  It has been empirically observed in both experiments and particle-in-cell
simulations that space-charge-dominated beams suffer strong growth in
statistical phase-space area (degraded quality) and particle losses in
alternating gradient quadrupole transport channels when the undepressed phase
advance sigma_0 increases beyond about 85 degrees per lattice period. Although
this criterion has been used extensively in practical designs of strong
focusing intense beam transport lattices, the origin of the limit has not been
understood. We propose a mechanism for the transport limit resulting from
classes of halo particle resonances near the core of the beam that allow
near-edge particles to rapidly increase in oscillation amplitude when the
space-charge intensity and the flutter of the matched beam envelope are both
sufficiently large. When coupled with a diffuse beam edge and/or perturbations
internal to the beam core that can drive particles outside the edge, this
mechanism can result in large and rapid halo-driven increases in the
statistical phase-space area of the beam, lost particles, and degraded
transport. A core-particle model is applied to parametrically analyze this
process. Extensive self-consistent particle in cell simulations are employed to
better quantify space-charge limit and verify core-particle model predictions.
