Nonlinear dynamics deals with parametric resonances and di usion. The phenomena are usually beam-intensity independent and rely on a particle Hamiltonian. Collective instabilities deal with beam coherent motion, where the Vlasov equation is frequently used in conjunction with a beam-intensity dependent Hamiltonian. We ad- dress the questions: Are the two descriptions the same? Are collective instabilities the results of encountering parametric resonances whose driving force is intensity depen- dent? We study here the example of a space-charge dominated beam governed by the Kapchinskij-Vladimirskij (K-V) envelope equation [1]. The stability and instability regions as functions of tune depression and envelope mismatch are compared in the two approaches. The study has been restricted to the simple example of a uniformly focusing channel.

Nonlinear dynamics deals with parametric resonances and diffusion, which are usually beam-intensity independent and rely on a particle Hamiltonian. Collective instabilities deal with beam coherent motion, where the Vlasov equation is frequently used in conjunction with a beam-intensity dependent Hamiltonian. The authors address the questions: Are the two descriptions the same? Are collective instabilities the results of encountering parametric resonances whose driving force is intensity dependent? The space-charge dominated beam governed by the Kapchinskij-Vladimirskij (K-V) envelope equation is used as an example.

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."

This indispensable work offers a broad synoptic description of beams, applicable to a wide range of other devices, such as low-energy focusing and transport systems and high-power microwave sources. The monograph develops the material from the basic principles in a systematic way and discusses the underlying physics and validity of theoretical relationships, design formulas and scaling laws. Assumptions and approximations are clearly indicated throughout. This new, revised and updated edition has 10% additional content, and features, among others, a new chapter on beam physics research from 1993 to 2007, significant enhancement of chapter 6 on emittance variation, updated references and color image plates.

An intense charged particle beam can be characterized as an organized charged particle flow for which the effects of beam self-fields are of major importance in describing the evolution of the flow. Research employing such beams is now a rapidly growing field with important applications ranging from the development of high power sources of coherent radiation to inertial confinement fusion. Major programs have now been established at several laboratories in the United States and Great Britain, as well as in the USSR, Japan, and several Eastern and Western European nations. In addition, related research activities are being pursued at the graduate level at several universities in the US and abroad. When the author first entered this field in 1973 there was no single reference text that provided a broad survey of the important topics, yet contained sufficient detail to be of interest to the active researcher. That situation has persisted, and this book is an attempt to fill the void. As such, the text is aimed at the graduate student, or beginning researcher; however, it contains ample information to be a convenient reference source for the advanced worker.

This is a graduate-level text - complete with 75 assigned problems - which covers a broad range of topics related to the fundamental properties of collective processes and nonlinear dynamics of intense charged particle beams in periodic focusing accelerators and transport systems. The subject matter is treated systematically from first principles, using a unified theoretical approach, and the emphasis is on the development of basic concepts that illustrate the underlying physical processes in circumstances where intense self fields play a major role in determining the evolution of the system. The theoretical analysis includes the full influence of dc space charge and intense self-field effects on detailed equilibrium, stability and transport properties, and is valid over a wide range of system parameters ranging from moderate-intensity, moderate-emittance beams to very-high-intensity, low-emittance beams. The statistical models used to describe the properties of intense charged particle beams are based on the Vlasov-Maxwell equations, the macroscopic fluid-Maxwell equations, or the Klimontovich-Maxwell equations, as appropriate.

Detailed enough to serve as both text and reference, this volume addresses topics vital to understanding high-power accelerators and high-brightness-charged particle beams, including stochastic cooling, high-brightness injectors, and the free electron laser. 1990 edition.