An Introduction to Beam Physics - Michigan State …bt.pa.msu.edu/pub/papers/IP127book/IP127book.pdf · Series in High Energy Physics, Cosmology, and Gravitation ... An Introduction

Series in High Energy Physics, Cosmology, and Gravitation Series in High Energy Physics, Cosmology, and Gravitation

Series Editors: Brian Foster and Edward W. Kolb

IP127

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The field of beam physics touches many areas of physics, engineering and the sciences. In general terms, beams describe ensembles of particles with initial conditions similar enough to be treated together as a group so that the motion is a weakly nonlinear perturbation of a chosen reference particle. Particle beams are used in a variety of areas, ranging from electron microscopes, particle spec-trometers, medical radiation facilities, powerful light sources and astrophysics to large synchrotrons and storage rings such as the LHC at CERN.

An Introduction to Beam Physics is based on lectures given at Michigan State University’s Department of Physics and Astronomy, the online VUBeam program, the U.S. Particle Accelerator School, the CERN Academic Training Programme and various other venues. It is accessible to beginning graduate and upper-division undergraduate students in physics, mathematics and engineering. The book begins with a historical overview of methods for generating and accelerat-ing beams, highlighting important advances through the eyes of their developers using their original drawings. The book then presents concepts of linear beam optics, transfer matrices, the general equations of motion and the main tech-niques used for single- and multi-pass systems. Some advanced nonlinear top-ics, including the computation of aberrations and a study of resonances, round out the presentation.

Features• Provides an introduction to the physics of beams from a historical

perspective• Describes the production, acceleration and optics of beams• Discusses transfer matrices and maps for particle accelerators and other

weakly nonlinear dynamical systems • Covers various important devices used for imaging and repetitive systems,

including electron microscopes, spectrometers and storage rings• Incorporates some advanced material such as aberration integrals

and the treatment of resonances

An Introduction to Beam Physics

Martin Berz, Kyoko Makino and Weishi Wan

BerzMakino

Wan

Physics

An Introduction to B

eam P

hysics

An Introduction to Beam PhysicsMartin Berz, Kyoko Makino and Weishi Wan

01052015

An Introduction to Beam Physics

Series in High Energy Physics, Cosmology, and Gravitation

Series Editors: Brian Foster, Oxford University, UK Edward W Kolb, Fermi National Accelerator Laboratory, USA

This series of books covers all aspects of theoretical and experimental high energy physics, cosmology and gravitation and the interface between them. In recent years the fields of particle physics and astrophysics have become increasingly interdependent and the aim of this series is to provide a library of books to meet the needs of students and researchers in these fields.

Other recent books in the series:

The Standard Model and BeyondP. Langacker

Particle and Astroparticle PhysicsU. Sakar

Joint Evolution of Black Holes and GalaxiesM. Colpi, V. Gorini, F. Haardt, and U. Moschella (Eds)

Gravitation: From the Hubble Length to the Planck Length I. Ciufolini, E. Coccia, V. Gorini, R. Peron, and N. Vittorio (Eds)

Neutrino PhysicsK. Zuber

The Galactic Black Hole: Lectures on General Relativity and AstrophysicsH. Falcke and F. Hehl (Eds)

The Mathematical Theory of Cosmic Strings: Cosmic Strings in the Wire ApproximationM. R. Anderson

Geometry and Physics of BranesU. Bruzzo, V. Gorini, and U. Moschella (Eds)

Modern CosmologyS. Bonometto, V. Gorini, and U. Moschella (Eds)

Gravitation and Gauge SymmetriesM. Blagojevic

Gravitational WavesI. Ciufolini, V. Gorini, U. Moschella, and P. Fré (Eds)

Neutrino Physics, Second EditionK. Zuber

Series in High Energy Physics, Cosmology, and Gravitation

Martin BerzMichigan State University

East Lansing, Michigan, USA

Kyoko MakinoMichigan State University

East Lansing, Michigan, USA

Weishi WanLawrence Berkeley National Laboratory

Berkeley, California, USA

An Introduction toBeam Physics

Contents

1 Beams and Beam Physics 11.1 What Is Beam Physics? . . . . . . . . . . . . . . . . . . . . . 11.2 Production of Beams . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 Electron Sources . . . . . . . . . . . . . . . . . . . . . 41.2.2 Proton Sources . . . . . . . . . . . . . . . . . . . . . . 81.2.3 Ion Sources . . . . . . . . . . . . . . . . . . . . . . . . 9

1.3 Acceleration of Beams . . . . . . . . . . . . . . . . . . . . . . 101.3.1 Electrostatic Accelerators . . . . . . . . . . . . . . . . 121.3.2 Linear Accelerators . . . . . . . . . . . . . . . . . . . . 151.3.3 Circular Accelerators . . . . . . . . . . . . . . . . . . . 19

2 Linear Beam Optics 312.1 Coordinates and Maps . . . . . . . . . . . . . . . . . . . . . 322.2 Glass Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.2.1 The Drift . . . . . . . . . . . . . . . . . . . . . . . . . 372.2.2 The Thin Lens . . . . . . . . . . . . . . . . . . . . . . 372.2.3 The Thin Mirror . . . . . . . . . . . . . . . . . . . . . 402.2.4 Liouville’s Theorem for Glass Optics . . . . . . . . . . 41

2.3 Special Optical Systems . . . . . . . . . . . . . . . . . . . . . 432.3.1 Imaging (Point–to–Point, • •) Systems . . . . . . . . . 442.3.2 Parallel–to–Point (‖ •) Systems . . . . . . . . . . . . . 452.3.3 Point–to–Parallel (• ‖) Systems . . . . . . . . . . . . . 462.3.4 Parallel–to–Parallel (‖ ‖) Systems . . . . . . . . . . . 472.3.5 Combination Systems . . . . . . . . . . . . . . . . . . 48

3 Fields, Potentials and Equations of Motion 493.1 Fields with Straight Reference Orbit . . . . . . . . . . . . . . 50

3.1.1 Expansion in Cylindrical Coordinates . . . . . . . . . 503.1.2 Quadrupole Fields . . . . . . . . . . . . . . . . . . . . 533.1.3 Sextupole and Higher Multipole Fields . . . . . . . . . 543.1.4 s–Dependent Fields . . . . . . . . . . . . . . . . . . . 55

