Analytical Treatment of Particle-Core Interaction

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.