Error tolerance of nonlinear integrable accelerator lattices
In plain words
Specially designed nonlinear magnets make orbits regular in theory; how much of that survives real magnet errors and energy spread is open.
Precise statement
Danilov-Nagaitsev nonlinear integrable optics keeps two invariants of transverse motion for a special elliptic potential inserted in a drift whose outside lattice acts as a phase-advance-pi lens. Determine the tune spread and dynamic aperture that survive relative magnet errors of $10^{-4}$, chromaticity, and synchrotron motion with energy spread $10^{-3}$, and compare with measurements of amplitude-dependent tune shift at IOTA.
What would settle it
Tracking with measured error models reproducing IOTA tune-spread and invariant-conservation data, plus tolerances stated for a proton ring.
Status in the literature
Electron experiments at the Fermilab IOTA ring from about 2019 reported quasi-integrable motion with large tune spread; tolerances to chromatic and error effects remain to be quantified.
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