3.2 Fields with Planar Reference Orbit . . . . . . . . . . . . . . 573.2.1 The Laplacian in Curvilinear Coordinates . . . . . . . 573.2.2 The Potential in Curvilinear Coordinates . . . . . . . 58

3.3 The Equations of Motion in Curvilinear Coordinates . . . . . 603.3.1 The Coordinate System and the Independent Variable 603.3.2 The Equations of Motion . . . . . . . . . . . . . . . . 65

v

vi Contents

4 The Linearization of the Equations of Motion 674.1 The Drift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.2 The Quadrupole without Fringe Fields . . . . . . . . . . . . 70

4.2.1 The Electric Quadrupole . . . . . . . . . . . . . . . . . 704.2.2 The Magnetic Quadrupole . . . . . . . . . . . . . . . . 72

4.3 Deflectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.3.1 The Homogeneous Magnetic Dipole . . . . . . . . . . 734.3.2 Edge Focusing . . . . . . . . . . . . . . . . . . . . . . 764.3.3 The Inhomogeneous Sector Magnet . . . . . . . . . . . 824.3.4 The Inhomogeneous Electric Deflector . . . . . . . . . 83

4.4 Round Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . 874.4.1 The Electrostatic Round Lens . . . . . . . . . . . . . . 894.4.2 The Magnetic Round Lens . . . . . . . . . . . . . . . 97

4.5 *Aberration Formulas . . . . . . . . . . . . . . . . . . . . . . 107

5 Computation and Properties of Maps 1155.1 Aberrations and Symmetries . . . . . . . . . . . . . . . . . . 115

5.1.1 Horizontal Midplane Symmetry . . . . . . . . . . . . . 1165.1.2 Double Midplane Symmetry . . . . . . . . . . . . . . . 1185.1.3 Rotational Symmetry . . . . . . . . . . . . . . . . . . 1195.1.4 Symplectic Symmetry . . . . . . . . . . . . . . . . . . 123

5.2 Differential Algebras . . . . . . . . . . . . . . . . . . . . . . . 1285.2.1 The Structure 1D1 . . . . . . . . . . . . . . . . . . . . 1295.2.2 The Structure nDv . . . . . . . . . . . . . . . . . . . . 1315.2.3 Functions on Differential Algebras . . . . . . . . . . . 133

5.3 The Computation of Transfer Maps . . . . . . . . . . . . . . 1345.3.1 An Illustrative Example . . . . . . . . . . . . . . . . . 1345.3.2 Generation of Maps Using Numerical Integration . . . 136

5.4 Manipulation of Maps . . . . . . . . . . . . . . . . . . . . . . 1375.4.1 Composition of Maps . . . . . . . . . . . . . . . . . . 1375.4.2 Inversion of Maps . . . . . . . . . . . . . . . . . . . . 1385.4.3 Reversion of Maps . . . . . . . . . . . . . . . . . . . . 139

6 Linear Phase Space Motion 1416.1 Phase Space Action . . . . . . . . . . . . . . . . . . . . . . . 142

6.1.1 Drifts and Lenses . . . . . . . . . . . . . . . . . . . . . 1426.1.2 Quadrupoles and Dipoles . . . . . . . . . . . . . . . . 143

6.2 Polygon–like Phase Space . . . . . . . . . . . . . . . . . . . . 1446.3 Elliptic Phase Space . . . . . . . . . . . . . . . . . . . . . . . 145

6.3.1 The Practical Meaning of α, β and γ . . . . . . . . . . 1476.3.2 The Algebraic Relations among the Twiss Parameters 1496.3.3 The Differential Relations among the Twiss Parameters 154

6.4 *Edwards-Teng Parametrization . . . . . . . . . . . . . . . . 1556.4.1 The Algebraic Relations with Coupling . . . . . . . . 157

Contents vii

7 Imaging Devices 161

7.1 The Cathode Ray Tube (CRT) . . . . . . . . . . . . . . . . . 161

7.2 The Camera and the Microscope . . . . . . . . . . . . . . . . 1627.3 Spectrometers and Spectrographs . . . . . . . . . . . . . . . 164

7.3.1 Aberrations and Correction . . . . . . . . . . . . . . . 1707.3.2 Energy Loss On–Line Isotope Separators . . . . . . . . 174

7.4 *Electron Microscopes and Their Correction . . . . . . . . . 176

7.4.1 Aberration Correction in SEM, STEM and TEM . . . 1787.4.2 Aberration Correction in PEEM and LEEM . . . . . . 183

8 The Periodic Transport 1898.1 The Transversal Motion . . . . . . . . . . . . . . . . . . . . . 189

8.1.1 The Eigenvalues . . . . . . . . . . . . . . . . . . . . . 1898.1.2 The Invariant Ellipse . . . . . . . . . . . . . . . . . . . 194

8.2 Dispersive Effects . . . . . . . . . . . . . . . . . . . . . . . . 198

8.2.1 The Periodic Solution . . . . . . . . . . . . . . . . . . 1988.2.2 Chromaticity . . . . . . . . . . . . . . . . . . . . . . . 200

8.3 A Glimpse at Nonlinear Effects . . . . . . . . . . . . . . . . . 205

9 Lattice Modules 207

9.1 The FODO Cell . . . . . . . . . . . . . . . . . . . . . . . . . 2089.1.1 The FODO Cell Based Achromat . . . . . . . . . . . . 214

9.1.2 The Dispersion Suppressor . . . . . . . . . . . . . . . 224

9.2 Symmetric Achromats . . . . . . . . . . . . . . . . . . . . . . 2269.2.1 The Double-Bend Achromat . . . . . . . . . . . . . . . 229

9.2.2 The Triple-Bend Achromat . . . . . . . . . . . . . . . 2309.2.3 The Multiple-Bend Achromat . . . . . . . . . . . . . . 230

9.2.4 The H Function . . . . . . . . . . . . . . . . . . . . . 231

9.3 Special Purpose Modules . . . . . . . . . . . . . . . . . . . . 2359.3.1 The Low Beta Insertion . . . . . . . . . . . . . . . . . 235

9.3.2 The Chicane Bunch Compressor . . . . . . . . . . . . 2369.3.3 Other Bunch Compressors . . . . . . . . . . . . . . . . 240

