Particle Accelerator Physics II
Nonlinear and Higher-Order Beam Dynamics
1st Edition
Published on 6. December 2012
XVI, 464 pages
978-3-642-97550-9 (ISBN)
Description
This text is a continuation of the first volume of "Particle Accelerator Physics" on "Basic Principles and Linear Beam Dynamics". While the first volume was written as an introductory overview into beam dynamics, it does not include more detailled discussion of nonlinear and higher-order beam dynamics or the full theory of synchrotron radiation from relativistic electron beams. Both issues are, however, of fundamental importance for the design of modern particle accelerators. In this volume, beam dynamics is formulated within the realm of Hamil tonian dynamics, leading to the description of multiparticle beam dynamics with the Vlasov equation and including statistical processes with the Fokker Planck equation. Higher-order perturbations and aberrations are discussed in detail, including Hamiltonian resonance theory and higher-order beam dynamics. The discussion of linear beam dynamics in Vol. I is completed here with the derivation of the general equation of motion, including kine matic terms and coupled motion. To build on the theory of longitudinal motion in Vol. I, the interaction of a particle beam with the rf system, in cluding beam loading, higher-order phase focusing, and the combination of acceleration and transverse focusing, is discussed. The emission of syn chrotron radiation greatly affects the beam quality of electron or positron beams and we therefore derive the detailled theory of synchrotron radiation, including spatial and spectral distribution as well as properties of polariza tion.
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Content
1. Hamiltonian Formulation of Beam Dynamics.- 1.1 Hamiltonian Formalism.- 1.2 Hamiltonian Resonance Theory.- 1.3 Hamiltonian and Coupling.- 1.4 Symplectic Transformation.- Problems.- 2. General Electromagnetic Fields.- 2.1 General Transverse Magnetic-Field Expansion.- 2.2 Third-Order Differential Equation of Motion.- 2.3 Periodic Wiggler Magnets.- 2.4 Superconducting Magnet.- Problems.- 3. Dynamics of Coupled Motion.- 3.1 Conjugate Trajectories.- 3.2 Particle Motion in a Solenoidal Field.- 3.3 Transverse Coupled Oscillations.- 3.3.5 Betatron Functions for Coupled Motion.- Problems.- 4. Higher-Order Perturbations.- 4.1 Kinematic Perturbation Terms.- 4.2 Control of the Central Beam Path.- 4.3 Dipole Field Errors and Dispersion Function.- 4.4 Dispersion Function in Higher Order.- 4.5 Perturbation Methods in Beam Dynamics.- Problems.- 5. Hamiltonian Nonlinear Beam Dynamics.- 5.1 Higher-Order Beam Dynamics.- 5.2 Aberrations.- 5.3 Hamiltonian Perturbation Theory.- Problems.- 6. Charged Particle Acceleration.- 6.1 Accelerating Fields in Resonant rf Cavities.- 6.2 Beam-Cavity Interaction.- 6.3 Higher-Order Phase Focusing.- 6.4 FODO Lattice and Acceleration.- Problems.- 7 Synchrotron Radiation.- 7.1 Theory of Synchrotron Radiation.- 7.2 Synchrotron Radiation Power and Energy Loss.- 7.3 Spatial Distribution of Synchrotron Radiation.- 7.4 Synchrotron Radiation Spectrum.- Problems.- 8. Hamiltonian Many-Particle Systems.- 8.1 The Vlasov Equation.- 8.2 Damping of Oscillations in Electron Accelerators.- 8.3 The Fokker-Planck Equation.- Problems.- 9. Particle Beam Parameters.- 9.1 Particle Distribution in Phase Space.- 9.2 Equilibrium Energy Spread and Bunch Length.- 9.3 Phase-Space Manipulation.- 9.4 Polarization of Particle Beam.- Problems.- 10. Collective Phenomena.- 10.1 Statistical Effects.- 10.2 Collective Self Fields.- 10.3 Beam-Current Spectrum.- 10.4 Wake Fields and Impedance.- 10.5 Coasting-Beam Instabilities.- 10.6 Longitudinal Single-Bunch Effects.- 10.7 Transverse Single-Bunch Instabilities.- 10.8 Multi-Bunch Instabilities.- Problems.- 11. Insertion Device Radiation.- 11.1 Particle Dynamics in an Undulator.- 11.2 Undulator Radiation.- 11.3 Undulator Radiation Distribution.- 11.4 Elliptical Polarization.- Problems.- References.- Author Index.
