dynamics concepts can be abstracted from them as approximate quantities which are valid in certain limiting cases