10 Synchrotron Motion 24110.1 RF Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . 241

10.2 The Phase Slip Factor . . . . . . . . . . . . . . . . . . . . . . 245

10.3 Longitudinal Dynamics . . . . . . . . . . . . . . . . . . . . . 25210.4 Transverse Dynamics of RF Cavities . . . . . . . . . . . . . . 257

11 *Resonances in Repetitive Systems 261

11.1 Integer Resonance . . . . . . . . . . . . . . . . . . . . . . . . 261

11.2 Half–Integer Resonance . . . . . . . . . . . . . . . . . . . . . 26411.3 Linear Coupling Resonance . . . . . . . . . . . . . . . . . . . 271

11.4 Third–Integer Resonance . . . . . . . . . . . . . . . . . . . . 281

viii Contents

References 295

Index 301

List of Figures

1.1 A beam — an ensemble of particles in the vicinity of a referenceparticle with phase space coordinate �Z0. . . . . . . . . . . . . 2

1.2 Sketch of an early thermionic emission electron source. . . . . 5

1.3 Sketch of one of the earliest electron sources using point cath-odes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4 Layout and field distribution of the RF gun at the Linac Co-herent Light Source (LCLS). . . . . . . . . . . . . . . . . . . 8

1.5 Drawing of a surface plasma source of the magnetron geometry. 9

1.6 Layout of the first electron cyclotron resonance (ECR) ionsource that produced multiple charged ions. . . . . . . . . . . 11

1.7 The general principle of the Cockcroft-Walton generator. . . . 12

1.8 Design sketch of the Van de Graaff high voltage generator. . . 13

1.9 Design sketch of the use of the Van de Graaff generator as aparticle accelerator. . . . . . . . . . . . . . . . . . . . . . . . . 14

1.10 The principle of the tandem Van de Graaff accelerator. . . . . 15

1.11 Sketch of the principle of the linear accelerator of the Wideroetype. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.12 Illustration of a linear accelerator, designed by E. O. Lawrenceand H. D. Sloan. . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.13 Sketches illustrating the basic principles of the linear accelera-tor of the Alvarez type. . . . . . . . . . . . . . . . . . . . . . 18

1.14 The structure of the RFQ, the radio-frequency quadrupole lin-ear accelerator. . . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.15 Sketch of the first Free Electron Laser (FEL). . . . . . . . . . 20

1.16 Illustration of the magnet of a betatron. . . . . . . . . . . . . 21

1.17 Illustration of the first microtron. . . . . . . . . . . . . . . . . 23

1.18 The principle of the cyclotron. . . . . . . . . . . . . . . . . . 24

1.19 The first model of an FFAG, the Fixed-Field Alternating Gra-dient accelerator. . . . . . . . . . . . . . . . . . . . . . . . . . 25

1.20 Sketch of the Bevatron, designed to achieve “Billions of eVSynchrotron,” at Lawrence Berkeley National Laboratory, Cal-ifornia, USA. . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

1.21 Layout of the Cooler Synchrotron (COSY) ring at the Insti-tute of Nuclear Physics (IKP) at Forschungszentrum Julich,Germany. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

ix

x List of Figures

1.22 Layout of the Super-ACO light source storage ring at Labo-ratoire pour l’Utilisation du Rayonnement Electromagnetique,Orsay, France. . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

1.23 Layout of the Advanced Light Source (ALS) at Lawrence Berke-ley National Laboratory, California, USA. . . . . . . . . . . . 29

2.1 Reference orbit, arc length s along it and local coordinates. . 322.2 Motion of particles inside the tube with radius rtube around the

reference orbit. . . . . . . . . . . . . . . . . . . . . . . . . . . 332.3 A ray passing through a drift. . . . . . . . . . . . . . . . . . . 372.4 A bundle of parallel rays passing through a focusing lens. . . 382.5 A bundle of parallel rays passing through a defocusing lens. . 392.6 A bundle of parallel rays is reflected by the focusing mirror. . 412.7 Liouville’s theorem. . . . . . . . . . . . . . . . . . . . . . . . . 422.8 Poincare’s recurrence theorem. . . . . . . . . . . . . . . . . . 432.9 Sketch of an imaging system. . . . . . . . . . . . . . . . . . . 442.10 Sketch of a parallel–to–point system. . . . . . . . . . . . . . . 462.11 Sketch of a point–to–parallel system. . . . . . . . . . . . . . . 462.12 Sketch of a parallel–to–parallel system. . . . . . . . . . . . . . 473.1 Ideal electrodes of an electrostatic quadrupole. . . . . . . . . 543.2 The s-dependence of the multipole strength. . . . . . . . . . . 553.3 Scalar potential, longitudinal and radial field distribution of a

rotationally symmetric lens. . . . . . . . . . . . . . . . . . . . 563.4 Reference orbit of a bending magnet. . . . . . . . . . . . . . . 573.5 The curvilinear coordinates in the plane of the reference orbit. 624.1 A homogeneous magnetic dipole. . . . . . . . . . . . . . . . . 734.2 Entrance and exit edge lines of a dipole magnet. . . . . . . . 774.3 Mechanism of edge focusing for the horizontal plane and the

vertical plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.4 An inhomogeneous sector magnet. . . . . . . . . . . . . . . . 824.5 An electric capacitor consisting of two parallel plates. The orbit

of a particle is parabolic. . . . . . . . . . . . . . . . . . . . . . 844.6 A concentric electric deflector. . . . . . . . . . . . . . . . . . . 844.7 An electric deflector with cylindrical plates. . . . . . . . . . . 864.8 An electric deflector with spherical plates. . . . . . . . . . . . 864.9 Layout and potential profile of the electrostatic three-plate

round lens. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 964.10 Transversal motion of particles entering initially parallel to the

reference axis in the magnetic solenoid. . . . . . . . . . . . . . 1005.1 Trajectories of particles in a system with horizontal midplane

symmetry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1175.2 Motion in a 90◦ homogeneous dipole magnet. . . . . . . . . . 1356.1 Mapping of individual points in phase space. . . . . . . . . . 1416.2 Mapping of a closed curve in phase space. . . . . . . . . . . . 1426.3 Action of a drift in phase space. . . . . . . . . . . . . . . . . . 1436.4 Action of a thin lens in phase space. . . . . . . . . . . . . . . 144

