The Integrable Optics Test Accelerator (IOTA) is being commissioned at Fermi National Laboratory for study of the concept of nonlinear integrable optics. The use of a special nonlinear magnetic element introduces large tune spread with amplitude while constraining the idealized dynamics by two integrals of motion. The nonlinear element should provide suppression of instabilities through nonlinear decoherence. We examine the case of a bunch injected off-axis and the resulting damping of centroid oscillations from decoherence. A simple model of the damping is described and compared to simulation.
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