Classical Mechanics and Electromagnetism in Accelerator Physics

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This self-contained textbook offers a comprehensive exploration of classical mechanics and electromagnetic theory as they relate to modern accelerators. Part I covers the fundamentals of Lagrangian and Hamiltonian mechanics, including canonical transformations, action-angle variables, and both linear and nonlinear oscillators. It utilizes the Hamiltonian for circular accelerators to analyze equations of motion, action, and betatron oscillations. The section also addresses the effects of field errors and nonlinear resonances, culminating in an introduction to the distribution function and kinetic equations for large ensembles of charged particles, enhancing the understanding of beam dynamics. Part II shifts focus to classical electromagnetism, beginning with an examination of electromagnetic fields from relativistic beams in various environments. It discusses plane electromagnetic waves, waveguides, and radio-frequency cavities, followed by radiation processes of relativistic beams, including transition, diffraction, synchrotron, and undulator radiation. Key concepts such as retarded time, coherent and incoherent radiation, and radiation formation length are introduced. The text concludes with insights into laser-driven acceleration and radiation damping effects. Appendices on electromagnetism and special relativity are included, along with references for further study. This resource is designed for graduate students new to ac