Longitudinal beam dynamics II. Lecture 1: single and double rf systems

In the first part of this lecture, the main characteristics of synchrotron motion, namely, synchronous particle and phase, bucket area and emittance, are introduced. The equations of longitudinal particle motion in a single rf system of a proton synchrotron are rederived and the phase equation is analyzed for small and large amplitude particles. The particle motion below and above transition energy is also considered. The main applications and operation modes of a double rf system are discussed in the second part of the lecture. The intensity effects and beam instabilities are the subject of the following lecture.