Does nonlinear integrable optics raise the space-charge limit
In plain words
Special magnet arrangements keep particle orbits regular even when they are nonlinear; whether they still help when the beam's own repulsion is included is unknown.
Precise statement
Nonlinear integrable lattices of the Danilov-Nagaitsev type preserve two invariants of single-particle transverse motion with large amplitude-dependent tune spread. 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.
What would settle it
Self-consistent space-charge simulations and a proton experiment comparing halo and loss for integrable and linear configurations of one ring.