  Conventional 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.
