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# 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