Analytical Treatment of Particle-Core Interaction

TL;DR

This paper presents an analytical solution for particle dynamics around a uniformly charged beam core, providing insights into halo formation in high-intensity beams and validating results with simulations.

Contribution

It introduces a novel analytical approach to model particle-core interactions using canonical transformations, enhancing understanding of beam halo formation.

Findings

Analytical expression for maximum particle deviation derived

Results agree well with numerical simulations

Provides new insights into nonlinear particle oscillations

Abstract

Particle-core interaction is the well-developed model of halo formation in high-intensity beams. In present paper an analytical solution for averaged single particle dynamics around uniformly charged beam core is obtained. The problem is analyzed through sequence of canonical transformations of Hamiltonian describing nonlinear particle oscillations. An analytical expression for maximum particle deviation from the axis is obtained. Results of the study are in good agreement with numerical simulations and with previously achieved data.