Current designs for muon accelerators require high-gradient radio frequency (RF) cavities to be placed in solenoidal magnetic fields. These... Show moreCurrent designs for muon accelerators require high-gradient radio frequency (RF) cavities to be placed in solenoidal magnetic fields. These fields help contain and efficiently reduce the phase space volume of source muons in order to create a usable muon beam for collider and neutrino experiments. In this context and in general, the use of RF cavities in strong magnetic fields has its challenges. It has been found that placing normal conducting RF cavities in strong magnetic fields reduces the threshold at which RF cavity breakdown occurs. To aid the effort to study RF cavity breakdown in magnetic fields, it would be helpful to have a diagnostic tool which can localize the source of breakdown sparks inside the cavity. These sparks generate thermal shocks to small regions of the inner cavity wall that can be detected and localized using microphones attached to the outer cavity surface. Details on RF cavity sound sources as well as the hardware, software, and algorithms used to localize the source of sound emitted from breakdown thermal shocks are presented. In addition, results from simulations and experiments on three RF cavities, namely the Aluminum Mock Cavity, the High-Pressure Cavity, and the Modular Cavity, are also given. These results demonstrate the validity and effectiveness of the described technique for acoustic localization of breakdown. Ph.D. in Physics, July 2016 Show less