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.

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.

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.

A semianalytic formalism was recently developed for investigating the transverse dynamics of a mismatched, space-charge-dominated beam propagating through a focusing channel. It uses the Fokker-Planck equation to account for the rapid evolution of the coarse-grained distribution function in the phase space of a single beam particle. A simple model of dynamical friction and diffusion represents the effects of turbulence resulting from charge redistribution. The initial application was to sheet beams. In this paper, the formalism is generalized to fully two-dimensional beams.

Proceedings of the October 1995 workshop on space charge dominated beams, which took a close look at major breakthroughs of the past few years. The workshop results are organized in sections on topics of general interest; experiments with space charge dominated beams and halo formation; statistical

In space-charge dominated beams the nonlinear space-charge forces produce a filamentation pattern, which results in a 2-component beam consisting of an inner core and an outer halo. The halo is very prominent in mismatched beams, and the potential for accelerator activation is of concern for a next generation of cw, high-power proton linacs that could be applied for intense neutron generators to process nuclear materials. We present new results about beam halo and the evolution of space-charge dominated beams from multiparticle simulation of initial laminar beams in a uniform linear focusing channel, and from a model consisting of single particle interactions with a uniform-density beam core. We study the energy gain from particle interactions with the space-charge field of the core, and we identify the resonant characteristic of this interaction as the basic cause of the separation of the beam into the two components. We identify three different particle-trajectory types, and we suggest that one of these types may lead to continuous halo growth, even after the halo is removed by collimators.