List of Figures xi

6.5 Action of a quadrupole or dipole in phase space. . . . . . . . 1446.6 Mapping of a polygon in phase space. . . . . . . . . . . . . . 1456.7 An ellipse in phase space. . . . . . . . . . . . . . . . . . . . . 1466.8 Characteristic points of an ellipse in phase space. . . . . . . . 1476.9 Sketch of horizontal and vertical β functions of a beamline. . 1486.10 Transformation of an ellipse under a drift. . . . . . . . . . . . 1526.11 Plot of the β function in a drift. . . . . . . . . . . . . . . . . 1537.1 Sketch of an imaging system. . . . . . . . . . . . . . . . . . . 1617.2 Curvature of the image. . . . . . . . . . . . . . . . . . . . . . 1637.3 The Browne-Buechner spectrograph. . . . . . . . . . . . . . . 1657.4 Illustration of the imaging condition arising from Barber’s rule. 1667.5 Sketch of a generic spectrograph consisting of a single dipole. 1687.6 Sketch of a generic spectrograph now subject to aberrations up

to order seven. . . . . . . . . . . . . . . . . . . . . . . . . . . 1697.7 The effect of the aberration (x|aδ). . . . . . . . . . . . . . . . 1707.8 A magnified drawing of the effect of the aberration (x|aδ). . . 1717.9 Layout of an example of a fragment separator. . . . . . . . . 1757.10 Spherical and chromatic aberrations. . . . . . . . . . . . . . . 1777.11 Cosine-like rays and sine-like rays of the quadruplet corrector. 1797.12 A quadrupole-octupole CS corrector. . . . . . . . . . . . . . . 1797.13 A sextupole CS corrector. . . . . . . . . . . . . . . . . . . . . 1817.14 Sine-like and cosine-like rays of a CS corrected TEM from ob-

jective lens to the end of the corrector section. . . . . . . . . 1817.15 Sine-like and cosine-like rays of the TEAM corrector. . . . . . 1827.16 Sine-like and cosine-like rays of the TEAM microscope from

objective lens to end of the corrector section. . . . . . . . . . 1827.17 Spherical and chromatic aberrations of an electron mirror. . . 1837.18 Geometry of the tetrode mirror in PEEM3. . . . . . . . . . . 1847.19 Layout of PEEM3. . . . . . . . . . . . . . . . . . . . . . . . . 1847.20 The beam separator of the first aberration-corrected PEEM. . 1857.21 The PEEM3 beam separator. . . . . . . . . . . . . . . . . . . 1867.22 Sine-like, cosine-like and dispersive rays of the PEEM3 beam

separator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1867.23 Aberration-corrected and energy-filtered LEEM at IBM. . . . 1878.1 Motion in phase space and in the eigenspace when | trM | > 2. 1908.2 Relation between the phase space variables and the eigenvec-

tors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1918.3 Relation between the eigenvalues when | trM | < 2. . . . . . . 1928.4 Motion in phase space and in the eigenspace when | trM | < 2. 1938.5 Possible movement of the eigenvalues under small perturbation

near | trM | = 2. . . . . . . . . . . . . . . . . . . . . . . . . . . 1948.6 Stable motion in phase space. . . . . . . . . . . . . . . . . . . 1978.7 Illustration of the case where the beam ellipse and the invariant

ellipses are matched. . . . . . . . . . . . . . . . . . . . . . . . 1988.8 Behavior of a mismatched beam. . . . . . . . . . . . . . . . . 199

xii List of Figures

9.1 Sketch of a FODO cell without bending magnets. . . . . . . . 2089.2 The “necktie” diagram showing the stability region of a FODO

cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2099.3 Sketch of a FODO cell with bending magnets. . . . . . . . . . 2099.4 Lattice functions of a FODO cell at the Fermilab Main Injector. 2129.5 The simplest double-bend achromat. . . . . . . . . . . . . . 2309.6 The double-bend achromat. . . . . . . . . . . . . . . . . . . 2309.7 Lattice functions of a double-bend achromat. . . . . . . . . . 2319.8 The triple-bend achromat. . . . . . . . . . . . . . . . . . . . 2319.9 Lattice functions of a triple-bend achromat of the Advanced

Light Source. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2329.10 Lattice functions of the MAX IV multiple-bend achromat lat-

tice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2339.11 Lattice functions of a typical low beta insertion with symmetric

quadrupole triplets. . . . . . . . . . . . . . . . . . . . . . . . . 2369.12 Layout of the chicane bunch compressor. . . . . . . . . . . . . 2379.13 Mechanism of an RF buncher cavity. . . . . . . . . . . . . . . 24010.1 Typical RF cavity field with fundamental mode TM010. . . . 24210.2 Dependence of transit time factor on length of the cavity. . . 24610.3 Sketch of phase stability for energy below transition. . . . . . 24910.4 Sketch of phase stability for energy above transition. . . . . . 25010.5 Phase space plots of longitudinal motion with φs = π/2 and

φs = π/3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25710.6 Longitudinal and transverse field distribution along the longi-

tudinal axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25811.1 Distinct eigenvalues around the unit circle. . . . . . . . . . . 27711.2 Crossing the difference resonance. . . . . . . . . . . . . . . . . 27911.3 Invariant obtained through first order perturbation theory and

tracking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28711.4 Invariant obtained through first order perturbation theory and

tracking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

Preface

This volume provides an introduction to the physics of beams. This fieldtouches many other areas of physics, engineering and the sciences, and inturn benefits from numerous techniques also used in other disciplines. Ingeneral terms, beams describe ensembles of particles with initial conditionssimilar enough to be treated together as a group, so that the motion is aweakly nonlinear perturbation of that of a chosen reference particle.

Applications of particle beams are very wide, including electron micro-scopes, particle spectrometers, medical irradiation facilities, powerful lightsources, astrophysics – to name a few – and reach all the way to the largestscientific instruments built by man, namely, large colliders like LHC at CERN.

The text is based on lectures given at Michigan State University’s Depart-ment of Physics and Astronomy, the online VUBeam program, the US ParticleAccelerator School, the CERN Academic Training Programme, and variousother venues. Selected additional material is included to round out the pre-sentation and cover other significant topics.

