Abstract
High-intensity beams in modern linacs are frequently encircled by diffuse halos, which drive sustained particle losses and result in the gradual degradation of accelerating structures. In large part, the growth of halos is facilitated by internal space-charge forces within the beams, and detailed characterization of this process constitutes an active area of ongoing research. A partial understanding of dynamics that ensue within space-charge dominated beams is presented by the particle-core interaction paradigm—a mathematical model wherein single particle dynamics, subject to the collective potential of the core, is treated as a proxy for the broader behavior of the beam. In this work, we investigate the conditions for the onset of large-scale chaos within the framework of this model and demonstrate that the propensity toward stochastic evolution is strongly dependent upon the charge distribution of the beam. In particular, we show that while particle motion within a uniformly charged beam is dominantly regular, rapid deterministic chaos readily arises within space-charge dominated Gaussian beams. Importantly, we find that for sufficiently high values of the beam's space charge and beam pulsation amplitude, enhanced chaotic mixing between the core and the halo can lead to an enhanced radial diffusion of charged particles. We explain our results from analytic grounds by demonstrating that chaotic motion is driven by the intersection of two principal resonances of the system and derives the relevant overlap conditions. Additionally, our analysis illuminates a close connection between the mathematical formulation of the particle-core interaction model and the Andoyer family of integrable Hamiltonians.
Highlights
An important and long-standing challenge to the performance of high-intensity particle accelerators is presented by the emergence of halos around space-charge dominated beams
The results presented in the proceeding section may illuminate the underlying structure of the even for large core pulsation amplitude (∆ = 0.4), particle motion remains quasi-periodic, as indicated by the fact that all trajectories fall on invariant tori
Lattice misalignments and beam mis-steering, together with nonlineaities arising from the RF field and focusing elements, act to restore the Gaussian nature of the beam, suggesting that while chaotic diffusion within the particle core interaction model is driven by nonlinear space-charge forces, the very nonlinearity of these effects are maintained through extrinsic forcing
Summary
An important and long-standing challenge to the performance of high-intensity particle accelerators is presented by the emergence of halos around space-charge dominated beams. That even though the appearance of nonlinear resonances and the materialization of chaotic bands in phasespace have been routinely observed in numerical simulations of the particle-core interaction model, the phasespace attributes of these resonances, the specific conditions for the onset of large-scale chaos, as well as the dependence of the beam’s stochastic behavior on its radial charge distribution remain to be quantified from analytic grounds. Carrying out this analysis is the primary purpose of this paper.
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