An Introduction to Beam Physics / Edition 1

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Overview

An Introduction to Beam Physics covers the principles and applications of differential algebra, a powerful new mathematical tool. The authors discuss the uses for the computation of transfer maps for all kinds of particle accelerators or any weakly nonlinear dynamical system, such as planetary orbits. The book is of interest to graduate students and researchers working in a broad range of disciplines, including applied mathematics, beam physics (accelerator physics, particle optics, geometric light optics), astronomy, and electrical engineering. Topics covered include transfer matrices, mechanics and electrodynamics, nonlinear motion, differential algebra, the structure of the classes, computer implementations, nonlinear maps, one pass systems, and repetitive systems.

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Table of Contents

Beams and Beam Physics
What Is Beam Physics
Production of Beams
Acceleration of Beams

Linear Beam Optics
Coordinates and Maps
Glass Optics
Special Optical Systems

Fields and Potentials
Fields with Straight Reference Orbit
Fields with Planar Reference Orbit

The Equations of Motion in Curvilinear Coordinates

The Linearization of the Equations of Motion
The Drift
The Electric Quadrupole without Fringe Field
The Magnetic Quadrupole without Fringe Field
The Homogeneous Magnetic Dipole
The Inhomogeneous Sector
The Inhomogeneous Electric Deflector
Electrostatic Round Lenses
Magnetic Round Lenses

Computation and Manipulation of Maps: Differential Algebraic Technique
The Map and its Aberrations
Differential Algebras
Important Functions on Differential Algebras
The Implementation of Differential Algebra on a Computer
The Computation of Transfer Maps
Manipulation of Maps

Symmetry Properties of the Transfer Maps
Horizontal Midplane Symmetry
Double Midplane Symmetry
Rotational Symmetry
Symplectic Symmetry

Imaging Devices
The Cathode Ray Tube (CRT)
The Camera, the Electron Microscope
The Spectrometers and Spectrographs

The Periodic Transport
The Invariant Ellipse
Dispersion: Periodic Solution
A Glimpse at Nonlinear Effects

Linear Phase Space Motion
Phase Space Action of Drifts and Lenses
Phase Space Action of Quads and Dipoles
Polygon-like Phase Space
Elliptic Phase Space
Practical Meaning of α, β, γ
The Relations among The Twiss Parameters
Chromaticity
The Explicit Transformation of the Ellipse
Invariant Ellipses versus Beam Ellipses

Lattice Modules
Weak and Strong Focusing
FODO Cells
Dispersion Suppressor
Double and Triple Bend Achromats
The Low Beta Insertion
Chicane Bunch Compressor

Resonances in Rings
Integer Resonance
Half-Integer Resonance
Linear Coupling Resonance
Third-Integer Resonance

Synchrotron Motion
RF Fundamentals
Phase Slip Factor
Longitudinal Dynamics

Appendix A: Edwards-Teng Parametrization
Appendix B: Aberration Formulas

References

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