The material is at a level to be accessible to students of physics, mathemat-ics and engineering at the beginning graduate or upper division undergraduatelevel and can be viewed as an introductory companion to the more advancedModern Map Methods in Particle Beam Physics by M. B., published by Aca-demic Press. Emphasis has been placed on showing major concepts in theiroriginal incarnations and through historic figures. Finally, some of the sec-tions and chapters that contain more advanced material are marked by a *symbol and can be omitted in a first reading.

Many organizations and individuals have helped directly and indirectly atvarious stages in the development of this book. MSU’s Physics and AstronomyDepartment provided an environment of support for this and other books, theVUBeam program, as well as many of our other activities.

For two decades of continuous financial support that were instrumentalto the success of the book, the VUBeam program, and indeed much of ourresearch, we are grateful to the US Department of Energy, and in particular toDr. Dave Sutter, the long-term coordinator of their beam physics activities.

K. M. would like to thank her daughter Kazuko for her own great interestin physics and science and much encouragement during the finalization of thistext.

W. W. would like to thank Dr. D. Robin for his encouragement, Dr. E.Forest for stimulating discussions on various aspects of beam dynamics suchas normal form theory, and his wife Juxiang Teng for her unwavering support

xiii

xiv Preface

throughout this project.All of us want to thank Bela Erdelyi, Gabi Weizman, Pavel Snopok and

He Zhang for thoughtful comments about the material. We also are thankfulto many authors, national laboratories and publishers allowing us to repro-duce published figures. The details are described in the corresponding figurecaptions.

Last but not least, we are very grateful to the entire staff of Taylor &Francis for their continuous support, in particular to Francesca McGowan forher great interest and productive comments.

Martin BerzKyoko Makino

Weishi Wan

Index

Aberration, 36, 115, 116, 167Chromatic, 163, 178, 235Derivation, 107Electron Microscope, 177, 178,

183Integral Form, 110Order-by-Order Computation, 109Spectrograph, 170Spherical, 169, 177

Acceleration, 4, 11Accelerator

Mass Spectrometer, 164Physics, 4

Acceptance, 164Achromat

Double-Bend (DBA), 226, 229–231, 234

Multiple-Bend (MBA), 230, 233Triple-Bend (TBA), 226, 230–232,

234Achromaticity, 236Adiabatic Damping, 212Advanced Light Source (ALS), 29,

30, 149, 232, 256Alpha, see Twiss ParameterALS, see Advanced Light SourceAlternate Gradient, 207

Focusing, 25Synchrotron, 28

Alvarez, L. W., 18Analytic

Complex Variables, 120Angular Momentum, 105Anode, 5Antiproton Source, 4Arc Length, 32, 60, 61Astrodynamics, 1

B Rho, 20Ballistic, 7

Bunching, 240Barber’s Rule, 166Barrel Distortion, 163Beam, 10

Current, 15Ellipse, 194Optics, 31Periodic Transport, 189Production, 4

Beating, 159, 198Bending Magnet, see DipoleBessel Function, 242Beta, see Twiss ParameterBetatron, 19, 21, 207

Condition, 22Bevatron, 26Binoculars, 163BMDO, see Strategic Defense

InitiativeBNL, see Brookhaven National

LaboratoryBρ, see B RhoBrightness, 7Brookhaven National Laboratory

(BNL), 28Browne-Buechner Spectrograph, 166Bunch Compressor, 236, 240Buncher, 240

Camera, 41, 162Capture, 9Carbon Foil, 8Cathode, 4, 5

Ray Tube, 161Cavity, 22, 29, 212, 232, 240, 241

Electromagnetic Field, 241

301

302 Index

Field Distribution, 241Longitudinal Dynamics, 252TM010, 242TM110, 243TransverseDynamics, 257Focusing, 259, 260

CC , see Aberration, ChromaticCEBAF, see Continuous Electron

Beam Accelerating FacilityCentroid, 263CERN, see European Organization

for Nuclear ResearchCesium, 7, 9

Cesiation, 7Charge, 1Chicane, 236, 240Child-Langmuir Law, 5Chromatic Aberration, see

Aberration, ChromaticChromaticity, 200, 213, 268, 281

Correction, 204Natural, 202

Closed Orbit, 232, 263Cockcroft, J. D., 12, 13Cockcroft-Walton, 12, 13Cold Field Emission Gun (CFEG), 7Collider, 19, 26, 28–30Coma, 163Combination Systems, 48Complex Coordinates

Rotational Symmetry, 119Continuous

Electron Beam AcceleratingFacility (CEBAF), 23

Rotational Symmetry, 120Wave, 15, 22

CoordinatesCurvilinear, 58, 60, 62Cylindrical, 50Particle Optical, 34, 62

Cosine-like Ray, 178, 179COSY Ring, 27, 28, 30Coupling, 157

Resonance, 271

CRT, see Cathode Ray TubeCS , see Aberration, SphericalCurvilinear Coordinates, see

Coordinates, CurvilinearCW, see Continuous, WaveCyclotron, 23, 24Cylindrical Deflector, see

Deflector, Cylindrical

DA, see Differential AlgebraDamping, 212

Rate, 232DBA, see Achromat, Double-BendDeflector

Cylindrical, 86Electrostatic, 83Spherical, 87Transfer Matrix, 86

Defocusing Lens, 40Delta Function, 78, 91, 99Determinism, 35DFELL, see Duke Free Electron Laser

LaboratoryDifference Resonance, see

Resonance, DifferenceDifferential Algebra (DA), 111, 115,

132, 159, 199, 200, 205, 249,292

1D1, 129

nDv, 131Arithmetic, 129, 131Concatenation, 137COSY INFINITY, 134Derivatives, 130Functions, 133MapComposition, 137Computation, 134Inversion, 138Manipulation, 137Numerical Integration, 136Reversion, 139

VariableMultiple, 131Single, 129

Index 303

Dipole, 73, 143, 210, 236Edge, 76Error, 261Rectangular, 79Sector, 76Transfer Matrix, 76, 81, 83

Dirac Delta Function, seeDelta Function

Discrete Rotational Symmetry, 120Dispersion, 165, 168, 198, 224, 227

Periodic Solution, 198Suppressor, 224

DLD, see Drift-Lens-Drift SystemDouble Midplane Symmetry, see

Symmetry, Double MidplaneDouble-Bend Achromat, see

Achromat, Double-BendDoublet, 178, 229, 230Dresden High Magnetic Field

Laboratory (HLD), 26Drift, 37, 69, 142Drift-Lens-Drift (DLD) System, 45–

47Driving Term, 110Duke Free Electron Laser Laboratory

(DFELL), 215Dynamic Aperture, 206

ECR Ion Source, seeElectron, CyclotronResonance, Ion Source

Eddy Current, 22Edge

Angle, 76Focusing, 76Dipole, 77Electrostatic Round Lens, 91Magnetic Round Lens, 101Solenoid, 101Transfer Matrix, 77, 91, 105

