Increasingly complicated accelerator systems depend more and more on computing power and computer simulations for their operation as progress in the field has led to cutting-edge advances that require finer control and better understanding to achieve optimal performance. Greater ambitions coupled with the technical complexity of today's state-of-the-art accelerators necessitate corresponding advances in available accelerator modeling resources. Modeling is a critical component of any field of physics, accelerator physics being no exception. It is extremely important to not only understand the basic underlying physics principles but to implement this understanding through the development of relevant modeling tools that provide the ability to investigate and study various complex effects. Moreover, these tools can lead to new insight and applications that facilitate control room operations and enable advances in the field that would not otherwise be possible. The ability to accurately model accelerator systems aids in the successful operation of machines designed specifically to deliver beams to experiments across a wide variety of fields, ranging from material science research to nuclear astrophysics. One such accelerator discussed throughout this work is the ReA facility at the National Superconducting Cyclotron Laboratory (NSCL) which re-accelerates rare isotope beams for nuclear astrophysics experiments. A major component of the ReA facility, as well as the future Facility for Rare Isotope Beams (FRIB) among other accelerators, is the Quarter-Wave Resonator (QWR), a coaxial accelerating cavity convenient for efficient acceleration of low-velocity particles. This device is very important to model accurately as it operates in the critical low-velocity region where the beam's acceleration gains are proportionally larger than they are through the later stages of acceleration. Compounding this matter, QWRs defocus the beam, and are also asymmetric with respect to the beam pipe, which has the potential to induce steering on the beam. These additional complications make this a significant device to study in order to optimize the accelerator's overall performance. The NSCL and ReA, along with FRIB, are first introduced to provide background and motivate the central modeling objectives presented throughout this work. In the next chapter, underlying beam physics principles are then discussed, as they form the basis from which modeling methods are derived. The modeling methods presented include multi-particle tracking and beam envelope matrix transport. The following chapter investigates modeling elements in more detail, including quadrupoles, solenoids, and coaxial accelerating cavities. Assemblies of accelerator elements, or lattices, have been modeled as well, and a method for modeling multiple charge state transport using linear matrix methods is also given.Finally, an experiment studying beam steering induced by QWR resonators is presented, the first systematic experimental investigation of this effect. As mentioned earlier, characterization of this steering on beam properties is important for accurate modeling of the beam transport through the linac. The measurement technique devised at ReA investigates the effect's dependence on the beam's vertical offset within the cavity, the cavity amplitude, and the beam energy upon entrance into the cavity. The results from this experiment agree well with the analytical predictions based on geometrical parameters calculated from on-axis field profiles. The incorporation of this effect into modeling codes has the potential to speed up complex accelerator operations and tuning procedures in systems using QWRs.
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