Field strength characteristics of nonlinear resonances and halo-chaos

Nonlinear resonances and halo-chaos behavior of an intense charged-particle beam are discussed. The influences of the focusing field strength and the beam perveance about the intense charged-particle beam are analyzed. The beam envelope oscillations and the orbits of the single-particle are simulated by using Poincar mapping technique. The simulation result clearly illustrates the nonlinear oscillations of the beam envelope and the spatial distribution of the corresponding test particle under different conditions. It shows that the beam self-field leads to the nonlinear oscillations of the beam envelope. With the increase of beam self-field and focusing field, a growing number of diffuse particles appear in the particle spatial distribution along with the emergence of the resonance island.