Statistical phenomena in particle beams

Particle beams are subject to a variety of apparently distinct statistical phenomena such as intrabeam scattering, stochastic cooling, electron cooling, coherent instabilities, and radiofrequency noise diffusion. In fact, both the physics and mathematical description of these mechanisms are quite similar, with the notion of correlation as a powerful unifying principle. In this presentation we will attempt to provide both a physical and a mathematical basis for understanding the wide range of statistical phenomena that have been discussed. In the course of this study the tools of the trade will be introduced, e.g., the Vlasov and Fokker-Planck equations, noise theory, correlation functions, and beam transfer functions. Although a major concern will be to provide equations for analyzing machine design, the primary goal is to introduce a basic set of physical concepts having a very broad range of applicability