An advanced spectral analysis of a mis-matched charged particle beam propagating through a periodic focusing transport lattice is utilized in particle-in-cell (PIC) simulations. It is found that the betatron frequency distribution function of a mismatched space-charge-dominated beam has a bump-on-tail structure attributed to the beam halo particles. Based on this observation, a new spectral method for halo particle definition is proposed that provides the opportunity to carry out a quantitative analysis of halo particle production by a beam mismatch. In addition, it is shown that the spectral analysis of the mismatch relaxation process provides important insights into the emittance growth attributed to the halo formation and the core relaxation processes. Finally, the spectral method is applied to the problem of space-charge transport limits.

High-power proton linacs for nuclear materials transmutation and production, and new accelerator-driven neutron spallation sources must be designed to control beam-halo formation, which leads to beam loss. The study of particle-core models is leading to a better understanding of the causes and characteristics of beam halo produced by space-charge forces in rms mismatched beams. Detailed studies of the models have resulted in predictions of the dependence of the maximum amplitude of halo particles on a mismatch parameter and on the space-charge tune-depression ratio. Scaling formulas have been derived which will provide guidance for choosing the aperture radius to contain the halo without loss.

We present an overview of the status of ongoing work on physics models describing beam matching and halo control for particle accelerators, particularly high power ion linacs. We consider moments and various new variables that more naturally describe beam halo evolution. We compute matched beams and ''mode invariants'' (analogs of moment invariants) using primarily symbolic techniques.

The Spallation Neutron Source (SNS), being built at the Oak Ridge National Laboratory, utilizes a high intensity particle accelerator for neutron production. One of the challenges in SNS, as with all high intensity accelerators, is to minimize the amount of beam lost. High beam losses can cause costly damage and lead to residual activation of accelerator components, which complicates routine maintenance. One of the key components in beam loss at SNS is the development and propagation of beam halo. Halo particles are those driven to large amplitudes by space charge forces between the beam particles or by mismatch between the beam and the accelerator optics. The research presented seeks to develop computational tools to quantify the halo in a beam by analyzing beam profiles and identifying the halo using the Gaussian area ratio and kurtosis methods. Simulations of various configurations using three types of initial simulated distributions, along with an analysis of their phase space and rms properties, provides insight into the development of halo in the SNS linear accelerator. Finally, comparisons with machine beam profile data, taken at the same conditions as that of the simulated data, shows how accurately the simulations model the beam and its halo development and provides a better understanding of the best machine configuration with which to minimize beam halo and losses. Results of simulated data are independent of the initial distribution for strongly mismatched cases; however, even relatively well matched cases generate some halo. Core analysis reveals an increase in beam size as halo decreases for simulated cases. Experimental comparison with simulation results shows poor correlation between halo plots but moderate agreement in profile plots.

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.

Particle Accelerator Physics covers the dynamics of relativistic particle beams, basics of particle guidance and focusing, lattice design, characteristics of beam transport systems and circular accelerators. Particle-beam optics is treated in the linear approximation including sextupoles to correct for chromatic aberrations. Perturbations to linear beam dynamics are analyzed in detail and correction measures are discussed, while basic lattice design features and building blocks leading to the design of more complicated beam transport systems and circular accelerators are studied. Characteristics of synchrotron radiation and quantum effects due to the statistical emission of photons on particle trajectories are derived and applied to determine particle-beam parameters. The discussions specifically concentrate on relativistic particle beams and the physics of beam optics in beam transport systems and circular accelerators such as synchrotrons and storage rings. This book forms a broad basis for further, more detailed studies of nonlinear beam dynamics and associated accelerator physics problems, discussed in the subsequent volume.