Particle Accelerator Physics II Nonlinear and Higher-Order Beam Dynamics - Wiedemann, Helmut (Springer Berlin Heidelberg, 1995)
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 Hamiltonian 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 kinematic 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, including beam loading, higher-order phase focusing, and the combination of acceleration and transverse focusing, is discussed. The emission of synchrotron 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 polarization