New regions of stability for periodically focused particle beams

In this paper we perform a comprehensive analysis of the transport of periodically focused particle beams within the new regions of stability recently found [R. Pakter and F. B. Rizzato, Phys. Rev. Lett., 87, 044801 (2001)] for vacuum phase advances well above the 90 degrees threshold. In particular, we investigate the stability as a function of the relevant parameters of the system, such as beam intensity and focusing field profile. Self-consistent numerical simulations are used to verify the findings.