Contents
Foreword
ix
Preface
xi
Section I Introduction to Accelerator Physics
Chapter 1 Basics of beam dynamics
3
1.1 BEAM MOTION IN MAGNET LATTICES
4
1.1.1 Hamiltonian and the equations of motion
4
1.1.2 Magnets and magnetic fields
7
1.2 TRANSVERSE DYNAMICS
9
1.2.1 Beam motion in linear components
9
1.2.2 Transfer matrix and transfer map
13
1.2.3 Strong focusing principle and orbit stability
15
1.2.4 Courant-Snyder parametrization
17
1.2.5 Propagation of linear optics functions
18
1.2.6 Beam distribution
21
1.3 LONGITUDINAL DYNAMICS
23
Chapter 2 Beam dynamics topics
31
2.1 BEAM ORBIT
31
2.2 LINEAR OPTICS ERRORS
36
2.3 DISPERSION
39
2.4 LINEAR COUPLING
44
2.5 CHROMATIC EFFECT
49
2.6 NONLINEAR BEAM DYNAMICS
51
2.6.1 Hamiltonian dynamics approach
51
2.6.2 Lie map approach
55
v
Foreword
ix
Preface
xi
Section I Introduction to Accelerator Physics
Chapter 1 Basics of beam dynamics
3
1.1 BEAM MOTION IN MAGNET LATTICES
4
1.1.1 Hamiltonian and the equations of motion
4
1.1.2 Magnets and magnetic fields
7
1.2 TRANSVERSE DYNAMICS
9
1.2.1 Beam motion in linear components
9
1.2.2 Transfer matrix and transfer map
13
1.2.3 Strong focusing principle and orbit stability
15
1.2.4 Courant-Snyder parametrization
17
1.2.5 Propagation of linear optics functions
18
1.2.6 Beam distribution
21
1.3 LONGITUDINAL DYNAMICS
23
Chapter 2 Beam dynamics topics
31
2.1 BEAM ORBIT
31
2.2 LINEAR OPTICS ERRORS
36
2.3 DISPERSION
39
2.4 LINEAR COUPLING
44
2.5 CHROMATIC EFFECT
49
2.6 NONLINEAR BEAM DYNAMICS
51
2.6.1 Hamiltonian dynamics approach
51
2.6.2 Lie map approach
55
v