The exploration of the characteristics of periodically focused intense charged particle beams is one of the main thrusts in beam physics research and is critical to many advanced accelerator applications such as heavy ion fusion. In this paper, we discuss several novel effects induced by the self-electric and self-magnetic fields of an intense beam in a periodic focusing channel consisting of either a periodic solenoidal field or an alternating-gradient quadrupole magnetic field. It is shown that the self fields induce rich nonlinear resonances and chaotic behavior in the envelope oscillations of mismatched beams. A parametric instability threshold is derived analytically for halo formation in a mismatched space-charge-dominated beam and is found to be in good agreement with two-dimensional particle-in-cell simulations. For envelope-matched beams with nonuniform density profiles, single-particle orbits are also found to exhibit nonlinear resonances and chaotic behavior in high-current regimes, suggesting a microscopic mechanism for emittance growth. The implications of these findings are discussed regarding the design of high-current accelerators and high-current transport systems.
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