Space-charge transport limits of ion beams in periodic quadrupole focusing channels

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 σ 0 increases beyond about 85 ∘ 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 strongly chaotic 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 is employed to better quantify properties of the space-charge limits and to verify core–particle model predictions.