Edwards-Teng Parametrization, 155Eigenvalues

Periodic Transport, 190Electric

Field, 2

Moment, 1Quadrupole, 70Rigidity, 64

ElectronCapture, 9Cyclotron Resonance (ECR)Heating, 10Ion Source, 9–11

Microscope, 57, 98, 162Low Energy (LEEM), 8, 176,177, 183, 185, 187

Photo Emission (PEEM), 176,177, 183, 185–187

Scanning (SEM), 176–179, 183Scanning Transmission (STEM),176, 177, 179, 181

TEAM Corrector, 183TEAM Project, 176, 182Transmission (TEM), 7, 176,177, 180–183

Transmission, Aberration - cor-rected (TEAM), 181, 182

Source, 4Volt, 4

ElectrostaticDeflector, 83Transfer Matrix, 86

Lens, 177, 183Mirror, 184Round Lens, 89

Ellipse, 144Axis Intersection, 148Beam, 194Invariant, 194MaximalPoints, 148Width, 149

Transformation, 147, 152Emission, 4Emittance, 2, 4, 141, 146, 189, 231

Equilibrium, 231Normalized, 211

EnergyLoss Separator, 174Mass Spectrometer, 164

304 Index

Spectrometer, 87Ensembles of Particles, 1Epsilon

Emittance, 146Equations of Motion, 65

Linearization, 67, 69Deflector, 85Dipole, Homogeneous, 73Dipole, Inhomogeneous, 82Drift, 69Quadrupole, Electric, 71Quadrupole, Magnetic, 72Round Lens, Electric, 90Round Lens, Magnetic, 98

Particle Optical Coordinates, 65Rotational Symmetry, 89

Equilibrium Emittance, seeEmittance, Equilibrium

European Organization for NuclearResearch (CERN), 26, 28–30

ExpansionFourier, 50Taylor, 50, 109, 115

Extended Schottky Emission, 7Extraction, 30

FEL, see Free Electron LaserFemri-Dirac Distribution, 5Fermi National Accelerator Labora-

tory (Fermilab, FNAL), 28,207, 211

FFAG, see Fixed-Field AlternatingGradient Accelerator

Field, 1, 2, 49Emission, 6Gun, 6

Midplane Symmetry, 59Multipole, 54Quadrupole, 53Rotational Symmetry, 56Sextupole, 54View, 180, 183

Fixed Target, 30

Fixed-Field Alternating GradientAccelerator, 25

Flashlight, 46FNAL, see Fermi National

Accelerator LaboratoryFocal Plane

Tilt, 170Focusing, 207

Lens, 38Quadrupole, 71Round LensElectric, 91, 92Magnetic, 101

Strong, 53, 207Synchrotron, 28

Weak, 56, 88, 207Synchrotron, 28

FODO Cell, 208, 214, 224, 226, 229Stability, 209

Forschungszentrum Julich, 27, 28, 30Fourier Transform Ion Cyclotron

Resonance Spectrometer, 164Free Electron Laser (FEL), 7, 19, 20,

28, 215, 236Fringe Field, 56

Electrostatic Round Lens, 90Magnetic Solenoid, 99

GaAs, 7Galilean Telescope, 48Gamma, see Twiss ParameterGaussian

Image, 177Lens, 38Optics, 36

Glass Optics, 36

H Function, 231–234H−, 8Half–Integer Resonance, see

Resonance, Half–IntegerHamiltonian, 3, 60Harmonic Number, 255Heaviside Function, 78, 90, 99, 258

Index 305

Hochfeld-Magnetlabor Dresden, HLD,see Dresden High MagneticField Laboratory

Homogeneous Dipole, 73Hyperbola, 191

ILC, see International Linear ColliderImaging, 161

System, 44Independent Variable

Arc Length, 61Induction Stovetop, 20Inert Gas, 14Inhomogeneous

Deflector, 83Transfer Matrix, 86

Sector Magnet, 82Transfer Matrix, 83

Injection, 8Integer Resonance, see

Resonance, IntegerIntegrability, 206Interaction Point, 235International Linear Collider (ILC),

19, 215Invariant Ellipse, see

Ellipse, InvariantIon

Source, 9, 14Trap Mass Spectrometer, 164

Ionization Cooling, 98Isochronous Cyclotron, 24Isotope Separator, 174

Jacobian, 123, 126, 127Jefferson Lab (JLab), see

Thomas Jefferson NationalAccelerator Facility

Julich, see Forschungszentrum Julich

K1200 Cyclotron, 24Kaon Source, 4Kerst, D. W., 21Kick, 203, 214, 217, 218, 243, 251,

253, 261, 262, 267

Approximation, 77, 79, 91, 99Kinematic Correction, 70

Laboratoire pour l’Utilisation du Ray-onnement Electromagnetique(LURE), 28

Lagrangian, 3, 60Langmuir Law, see

Child-Langmuir LawLANL, see Los Alamos National

LaboratoryLaplace’s Equation, 49Laplacian

Curvilinear Coordinates, 58Cylindrical Coordinates, 50, 58Particle Optical Coordinates, 58

LargeElectron-PositronCollider (LEP),

30Hadron Collider (LHC), 26, 28–

30, 32Lattice Modules, 207Lawrence Berkeley National

Laboratory (LBNL, LBL),26, 27, 149, 184, 186, 230,256

Lawrence, E. O., 24LBNL, see Lawrence Berkeley

National LaboratoryLCD, see Liquid Crystal DisplayLCLS, see Linac Coherent Light SourceLDL, see Lens-Drift-Lens SystemLEEM, see Electron, Microscope,

