  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.
