  Integrable optics is an innovation in particle accelerator design that
enables strong nonlinear focusing without generating parametric resonances. We
use the Synergia tracking code to investigate the application of integrable
optics to high-intensity hadron rings. We consider an integrable rapid-cycling
synchrotron (iRCS) designed to replace the Fermilab Booster. We find that
incorporating integrability into the design suppresses the beam halo generated
by a mismatched KV beam. Our iRCS design includes other features of modern ring
design such as low momentum compaction factor and harmonically canceling
sextupoles. Experimental tests of high-intensity beams in integrable lattices
will take place over the next several years at the Fermilab Integrable Optics
Test Accelerator (IOTA) and the University of Maryland Electron Ring (UMER).
