We present simulation results of 2.5 MeV proton beams in the IOTA ring  with significant space charge tune shift. We consider issues of nonlinearities in the underlying lattice, including dispersion and chromaticity, as well as the impact of incoherent tune shifts on integrable motion.
Tune spread with amplitude suppresses intensity-driven parametric instabilities such as beam halo. Conventional approaches to achieving high tune spreads, such as the use of octupoles, reduce dynamic aperture. The nonlinear integrable optics  promise to introduce large tune spreads with amplitude without introducing resonances that limit the dynamic aperture . The Integrable Optics Test Accelerator (IOTA) is a small ring, currently under construction at Fermilab, which will explore these concepts with low-energy proton beams with at high intensity. The stability of these invariants is particularly sensitive to collective effects such as space charge induced tune shift, as well as intrinsic nonlinearities in the single particle motion, such as dispersion and chromaticity .
We present results from simulations of IOTA using the accelerator simulation package Synergia and the particle-in-cell framework Warp exploring the behavior of proton beams in the IOTA lattice. In the high current regime, we examine potential lattice variations that correct for tune depression and beam mismatch while minimizing deviations from integrability. For operation at low intensity, we consider the nonlinear response due to finite phase advance across the nonlinear magnet as well as nonlinear dispersive and chromatic effects. We present evidence for these effects, and illustrate the sensitivity of the dynamics to sextupole fields, showing that their proper pairing can preserve integrability and reduce beam loss.
 Nagaitsev et al., “Design and Simulation of IOTA – a Novel Concept of Integrable Optics Test Accelerator” (2013) https://arxiv.org/abs/1301.7032
 V. Danilov and S. Nagaitsev, Phys. Rev. ST-AB 13, 84002 (2010).
 S. Webb et al., “Effects of Nonlinear Decoherence on Halo Formation” (2013) http://arxiv.org/abs/1205.7083
 S. Webb et al., “Chromatic and Dispersive Effects in Nonlinear Integrable Optics” (2015), submitted to PRSTAB; http://arxiv.org/abs/1504.05981
This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics under Award Number DE-SC0011340.
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