x
List of Figures
1.22 Layout of the Super-ACO light source storage ring at Laboratoire pour l’Utilisation du Rayonnement Electromagn´ etique,
Orsay, France. . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
1.23 Layout of the Advanced Light Source (ALS) at Lawrence Berkeley National Laboratory, California, USA. . . . . . . . . . . .
29
2.1 Reference orbit, arc length s along it and local coordinates. .
32
2.2 Motion of particles inside the tube with radius r tube around the
reference orbit. . . . . . . . . . . . . . . . . . . . . . . . . . .
33
2.3 A ray passing through a drift. . . . . . . . . . . . . . . . . . .
37
2.4 A bundle of parallel rays passing through a focusing lens. . .
38
2.5 A bundle of parallel rays passing through a defocusing lens. .
39
2.6 A bundle of parallel rays is reflected by the focusing mirror. .
41
2.7 Liouville’s theorem. . . . . . . . . . . . . . . . . . . . . . . . .
42
2.8 Poincar´ e’s recurrence theorem. . . . . . . . . . . . . . . . . .
43
2.9 Sketch of an imaging system. . . . . . . . . . . . . . . . . . .
44
2.10 Sketch of a parallel–to–point system. . . . . . . . . . . . . . .
46
2.11 Sketch of a point–to–parallel system. . . . . . . . . . . . . . .
46
2.12 Sketch of a parallel–to–parallel system. . . . . . . . . . . . . .
47
3.1 Ideal electrodes of an electrostatic quadrupole. . . . . . . . .
54
3.2 The s-dependence of the multipole strength. . . . . . . . . . .
55
3.3 Scalar potential, longitudinal and radial field distribution of a
rotationally symmetric lens. . . . . . . . . . . . . . . . . . . .
56
3.4 Reference orbit of a bending magnet. . . . . . . . . . . . . . .
57
3.5 The curvilinear coordinates in the plane of the reference orbit. 62
4.1 A homogeneous magnetic dipole. . . . . . . . . . . . . . . . .
73
4.2 Entrance and exit edge lines of a dipole magnet. . . . . . . .
77
4.3 Mechanism of edge focusing for the horizontal plane and the
vertical plane. . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
4.4 An inhomogeneous sector magnet. . . . . . . . . . . . . . . .
82
4.5 An electric capacitor consisting of two parallel plates. The orbit
of a particle is parabolic. . . . . . . . . . . . . . . . . . . . . .
84
4.6 A concentric electric deflector. . . . . . . . . . . . . . . . . . .
84
4.7 An electric deflector with cylindrical plates. . . . . . . . . . .
86
4.8 An electric deflector with spherical plates. . . . . . . . . . . .
86
4.9 Layout and potential profile of the electrostatic three-plate
round lens. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
4.10 Transversal motion of particles entering initially parallel to the
reference axis in the magnetic solenoid. . . . . . . . . . . . . . 100
5.1 Trajectories of particles in a system with horizontal midplane
symmetry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.2 Motion in a 90 ◦ homogeneous dipole magnet. . . . . . . . . . 135
6.1 Mapping of individual points in phase space. . . . . . . . . . 141
6.2 Mapping of a closed curve in phase space. . . . . . . . . . . . 142
6.3 Action of a drift in phase space. . . . . . . . . . . . . . . . . . 143
6.4 Action of a thin lens in phase space. . . . . . . . . . . . . . . 144
List of Figures
1.22 Layout of the Super-ACO light source storage ring at Laboratoire pour l’Utilisation du Rayonnement Electromagn´ etique,
Orsay, France. . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
1.23 Layout of the Advanced Light Source (ALS) at Lawrence Berkeley National Laboratory, California, USA. . . . . . . . . . . .
29
2.1 Reference orbit, arc length s along it and local coordinates. .
32
2.2 Motion of particles inside the tube with radius r tube around the
reference orbit. . . . . . . . . . . . . . . . . . . . . . . . . . .
33
2.3 A ray passing through a drift. . . . . . . . . . . . . . . . . . .
37
2.4 A bundle of parallel rays passing through a focusing lens. . .
38
2.5 A bundle of parallel rays passing through a defocusing lens. .
39
2.6 A bundle of parallel rays is reflected by the focusing mirror. .
41
2.7 Liouville’s theorem. . . . . . . . . . . . . . . . . . . . . . . . .
42
2.8 Poincar´ e’s recurrence theorem. . . . . . . . . . . . . . . . . .
43
2.9 Sketch of an imaging system. . . . . . . . . . . . . . . . . . .
44
2.10 Sketch of a parallel–to–point system. . . . . . . . . . . . . . .
46
2.11 Sketch of a point–to–parallel system. . . . . . . . . . . . . . .
46
2.12 Sketch of a parallel–to–parallel system. . . . . . . . . . . . . .
47
3.1 Ideal electrodes of an electrostatic quadrupole. . . . . . . . .
54
3.2 The s-dependence of the multipole strength. . . . . . . . . . .
55
3.3 Scalar potential, longitudinal and radial field distribution of a
rotationally symmetric lens. . . . . . . . . . . . . . . . . . . .
56
3.4 Reference orbit of a bending magnet. . . . . . . . . . . . . . .
57
3.5 The curvilinear coordinates in the plane of the reference orbit. 62
4.1 A homogeneous magnetic dipole. . . . . . . . . . . . . . . . .
73
4.2 Entrance and exit edge lines of a dipole magnet. . . . . . . .
77
4.3 Mechanism of edge focusing for the horizontal plane and the
vertical plane. . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
4.4 An inhomogeneous sector magnet. . . . . . . . . . . . . . . .
82
4.5 An electric capacitor consisting of two parallel plates. The orbit
of a particle is parabolic. . . . . . . . . . . . . . . . . . . . . .
84
4.6 A concentric electric deflector. . . . . . . . . . . . . . . . . . .
84
4.7 An electric deflector with cylindrical plates. . . . . . . . . . .
86
4.8 An electric deflector with spherical plates. . . . . . . . . . . .
86
4.9 Layout and potential profile of the electrostatic three-plate
round lens. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
4.10 Transversal motion of particles entering initially parallel to the
reference axis in the magnetic solenoid. . . . . . . . . . . . . . 100
5.1 Trajectories of particles in a system with horizontal midplane
symmetry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.2 Motion in a 90 ◦ homogeneous dipole magnet. . . . . . . . . . 135
6.1 Mapping of individual points in phase space. . . . . . . . . . 141
6.2 Mapping of a closed curve in phase space. . . . . . . . . . . . 142
6.3 Action of a drift in phase space. . . . . . . . . . . . . . . . . . 143
6.4 Action of a thin lens in phase space. . . . . . . . . . . . . . . 144