Phenomenology of creation of antihydrogen and measurement of antihydrogen properties

This dissertation focuses on three ideas useful to the nonneutral plasma experiment atUC Berkeley and the ALPHA experiment at CERN. While these may seem like disparateideas, in all cases, a careful mathematical treatment of the problems yield useful insights.First, we present improvements to the analysis for diagnostics of temperature and den-sity of plasmas in Penning-Malmberg trap experiments. Our new methods are faster andmore accurate than previously used methods of analysis. This allows us to conduct thesediagnostics in real-time without any input from a human.We then theoretically consider the problem of enhanced cooling of an electron plasmafrom a coupling of the plasma to cavity modes. We make more rigorous the previous analysisthat was done on the topic, and then extend these results to a longitudinally dynamic plasma.We compare our theoretical results with experimental observations from the Berkeley plasmatrap and with simulations and find good agreement.Finally, we consider analyses of ALPHA data to measure antihydrogen properties. Weplace a statistically rigorous bound on the antihydrogen charge from ALPHA data. Thisimproves the previous bound on antihydrogen charge by a factor of 20, and assuming super-position, improves the bound on the positron charge anomaly by a factor of 25. Finally, weconsider analyses for a future measurement of the gravitational mass of antihydrogen. Wefind that with reasonable constraints, a measurement of the gravitational mass of antihydro-gen with a precision of 1% should be feasible