A new class of self-consistent 6-D phase space stationary distributions is constructed both analytically and numerically. The beam is then mismatched longitudinally and/or transversely, and we explore the beam stability and halo formation for the case of 3-D axisymmetric beam bunches using particle-in-cell simulations. We concentrate on beams with bunch length-to-width ratios varying from 1 to 5, which covers the typical range of the APT linac parameters. We find that the longitudinal halo forms first for comparable longitudinal and transverse mismatches. An interesting coupling phenomenon -a longitudinal or transverse halo is observed even for very small mismatches if the mismatch in the other plane is large -is discovered.

A detailed study of the influence of space charge on the crossing of second-order resonances is presented and associated with the space-charge limit of high-intensity rings. Two-dimensional simulation studies are compared with envelope models, which agree in the finding of an increased intensity limit due to the coherent frequency shift. This result is also found for realistic bunched beams with multiturn injection painting. Characteristic features such as the influence of tune splitting, structure resonances, and the role of envelope instabilities are discussed in detail. The theoretical limits are found to be in good agreement with the performance of high-intensity proton machines.

A realistic treatment of halo formation must take into account 3D beam bunches and 6D phase space distributions. We recently constructed, analytically and numerically, a new class of self-consistent 6D phase space stationary distributions, which allowed us to study the halo development mechanism without being obscured by the effect of beam redistribution. In this paper we consider nonstationary distributions and study how the halo characteristics compare with those obtained using the stationary distribution. We then discuss the effect of redistribution on the halo development mechanism. In contrast to bunches with a large aspect ratio, we find that the effect of coupling between the r and z planes is especially important as the bunch shape becomes more spherical. [S1098-4402(98)00025-1]

Resonance-driven collective instabilities of charged-particle beams were extensively studied in connection with high-current transport systems, leading to restrictions imposed on the zero-current phase advance. In this paper, we discuss application of such parametric instabilities to circular machines. This effect is directly related to the space-charge limit in rings and its understanding is of crucial importance. Its relation to the coherent resonance condition of an integer type is explained. Practical application of such resonant responses to both structural and imperfection driven harmonics is addressed.

Uncontrolled beam loss leads to excessive radioactivation in high-intensity machines. At the same time, it strongly affects performance of high-energy accelerators and colliders. For the well controlled beam, the loss is typically associated with the low density halo surrounding beam core. There are many mechanisms which contribute to halo formation. Some of them are more important for linear accelerators while other are more relevant to circular machines. In order to minimize uncontrolled beam loss or improve performance of an accelerator, it is very important to understand what are the sources of halo formation, as well as which of them can have significant contribution for a specific machine of interest. In this paper, we overview various mechanisms of halo formation. We then specifically discuss which effects are expected to be dominant in linear accelerator and which effects dominate in rings, concentrating on high-intensity machines.