Space-Charge Transport Limits in Periodic Channels

It has been empirically observed in both experiments and particle-in-cell simulations that space-charge-dominated beams suffer strong emittance growth and particle losses in alternating gradient quadrupole transport channels when the undepressed phase advance σ0increases beyond about 85° per lattice period. Although this criteria has been used extensively in practical designs of intense beam transport lattices, no theory exists that explains the limit. 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. Due to a finite beam edge and/or perturbations, this mechanism can result in dramatic halo-driven increases in statistical beam phase space area, lost particles, and degraded transport. A core-particle model for a uniform density elliptical beam in a periodic focusing lattice is applied to parametrically analyze this process.