By Harald Klingbeil, Ulrich Laier, and Dieter Lens
Springer
Also available at the CERN bookshop
This book is one of few, if not the only one, dedicated to radiofrequency (RF) accelerator systems and longitudinal dynamics in synchrotrons, providing a self-contained and clear theoretical introduction to the subject. Some of these topics can be found in separate articles of specialised schools, but not in such a comprehensive form in a single source. The content of the book is based on a university course and it is addressed to graduate students who want to study accelerator physics and engineering.
After a short introduction on accelerators, the second chapter provides a concise but complete overview of the mathematical-physics tools that are required in the following chapters, such as Fourier analysis and Laplace transform. Ordinary differential equations and the basics of non-linear dynamics are presented with the notions of phase space, phase flow and velocity vector fields, leading naturally to the continuity equation and to the Liouville theorem. Hamiltonian systems are elegantly introduced, and the mathematical pendulum as well as a LC circuit are used as examples. This second chapter provides the necessary background for any engineer or physicist willing to enter the field of accelerator physics. The basic formulas and concepts of electromagnetism and special relativity are briefly recalled. The text is completed by a useful set of tables and diagrams in the appendix. An extensive set of references is given, although a non-negligible number are in German and might not be of help for the English-speaking reader. This feature is also found in other chapters.
In the third chapter, the longitudinal dynamics in synchrotrons is detailed. The basic equations and formulas describing synchrotron motion, bunch and bucket parameters are derived step-by-step, confirming the educational vocation of the book. The examples of a ramp and of multicavity operation are sketched out. I would have further developed the evolution of the RF parameters in a ramp using one of the GSI accelerators as a more concrete numerical example.
In the fourth chapter, the two most common types of RF cavities (ferrite-loaded and pillbox) are discussed in detail (in particular, the ferrite-loaded ones used in low- and medium-energy accelerators), providing detailed derivations of the various parameters and completing them with two examples referring to two specific applications.
The fifth chapter contains an interesting and thorough discussion on the theoretical description of beam manipulation in synchrotrons, with particular emphasis on the notion of adiabaticity, which is critical for emittance preservation in operation with high-brightness beams. This concept is normally dealt with in a qualitative way, while in this book a more solid background, derived from classical Hamiltonian mechanics, is provided. In the second part of the chapter, after an introduction to the description of a bunch by means of moments, including the concept of RMS emittance, a description of longitudinal bunch oscillations and their spectral representation is given, providing the basis for the study of longitudinal beam stability. This is not addressed in the book, and the notion of impedance is briefly introduced in the case of space charge, while some references covering these subjects are provided.
The last two chapters are devoted to the engineering aspects of RF accelerator systems: power amplifiers and closed-loop controls. The chapter on power amplifiers is mainly focused on the solutions of interest for low- and medium-energy synchrotrons, whereas high-frequency narrowband power amplifiers like klystrons are very briefly discussed. The chapter on low-level RF is rather dense but still clearly written, and is built around a specific example of an amplitude control loop. That eases the understanding of concepts and criteria underlying feedback stability and the impact of time delays and disturbances. The necessary mathematical tools are presented with a due level of detail, before delving into the stability criteria and into a discussion of the chosen example.
The volume is completed by a rich appendix summarising basic concepts and formulas required elsewhere in the book (e.g. some notions of transverse beam dynamics and the characterisation of fixed points) or working out in detail some examples of subjects treated in the main text. Some handy recalls of calculus and algebra are also provided.
This book undoubtedly fills a gap in the panorama of textbooks dedicated to accelerator physics. I would recommend it to any physicist or engineer entering the field. I enjoyed reading it as a comprehensive and clear introduction to some aspects of accelerator RF engineering, as well as to some of the theoretical foundations of accelerator physics and, in general, of classical mechanics.
