Nonlinear dynamics of periodically focused intense particle beams

We extend a previous study [R. Pakter and F. B. Rizzato, Phys. Rev. Lett. 87, 044801 (2001)] and investigate the nonlinear dynamics of periodically focused intense particle beams. We show that (i) the scenario as the focusing field increases is not the existence of a single threshold above which stable matched (equilibrium) solutions are absent, as believed so far, but the existence of successive regions of stability interrupted by gaps where periodic solutions are either unstable or simply do not exist; (ii) the beam can be focused to tighter radii using stable matched solutions found for focusing field strengths greater than the previous threshold. A comprehensive analysis is carried out as a function of the relevant parameters of the system. Self-consistent simulations validate the findings. The gaps are of crucial importance because they must be avoided if the goal is beam confinement with matched solutions; we develop an analytical model to determine the gap structure, which agrees well with computer simulations.