Analytical treatment of particle–core interaction

Particle–core interaction is a well-developed model of halo formation in high-intensity beams. In this paper, we present an analytical solution for averaged, single particle dynamics, around a uniformly charged beam. The problem is analyzed through a sequence of canonical transformations of the Hamiltonian, which describes nonlinear particle oscillations. A closed form expression for maximum particle deviation from the axis is obtained. The results of this study are in good agreement with numerical simulations and with previously obtained data.