Ruisard, KierstenConventional particle accelerators use linear focusing forces for transverse confinement. As a consequence of linearity, accelerating rings are sensitive to myriad resonances and instabilities. At high beam intensity, uncontrolled resonance-driven losses can deteriorate beam quality and cause damage or radio-activation in beam line components and surrounding areas. This is currently a major limitation of achievable current densities in state-of-the-art accelerators. Incorporating nonlinear focusing forces into machine design should provide immunity to resonances through nonlinear detuning of particle orbits from driving terms. A theory of nonlinear integrable beam optics is currently being investigated for use in accelerator rings. Such a system has potential to overcome the limits on achievable beam intensity. This dissertation presents a plan for implementing a proof-of-principle quasi-integrable octupole lattice at the University of Maryland Electron Ring (UMER). UMER is an accelerator platform that supports the study of high-intensity beam dynamics. In this dissertation, two designs are presented that differ in both complexity and strength of predicted effects. A configuration with a single, relatively long octupole magnet is expected to be more stabilizing than an arrangement of many short, distributed octupoles. Preparation for this experiment required the development and characterization of a low-intensity regime previously not operated at UMER. Additionally, required tolerances for the control of first and second order beam moments in the proposed experiments have been determined on the basis of simulated beam dynamics. In order to achieve these tolerances, a new method for improved orbit correction is developed. Finally, a study of resonance-driven losses in the linear UMER lattice is discussed.enDissertationPhysicsElectromagneticsAcceleratorBeam dynamicsCharged particlesNonlinearOctupoleResonance