xii
List of Figures
9.1 Sketch of a FODO cell without bending magnets. . . . . . . . 208
9.2 The “necktie” diagram showing the stability region of a FODO
cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
9.3 Sketch of a FODO cell with bending magnets. . . . . . . . . . 209
9.4 Lattice functions of a FODO cell at the Fermilab Main Injector. 212
9.5 The simplest double-bend achromat. . . . . . . . . . . . . . 230
9.6 The double-bend achromat. . . . . . . . . . . . . . . . . . . 230
9.7 Lattice functions of a double-bend achromat. . . . . . . . . . 231
9.8 The triple-bend achromat. . . . . . . . . . . . . . . . . . . . 231
9.9 Lattice functions of a triple-bend achromat of the Advanced
Light Source. . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
9.10 Lattice functions of the MAX IV multiple-bend achromat lattice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
9.11 Lattice functions of a typical low beta insertion with symmetric
quadrupole triplets. . . . . . . . . . . . . . . . . . . . . . . . . 236
9.12 Layout of the chicane bunch compressor. . . . . . . . . . . . . 237
9.13 Mechanism of an RF buncher cavity. . . . . . . . . . . . . . . 240
10.1 Typical RF cavity field with fundamental mode TM 010 . . . . 242
10.2 Dependence of transit time factor on length of the cavity. . . 246
10.3 Sketch of phase stability for energy below transition. . . . . . 249
10.4 Sketch of phase stability for energy above transition. . . . . . 250
10.5 Phase space plots of longitudinal motion with φ s = π/2 and
φ s = π/3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
10.6 Longitudinal and transverse field distribution along the longitudinal axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
11.1 Distinct eigenvalues around the unit circle. . . . . . . . . . . 277
11.2 Crossing the difference resonance. . . . . . . . . . . . . . . . . 279
11.3 Invariant obtained through first order perturbation theory and
tracking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
11.4 Invariant obtained through first order perturbation theory and
tracking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
List of Figures
9.1 Sketch of a FODO cell without bending magnets. . . . . . . . 208
9.2 The “necktie” diagram showing the stability region of a FODO
cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
9.3 Sketch of a FODO cell with bending magnets. . . . . . . . . . 209
9.4 Lattice functions of a FODO cell at the Fermilab Main Injector. 212
9.5 The simplest double-bend achromat. . . . . . . . . . . . . . 230
9.6 The double-bend achromat. . . . . . . . . . . . . . . . . . . 230
9.7 Lattice functions of a double-bend achromat. . . . . . . . . . 231
9.8 The triple-bend achromat. . . . . . . . . . . . . . . . . . . . 231
9.9 Lattice functions of a triple-bend achromat of the Advanced
Light Source. . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
9.10 Lattice functions of the MAX IV multiple-bend achromat lattice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
9.11 Lattice functions of a typical low beta insertion with symmetric
quadrupole triplets. . . . . . . . . . . . . . . . . . . . . . . . . 236
9.12 Layout of the chicane bunch compressor. . . . . . . . . . . . . 237
9.13 Mechanism of an RF buncher cavity. . . . . . . . . . . . . . . 240
10.1 Typical RF cavity field with fundamental mode TM 010 . . . . 242
10.2 Dependence of transit time factor on length of the cavity. . . 246
10.3 Sketch of phase stability for energy below transition. . . . . . 249
10.4 Sketch of phase stability for energy above transition. . . . . . 250
10.5 Phase space plots of longitudinal motion with φ s = π/2 and
φ s = π/3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
10.6 Longitudinal and transverse field distribution along the longitudinal axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
11.1 Distinct eigenvalues around the unit circle. . . . . . . . . . . 277
11.2 Crossing the difference resonance. . . . . . . . . . . . . . . . . 279
11.3 Invariant obtained through first order perturbation theory and
tracking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
11.4 Invariant obtained through first order perturbation theory and
tracking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287