Neutrinos are fundamental particles in the standard model and play an important role in the current understanding of the universe; however, the mass of the neutrino one of the most fundamental parameters for any particle, is currently unknown. This fact represents a gaping hole in our current knowledge of the universe that may provide clues to the energy scale of physics beyond the standard model. This dissertation summarizes research and development as a member of the Project 8 collaboration towards an experiment to measure the neutrino mass with a sensitivity below $50$~$\mathrm{meV}/\mathrm{c}^2$, which is an order of magnitude less than the most sensitive direct measurements of the neutrino mass to date. Project 8 will perform this measurement using Cyclotron Radiation Emission Spectroscopy (CRES) to measure the beta-decay endpoint spectrum of atomic tritium. I present an analysis of the signal reconstruction performance of an antenna array system designed to perform large-scale CRES measurements in cubic-meter volumes. Next, I discuss an approach to calibrating an antenna-based CRES experiment using a unique probe antenna designed to mimic radiation from CRES events. Finally, I present design studies for a resonant cavity that could be used to perform a CRES experiment with atomic tritium at multi-cubic-meter scales.

This volume offers a valuable insight into various aspects of the ongoing work directed at measuring neutrino mass. It took twenty years to refute the assertions of Bethe and Peierls that neutrinos were not observable, but it has since been realised that much can be learnt from these particles. The moral is, as Fiorini argues here, that the study of neutrinos was and remains demanding but rewarding. Subjects addressed in this volume include; clarifying the meaning of the Klapdor-Kleingrothaus results, probing the Majorana nature of neutrinos, observing lepton number violating effects for the first time, studying the end point of the spectrum in the search for neutrino masses and speculating whether it is possible to measure neutrino masses in cosmology. Lectures are enriched with rich historical overviews and valuable introductory material. Attention is also given to theoretical topics such as the evolution of the concept of mass in particle physics, a status report on neutrino oscillations and current discussion on neutrino masses. The reader is further reminded that neutrino masses may also have some bearing on the very origin of the matter among us, and have many deep links with other important lines of current physics research.

This thesis documents efforts performed in the service to two direct neutrino mass experiments, namely KATRIN at the Karlsruhe Institute of Technology in Karlsruhe, Germany and Project8 at the University of Washington in Seattle. These experiments aim to utilize a measurement of the shape of the endpoint of the tritium beta decay spectrum to determine the neutrino mass, which is a technique that relies only on basic kinematics and enjoys a long and distinguished history. Additionally, these experiments utilize classical electrodynamics in their analysis of the beta electron spectrum, at KATRIN through the use of a MAC-E filter and at Project8 through magnetic confinement of electrons within a waveguide and the measurement of their weakly energy dependent relativistic cyclotron frequencies, which is an entirely new technique. In the thesis, both experiments are described in detail with particular attention paid to the components involved in energy analysis. Exploiting these experiments' similarities, an extensive simulation package called KASSIOPEIA has been prepared, which is the principal effort described herein. KASSIOPEIA is applied to both KATRIN and Project8, which in the case of KATRIN delivers valuable and detailed information regarding the performance of the electrostatic spectrometers used there, in particular the main and monitor spectrometers. In its application to Project8, KASSIOPEIA is used to determine precise electron trajectories, which can be used to simulate the signals these electrons induce in the waveguide. This thesis also includes experimental results obtained at the monitor spectrometer of the KATRIN experiment, which demonstrate the efficacy of the magnetic pulse technique at ejecting problematic stored electrons at MAc-E filters. The magnetic pulse technique relies on using a set of external aircoils surrounding a MAC-E filter to reverse and rapidly restore the magnetic field in the spectrometer symmetry plane, causing stored particle to hit the vessel walls. Owing to its success as demonstrated in this work, this technique will be employed at the main spectrometer during the upcoming data taking run at KATRIN. Finally, this thesis presents some results from the inaugural run at Project8, which showed that the theretofore undemonstrated technique, named Cyclotron Radiation Emission Spectroscopy (CRES), is capable of detecting the signal a single electron excites in a waveguide as it its magnetically trapped inside. In the history of tritium based neutrino mass experiments this technique is unique, and presents an entirely complimentary approach to that used at KATRIN. Based as it is on a frequency measurement, the technique shows great promise to mature into an extremely high precision form of electron spectroscopy, with many applications throughout nuclear physics.

The experimental efforts of the Neutrino Physics Group at MIT center primarily around the exploration of neutrino mass and its significance within the context of nuclear physics, particle physics, and cosmology. The group has played a prominent role in the Sudbury Neutrino Observatory, a neutrino experiment dedicated to measure neutrino oscillations from 8B neutrinos created in the sun. The group is now focusing its efforts in the measurement of the neutrino mass directly via the use of tritium beta decay. The MIT group has primary responsibilities in the Karlsruhe Tritium Neutrino mass experiment, expected to begin data taking by 2013. Specifically, the MIT group is responsible for the design and development of the global Monte Carlo framework to be used by the KATRIN collaboration, as well as responsibilities directly associated with the construction of the focal plane detector. In addition, the MIT group is sponsoring a new research endeavor for neutrino mass measurements, known as Project 8, to push beyond the limitations of current neutrino mass experiments.

Reviews the current state of knowledge of neutrino masses and the related question of neutrino oscillations. After an overview of the theory of neutrino masses and mixings, detailed accounts are given of the laboratory limits on neutrino masses, astrophysical and cosmological constraints on those masses, experimental results on neutrino oscillations, the theoretical interpretation of those results, and theoretical models of neutrino masses and mixings. The book concludes with an examination of the potential of long-baseline experiments. This is an essential reference text for workers in elementary-particle physics, nuclear physics, and astrophysics.

The Project 8 experiment aims to measure the electron neutrino mass by obtaining and analyzing [beta] spectra from tritium decay. Using an inferential model of the experiment's anticipated data, I evaluate its projected sensitivity to certain parameters of interest. I focus on the precision and accuracy with which Project 8 can expect to resolve the [beta]-decay spectrum's endpoint in an upcoming stage of the experiment. I also present an initial prediction of Project 8's eventual expected sensitivity to the electron neutrino mass. This analysis involved generating and analyzing [beta]-decay spectral data using a model implemented in Stan, a platform for Bayesian statistical inference. The sensitivity analysis was designed to account for the anticipated distribution of results (mass and endpoint measurements) produced by the potential variation in a number of physical and experimental parameters. In addition, the method used here allows for a calibration of the consequences of inferences and decisions made in reaching those results. I find that, using one year of Project 8 Phase II data, the T2 endpoint can be resolved within a 13.7 eV window (90% C.I.) with 62% coverage (or accuracy), corresponding to a 4.1 eV posterior standard deviation. Preliminarily, using one year of Phase IV data, the electron neutrino mass can be resolved within a 0.051 eV window (90% C.I.) with 56% coverage. I also outline a way that model-based sensitivity procedures and calibration of inference can be extended to the neutrino mass hierarchy problem.