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Determine whether, for a beam with $\\left|\\Delta Q_{\\mathrm{sc}}\\right| \\sim 0.1\\text{-}0.5$, a ring with such an insert shows lower halo growth and loss than an equivalent linear lattice, either through a self-consistent equilibrium that keeps the invariants or through Landau damping of envelope and coherent resonances.","problem_ref":"d96f4dd373bea031deac17c645f7c7f1fe02050e04d9bf09cf1847be1d3faf78","references":"","settled_by":"Self-consistent space-charge simulations and a proton experiment comparing halo and loss for integrable and linear configurations of one ring.","status_note":"","title":"Does nonlinear integrable optics raise the space-charge 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