Chaotic dynamics driven by particle-core interactions

TL;DR

This paper investigates how particle-core interactions in high-intensity beams can lead to chaos, especially in Gaussian beams, affecting beam stability and particle diffusion, with implications for accelerator design.

Contribution

It demonstrates the conditions under which large-scale chaos arises in particle-core models, highlighting the influence of charge distribution and resonance overlap.

Findings

Chaotic motion is more prevalent in Gaussian beams than uniform beams.

High space charge and pulsation amplitude promote chaotic mixing and particle diffusion.

Chaos is driven by resonance intersection, explained through analytic resonance overlap conditions.

Abstract

High-intensity beams in modern linacs are frequently encircled by diffuse halos, which drive sustained particle losses and result in 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, are 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 towards 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 derive 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.