# Modern Map Methods in Particle Beam Physics

### Abstract

This book provides a general introduction to the single particle dynamics of beams.
It is based on lectures given at Michigan State University, including the Virtual University Program
in Beam Physics, as well as the US Particle Accelerator School and the CERN Academic Training Programme.
It is rounded out by providing as much as possible of the necessary physics and mathematics background,
and as such is rather self-contained. In an educational curriculum for beam physics, it represents an
intermediate level following an introduction of general concepts of beam physics, although much of it
can also be mastered independently of such previous knowledge. Its level of treatment should be
suitable for graduate students, and much of it can also be mastered by upper division undergraduate
students.
The expose is based on map theory for the description of the motion, and extensive use is made of the
framework of the differential algebraic approach developed by the author, which is the only method that
allows computations of nonlinearities of the maps to arbitrary order. Furthermore, it lends itself to a
particularly transparent presentation and analysis of all relevant nonlinear effects. The tools and
algorithms presented here are available directly in the code COSY INFINITY. Many tools from the theory
of dynamical systems and electrodynamics are included; in particular, we provide a modern and rigorous
account of Hamiltonian theory.

### Errata

The following items have been confirmed as mistakes in the first edition
of the book, and are corrected in the downloadable pdf on this page.
Please contact Martin Berz
if you feel like you have identified other typographical errors.

__Page 98:__
- In the first line of Equation 2.72, the last argument "a" of the
operator O should be a "b"
__Page 111:__
- In the first line of the equation for V, the second term in the
right hand side misses "b_2", i.e.
\int_y 1/b_2 { ( b_2 \partial V / \partial y )|_{y=0}
__Page 190:__
- In the second term inside the curly brackets of Equation 5.55,
proportional to ( \vec p * \vec B ) \vec p,
"m" in the denominator should be squared and read "m^2".
__Page 283:__
- The first and second pictures in Figure 7.16 are incorrect, they merely
repeat the third and fourth pictures from page 284.
__Page 294:__
- The text refers to two different tracking pictures in Figure 7.23.
In fact, the figure shows only one tracking picture.

M. Berz,
Academic Press, 1999, ISBN 0-12-014750-5

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