Chapter 3
Non-linear Dynamics in Accelerators
Werner Herr and Etienne Forest
3.1 Introduction
Non-linear effects in accelerator physics are important both during the design stage
and for successful operation of accelerators. Since both of these aspects are closely
related, they will be treated together in this overview. Some of the most important
aspects are well described by methods established in other areas of physics and
mathematics. Given the scope of this handbook, the treatment will be focused on
the problems in accelerators used for particle physics experiments. Although the
main emphasis will be on accelerator physics issues, some of the aspects of more
general interest will be discussed. In particular to demonstrate that in recent years
a framework has been built to handle the complex problems in a consistent form,
technically superior and conceptually simpler than the traditional techniques. The
need to understand the stability of particle beams has substantially contributed to the
development of new techniques and is an important source of examples which can
be verified experimentally. Unfortunately the documentation of these developments
is often poor or even unpublished, in many cases only available as lectures or
conference proceedings.
This article is neither rigorous nor a complete treatment of the topic, but rather an
introduction to a limited set of contemporary tools and methods we consider useful
in accelerator theory.
W. Herr ()
CERN (European Organization for Nuclear Research), Meyrin, Genève, Switzerland
e-mail: werner.herr@cern.ch
E. Forest
KEK, High Energy Research Organisation, Tsukuba, Japan
© The Author(s) 2020
S. Myers, H. Schopper (eds.), Particle Physics Reference Library,
https://doi.org/10.1007/978-3-030-34245-6_3
51
Non-linear Dynamics in Accelerators
Werner Herr and Etienne Forest
3.1 Introduction
Non-linear effects in accelerator physics are important both during the design stage
and for successful operation of accelerators. Since both of these aspects are closely
related, they will be treated together in this overview. Some of the most important
aspects are well described by methods established in other areas of physics and
mathematics. Given the scope of this handbook, the treatment will be focused on
the problems in accelerators used for particle physics experiments. Although the
main emphasis will be on accelerator physics issues, some of the aspects of more
general interest will be discussed. In particular to demonstrate that in recent years
a framework has been built to handle the complex problems in a consistent form,
technically superior and conceptually simpler than the traditional techniques. The
need to understand the stability of particle beams has substantially contributed to the
development of new techniques and is an important source of examples which can
be verified experimentally. Unfortunately the documentation of these developments
is often poor or even unpublished, in many cases only available as lectures or
conference proceedings.
This article is neither rigorous nor a complete treatment of the topic, but rather an
introduction to a limited set of contemporary tools and methods we consider useful
in accelerator theory.
W. Herr ()
CERN (European Organization for Nuclear Research), Meyrin, Genève, Switzerland
e-mail: werner.herr@cern.ch
E. Forest
KEK, High Energy Research Organisation, Tsukuba, Japan
© The Author(s) 2020
S. Myers, H. Schopper (eds.), Particle Physics Reference Library,
https://doi.org/10.1007/978-3-030-34245-6_3
51