The connection between the Van Kampen and Landau representations of the Vlasov equations has been extended to Fourier-Hermite expansions containing more than 1000 terms by taking advantage of the properties of tridiagonal matrices. These numerical results are regarded as conclusive indications of the nonuniformly convergent behavior of the approximation curve in the limit of an infinite number of terms and represent an extension of work begun by Grant (1967) and by Grant and Feix (1967).

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This book provides a comprehensive treatment of intensity dependent particle beam instabilities in accelerating rings. Written for researchers, the material is also suitable for use as a textbook in an advanced graduate course for students studying accelerator physics. The presentation starts with a brief review of the basic concept of wake potentials and coupling impedances in the vacuum chamber followed by a discussion on static and dynamic solutions of their effects on the particle beams. Special emphasis is placed separately on proton and electron machines. Other special topics of interest covered include Landau damping, BalakinOCoNovokhatskyOCoSmirnov damping, Sacherer''s integral equations, Landau cavity, saw-tooth instability, Robinson stability criteria, beam loading, transition crossing, two-stream instabilities, and collective instability issues of isochronous rings. After the formulation of an instability, readers are provided a thorough description of one or more experimental observations together with a discussion of the cures for the instability. Although the book is theory oriented, the use of mathematics has been minimized. The presentation is intended to be rigorous and self-contained with nearly all the formulas and equations derived."

Introductory text for graduate students in physics taking a year-long course in quantum mechanics in which the third quarter is devoted to relativistic wave equations and field theory. Answers to selected problems. 1972 edition.