By Andrzej Wolski

ISBN-10: 178326277X

ISBN-13: 9781783262779

Particle accelerators are crucial instruments for clinical learn in fields as assorted as excessive power physics, fabrics technology and structural biology. also they are regularly occurring in and drugs. generating the optimal layout and reaching the simplest functionality for an accelerator is determined by an in depth realizing of many (often complicated and occasionally sophisticated) results that make sure the houses and behaviour of the particle beam. Beam Dynamics in excessive strength Particle Accelerators presents an advent to the innovations underlying accelerator beam line layout and research, taking an procedure that emphasizes the attractiveness of the topic and leads into the advance of more than a few strong concepts for realizing and modeling charged particle beams.

Readership: Undergraduate scholars who're trying to find an creation to beam dynamics, and graduate scholars and researchers within the box.

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**Extra resources for Beam Dynamics in High Energy Particle Accelerators**

**Sample text**

In the figure, we show a quadrupole; however, the generalisation to other orders of multipole is straightforward. In principle, the coils carrying the electric current, and the line segment C2 , should be an infinite distance from the origin (the centre of the magnet). 3), with constant (zero) electric displacement, and integrating over the surface S bounded by the curve C1 + C2 + C3 gives: ∇ × H · dA = S J · dA = N I. 74) S The surface S is oriented so that the normal to S (in the direction of the area element dA) is parallel to the negative z axis; and the coil around each pole consists of N turns of wire carrying current I.

A further advantage of using the polar basis instead of the Cartesian basis comes from the dependence of the field on the radial distance. Consider a multipole field with a single component Cn . Suppose that field data are measured (or obtained from a model) with accuracy ∆Bm . Then the accuracy in the multipole coefficients will vary with the reference radius r0 (at which the measurements are made) as: ∆Cn ∝ ∆Bm . 92) Better accuracy in the multipole coefficients is obtained by choosing the radius r0 to be as large as possible.

There are even cases where conventional multipoles designed for special situations (for example, where a very wide aperture is required, and where the length of the magnet needs to be short because of space constraints) can have fringe fields that affect the dynamics to a significant extent. It is therefore of more than purely academic interest to consider how two-dimensional multipole representations may be generalised to three dimensions. As usual, there are many different ways to approach the problem: the method that is chosen will often depend on the problem to be solved.

### Beam Dynamics in High Energy Particle Accelerators by Andrzej Wolski

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