TRISTAN Data Acquisition Development and Systematics Studies for KATRIN

Although neutrinos are the most abundant particles in the universe, some of their properties remain unknown to us, in part due to their small interaction cross sections.Model-independent measurements of neutrino properties can be performed through precision measurements of electrons produced in $\upbeta$-decays.The KArlsruhe TRItium Neturino (KATRIN) experiment places the most stringent laboratory upper limit on the effective electron neutrino mass, $m_{\nu} < \SI{0.45}{\electronvolt} \, (90\% \, \text{C.L.})$, through an integral measurement of the tritium spectrum.Near the end of $2025$, KATRIN will reach its design goal of 1000 days of data taking and become a systematics dominated experiment, limited by source effects and background electrons.After this, the TRISTAN detector upgrade is slated to use the KATRIN beamline to search for keV scale sterile neutrinos through a differential measurement of the $\upbeta$-decay spectrum with nine 166-pixel silicon drift detectors.Statistical sensitivities to sterile-to-active mixing of $\sin^2(\theta) = 10^{-6}$ are projected within months of operation. This dissertation outlines the development and testing of the Data Acquisition (DAQ) system for TRISTAN that will enable the precision readout of $\mathcal{O}(1000)$ pixels operating at $100$ kcps each, called the Remote Analog-to-Digital Conversion (RADC) DAQ.Waveform readout and filtering performance of an RADC demonstrator are presented along with the design of the TRISTAN RADC system. Systematic effects that distort the measured $\upbeta$-decay spectrum weaken the ability to constrain the sterile neutrino mixing. An updated modeling of ADC non-linearity induced distortions is developed along with methods of distortion mitigation.Operation of the DAQ system with the proposed mitigation strategies is shown to decrease the projected sensitivity to $\sin^2(\theta)$ by a factor of less than 1.002, which is negligible in comparison to dominant systematics that can decrease the sensitivity by factors of $\mathcal{O}(10)$. Additional studies of systematics in the KATRIN experiment are presented, including the reduction of background and increased statistical power of a potential differential measurement of the neutrino mass afforded by performing a time-of-flight measurement with an electron tagger.Limitations to the technologies that are applicable to non-destructive measurement of passing electrons are discussed, along with a proposal of utilizing cyclotron radiation, inspired by recently demonstrated Cyclotron Radiation Electron Spectroscopy measurements.