Contents
1 Beams and Beam Physics
1
1.1 What Is Beam Physics? . . . . . . . . . . . . . . . . . . . . .
1
1.2 Production of Beams . . . . . . . . . . . . . . . . . . . . . .
4
1.2.1 Electron Sources . . . . . . . . . . . . . . . . . . . . .
4
1.2.2 Proton Sources . . . . . . . . . . . . . . . . . . . . . .
8
1.2.3 Ion Sources . . . . . . . . . . . . . . . . . . . . . . . .
9
1.3 Acceleration of Beams . . . . . . . . . . . . . . . . . . . . . .
10
1.3.1 Electrostatic Accelerators . . . . . . . . . . . . . . . .
12
1.3.2 Linear Accelerators . . . . . . . . . . . . . . . . . . . .
15
1.3.3 Circular Accelerators . . . . . . . . . . . . . . . . . . .
19
2 Linear Beam Optics
31
2.1 Coordinates and Maps . . . . . . . . . . . . . . . . . . . . .
32
2.2 Glass Optics . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
2.2.1 The Drift . . . . . . . . . . . . . . . . . . . . . . . . .
37
2.2.2 The Thin Lens . . . . . . . . . . . . . . . . . . . . . .
37
2.2.3 The Thin Mirror . . . . . . . . . . . . . . . . . . . . .
40
2.2.4 Liouville’s Theorem for Glass Optics . . . . . . . . . .
41
2.3 Special Optical Systems . . . . . . . . . . . . . . . . . . . . .
43
2.3.1 Imaging (Point–to–Point, • •) Systems . . . . . . . . .
44
2.3.2 Parallel–to–Point ( •) Systems . . . . . . . . . . . . .
45
2.3.3 Point–to–Parallel (• •) Systems . . . . . . . . . . . . .
46
2.3.4 Parallel–to–Parallel ( ) Systems . . . . . . . . . . .
47
2.3.5 Combination Systems . . . . . . . . . . . . . . . . . .
48
3 Fields, Potentials and Equations of Motion
49
3.1 Fields with Straight Reference Orbit . . . . . . . . . . . . . .
50
3.1.1 Expansion in Cylindrical Coordinates . . . . . . . . .
50
3.1.2 Quadrupole Fields . . . . . . . . . . . . . . . . . . . .
53
3.1.3 Sextupole and Higher Multipole Fields . . . . . . . . .
54
3.1.4 s–Dependent Fields . . . . . . . . . . . . . . . . . . .
55
3.2 Fields with Planar Reference Orbit . . . . . . . . . . . . . .
57
3.2.1 The Laplacian in Curvilinear Coordinates . . . . . . .
57
3.2.2 The Potential in Curvilinear Coordinates . . . . . . .
58
3.3 The Equations of Motion in Curvilinear Coordinates . . . . .
60
3.3.1 The Coordinate System and the Independent Variable
60
3.3.2 The Equations of Motion . . . . . . . . . . . . . . . .
65
v
1 Beams and Beam Physics
1
1.1 What Is Beam Physics? . . . . . . . . . . . . . . . . . . . . .
1
1.2 Production of Beams . . . . . . . . . . . . . . . . . . . . . .
4
1.2.1 Electron Sources . . . . . . . . . . . . . . . . . . . . .
4
1.2.2 Proton Sources . . . . . . . . . . . . . . . . . . . . . .
8
1.2.3 Ion Sources . . . . . . . . . . . . . . . . . . . . . . . .
9
1.3 Acceleration of Beams . . . . . . . . . . . . . . . . . . . . . .
10
1.3.1 Electrostatic Accelerators . . . . . . . . . . . . . . . .
12
1.3.2 Linear Accelerators . . . . . . . . . . . . . . . . . . . .
15
1.3.3 Circular Accelerators . . . . . . . . . . . . . . . . . . .
19
2 Linear Beam Optics
31
2.1 Coordinates and Maps . . . . . . . . . . . . . . . . . . . . .
32
2.2 Glass Optics . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
2.2.1 The Drift . . . . . . . . . . . . . . . . . . . . . . . . .
37
2.2.2 The Thin Lens . . . . . . . . . . . . . . . . . . . . . .
37
2.2.3 The Thin Mirror . . . . . . . . . . . . . . . . . . . . .
40
2.2.4 Liouville’s Theorem for Glass Optics . . . . . . . . . .
41
2.3 Special Optical Systems . . . . . . . . . . . . . . . . . . . . .
43
2.3.1 Imaging (Point–to–Point, • •) Systems . . . . . . . . .
44
2.3.2 Parallel–to–Point ( •) Systems . . . . . . . . . . . . .
45
2.3.3 Point–to–Parallel (• •) Systems . . . . . . . . . . . . .
46
2.3.4 Parallel–to–Parallel ( ) Systems . . . . . . . . . . .
47
2.3.5 Combination Systems . . . . . . . . . . . . . . . . . .
48
3 Fields, Potentials and Equations of Motion
49
3.1 Fields with Straight Reference Orbit . . . . . . . . . . . . . .
50
3.1.1 Expansion in Cylindrical Coordinates . . . . . . . . .
50
3.1.2 Quadrupole Fields . . . . . . . . . . . . . . . . . . . .
53
3.1.3 Sextupole and Higher Multipole Fields . . . . . . . . .
54
3.1.4 s–Dependent Fields . . . . . . . . . . . . . . . . . . .
55
3.2 Fields with Planar Reference Orbit . . . . . . . . . . . . . .
57
3.2.1 The Laplacian in Curvilinear Coordinates . . . . . . .
57
3.2.2 The Potential in Curvilinear Coordinates . . . . . . .
58
3.3 The Equations of Motion in Curvilinear Coordinates . . . . .
60
3.3.1 The Coordinate System and the Independent Variable
60
3.3.2 The Equations of Motion . . . . . . . . . . . . . . . .
65
v