Low EnergyLens, 37, 40, 142, 143

Electrostatic Round, 89, 177Imaging, 45Magnetic Round, 97, 177

Lens-Drift-Lens (LDL) System, 47LEP, see Large Electron-Positron

ColliderLHC, see Large Hadron ColliderLight

Optics, 1Source, 28–30

306 Index

Linac, see Linear, AcceleratorLinac Coherent Light Source (LCLS),

8, 239Linear

Accelerator, 15–18, 235Coupling Resonance, 271Dynamics, 205Map, 35Motion, 141

Linearization, 31, 67, 108Liouville’s Theorem, 41, 48, 126, 165,

189Liquid Crystal Display (LCD), 162Longitudinal Dynamics, 33, 252Lorentz Force, 2, 11, 54, 60Los Alamos National Laboratory

(LANL), 215Los Alamos National Laboratory

(LANL), 18, 26Low

Beta Insertion, 235Energy ElectronMicroscope, see

Electron, Microscope,Low Energy

LURE, see Laboratoire pourl’Utilisation du RayonnementElectromagnetique

MagneticDipole, 73, 134Field, 2Lens, 177Mirror, 10Moment, 1Quadrupole, 72Rigidity, 20, 64Round Lens, 97

Magnetron, 8Magnification, 44, 48, 162Main Injector (Fermilab), 211Map, see Transfer MapMass, 1

Spectrograph, 170Spectrometer, 164

Matching, 198

MAX IV Laboratory, 230, 233Maxwell’s Equations, 49MBA, see Achromat, Multiple-BendMicroscope, 46Microtron, 22, 23Microwave, 9Midplane

Field, 59Symmetry, 116Double, 118Stable Motion, 190

Mirror, 40Electrostatic, 184Symmetry, 227

Misalignment, 271MIT-Bates Linear Accelerator

Center, 215Momentum, 1, 60

Acceptance, 168Dynamical, 32Spectrometer, 164Browne-Buechner, 166Q Value, 167Resolution, 166

Multiple-Bend Achromat, seeAchromat, Multiple-Bend

Multipole Order, 52

NationalHigh Magnetic Field Laboratory

(NHMFL), 26Superconducting Cyclotron

Laboratory (NSCL), 24Natural Chromaticity, 202Necktie Diagram, 209Needle, 6Newtonian Telescope, 48NHMFL, see National High Magnetic

Field LaboratoryNonlinear Dynamics, 115, 205Normal Form, 191, 261Normalized Emittance, see

Emittance, NormalizedNSCL, see National Superconduct-

ing Cyclotron Laboratory

Index 307

Optical Systems, 43Optics, 1, 36Oscilloscope, 161

Packing Factor, 226Parallel–to–Parallel, 47

Periodic Transport, 190Parallel–to–Point, 46

Periodic Transport, 190Parallelogram, 145Particle Optical Coordinates, see

Coordinates,Particle Optical

PEEM, see Electron, Microscope,Photo Emission

PEEM3, 184, 186Periodic

Solution, 263, 267Transport, 189

Perpetual Motion Machine, 12Perturbation Theory, 31, 35, 115Phase, 261

Advance, 149Multipole, 52Slip Factor, 245, 247, 256Leading Order, 247Second Order, 248, 250

Phase Space, 1Linear Motion, 141Dipole, 143Drift, 142Ellipse, 144Lens, 142Polygon, 144Quadrupole, 143

Volume, 41Photo

Cathode, 7Effect, 7Emission, 7Electron Microscope, seeElectron, Microscope,Photo Emission

Pillbox Cavity, 241Electromagnetic Field, 241

Field Distribution, 241TM010, 242TM110, 243

Pincushion Distortion, 163Pion Source, 4Plasma Physics, 1Poincare Recurrence Theorem, 42Point Filament, 7Point–to–Parallel, 46

Periodic Transport, 190Point–to–Point, 44

Periodic Transport, 190Polygon, 144Position, 1Positron Source, 4Potential, 2, 49

Electrostatic, 63Pre-Accelerator, 19Production of Beam, 4Projector, 44Proton Source, 8

Q Value, 167Quad, see QuadrupoleQuadrupole, 52, 143, 173, 208, 229,

235, 271Electric, 70Error, 264Magnetic, 72Mass Spectrometer, 164Rotational Symmetry, 122Transfer Matrix, 70

Radio Frequency (RF), 15, 22Cavity, 17, 22, 29, 212, 232, 241Gun, 7, 8Quadrupole Accelerator (RFQ),

18Radioactive Beam, 4, 174Rectangular Dipole, 79Recurrence Theorem, 42, 43Reference

Orbit, 32, 50Particle, 2, 10, 31

Relative

308 Index

Coordinates, 31Dynamics, 32

Relativistic Heavy Ion Collider(RHIC), 28

Repetitive System, 261Resolution, 164, 166

Linear, 166Nonlinear, 167

Resolving Power, 166Resonance, 206, 261, 263

Coupling, 271Difference, 276, 279, 280Half–Integer, 264, 266Integer, 261Sum, 276, 279, 280Third OrderTune Shift, 293Tune Shift, Amplitude, 292

Third–Integer, 281Perturbed Invariant, 286

RF, see Radio FrequencyRFQ, see Radio Frequency,

Quadrupole AcceleratorRHIC, see Relativistic Heavy Ion

ColliderRichardson-Dushman Equation, 5Rigidity, 20, 64

Electric, 64Magnetic, 64

Ring, see Storage RingRotational Symmetry, see

Symmetry, RotationalRound Lens, 87, 123, 177

Electric, 89Magnetic, 97

Scalar Potential, 2, 49Scanning Electron Microscope, see

Electron, Microscope,Scanning

Scanning Transmission ElectronMicroscope, seeElectron, Microscope,Scanning Transmission

Schottky Emission, 7

SDI, see Strategic Defense InitiativeSector

Field Mass Spectrometer, 164Magnet, 76Inhomogeneous, 82

Self Interaction, 2SEM, see Electron, Microscope,

ScanningSextupole, 180, 213, 235, 271Shanghai Synchrotron Radiation

Facility (SSRF), 235Shearing

Horizontal, 142Vertical, 143

SigmaEllipse Matrix, 145

Sine-like Ray, 178, 179SLAC National Accelerator

Laboratory, 8, 19, 215, 239SLC, see Stanford Linear ColliderSmall Oscillation, 67SMART, see SpectroMicroscopy for

All Relevant TechniquesSolenoid, 97, 271

Edge, 99Rotational Symmetry, 121

SourceElectron, 4Ion, 9, 14Proton, 8

South Hall Ring (MIT), 215Space Charge, 2Spark, 14, 16Spectrograph, 164Spectrometer, 87, 164

Mass, 164Momentum, 164Resolution, 166

SpectroMicroscopy for All RelevantTechniques Project(SMART), 184

SphericalAberration, see

Aberration, Spherical

Index 309

Deflector, seeDeflector, Spherical

Lens, 39Spin, 1SSRF, see Shanghai Synchrotron

Radiation FacilityStanford Linear Collider (SLC), 19Steering, 207STEM, see Electron, Microscope,

Scanning TransmissionStep Function, see

Heaviside FunctionStigmatic Image, 87Stop Band, 263, 268, 275, 280

Half–Integer, 270Integer, 269, 270

Storage Ring, 4, 27–30, 261Strategic Defense Initiative (SDI), 46Stripping, 8, 15Strong Focusing, see Focusing, StrongSum Resonance, see Resonance, SumSuper-ACO Ring, 28Surface Plasma Source, 8Symmetry, 115

Double Midplane, 118Midplane, 116Mirror, 227Rotational, 50, 119, 120Quadrupole, 122Round Lens, 87

Symplectic, 123Transfer Map, 116

SymplecticCondition, 124, 126Edwards-Teng Parametrization,

155Symmetry, see

Symmetry, SymplecticSynchrocyclotron, 25Synchronicity Condition, 23Synchrotron, 25, 27, 30, 207

Light Source, 30Motion, 241Radiation, 6, 19, 30, 231Tune, 256

Tandem Van de Graaff, 15TBA, see Achromat, Triple-BendTEAM, see Electron, Microscope,

Transmission, Aberration-corrected

Telescope, 41, 47, 235Television Tube (TV), 161TEM, see Electron, Microscope,

TransmissionTevatron, 28, 207Thermionic

Emission, 5Gun, 5

ThinLens, 37Edge Focusing, 77

Mirror, 40Third Order Resonance, see

Resonance, Third OrderThird–Integer Resonance, see

Resonance, Third IntegerThomas Jefferson National

Accelerator Facility(Jefferson Lab, JLab,TJNAF), 23

Tilt of Focal Plane, 170Time Reversal, 8Time-of-Flight, 33

Mass Spectrometer, 164Time-Resolved Spectroscopy, 7TJNAF, see Thomas Jefferson

National AcceleratorFacility

Transfer Map, 35, 36, 115Differential Algebra, 134Symmetry, 116

Transfer Matrix, 36Drift, 37, 70Edge FocusingElectrostatic Round Lens, 91Magnetic Dipole, 77Solenoid, 105

ElectricDeflector, Cylindrical, 86Deflector, Inhomogeneous, 86

310 Index

Deflector, Spherical, 87Quadrupole, 71Round Lens, 95, 97

LensDefocusing, 40Drift-Lens-Drift (DLD), 45Focusing, 38Lens-Drift-Lens (LDL), 47

MagneticDipole, Homogeneous, 76Dipole, Inhomogeneous, 83Dipole, Rectangular, 81Dipole, Sector, 76Quadrupole, 72Round Lens, 105Solenoid, 105

MirrorDefocusing, 41Focusing, 40

Transit Time Factor, 244, 245Transition, 248

Jump, 248Transmission Electron Aberration-

corrected Microscope, seeElectron, Microscope,Transmission,Aberration-corrected

Transmission ElectronMicroscope, seeElectron, Microscope,Transmission

Transport, 4Transversal Dynamics, 33Triple-Bend Achromat, see

Achromat, Triple-BendTriplet, 229, 230, 235Tune, 192, 193, 206, 208

Shift, 293Amplitude, 292

Synchrotron, 256Tungsten, 7Tunneling, 6TV Tube, see Television TubeTwiss Parameter, 146

Alpha, 146Beating, 159

Beta, 146Function, 149

Gamma, 146

Ultra-Slow Extraction, 30Undulator, 19, 30Unstable Motion, 191

Perturbation, 194

Van de Graaff, R. J., 13–15Vector Potential, 2, 49Veksler, V., 22, 23Velocity, 60Voltage Multiplier, 12

Waist, 153Walton, E. T. S., 12, 13Weak Focusing, see Focusing, WeakWeakly Nonlinear, 35, 66Wideroe, R., 16Wien Filter Quadrupole, 179Wiggler, 30Work Function, 4

Zirconium, 7

Series in High Energy Physics, Cosmology, and Gravitation Series in High Energy Physics, Cosmology, and Gravitation

Series Editors: Brian Foster and Edward W. Kolb

IP127

w w w . c r c p r e s s . c o m

The field of beam physics touches many areas of physics, engineering and the sciences. In general terms, beams describe ensembles of particles with initial conditions similar enough to be treated together as a group so that the motion is a weakly nonlinear perturbation of a chosen reference particle. Particle beams are used in a variety of areas, ranging from electron microscopes, particle spec-trometers, medical radiation facilities, powerful light sources and astrophysics to large synchrotrons and storage rings such as the LHC at CERN.

An Introduction to Beam Physics is based on lectures given at Michigan State University’s Department of Physics and Astronomy, the online VUBeam program, the U.S. Particle Accelerator School, the CERN Academic Training Programme and various other venues. It is accessible to beginning graduate and upper-division undergraduate students in physics, mathematics and engineering. The book begins with a historical overview of methods for generating and accelerat-ing beams, highlighting important advances through the eyes of their developers using their original drawings. The book then presents concepts of linear beam optics, transfer matrices, the general equations of motion and the main tech-niques used for single- and multi-pass systems. Some advanced nonlinear top-ics, including the computation of aberrations and a study of resonances, round out the presentation.

Features• Provides an introduction to the physics of beams from a historical

perspective• Describes the production, acceleration and optics of beams• Discusses transfer matrices and maps for particle accelerators and other

weakly nonlinear dynamical systems • Covers various important devices used for imaging and repetitive systems,

including electron microscopes, spectrometers and storage rings• Incorporates some advanced material such as aberration integrals

and the treatment of resonances

An Introduction to Beam Physics

Martin Berz, Kyoko Makino and Weishi Wan

BerzMakino

Wan

Physics

An Introduction to B

eam P

hysics

An Introduction to Beam PhysicsMartin Berz, Kyoko Makino and Weishi Wan

01052015