Antenna arrays for neutrino mass measurements with cyclotron radiation emission spectroscopy

Cyclotron Radiation Emission Spectroscopy (CRES) is a technique for precision measurements of kinetic energies of charged particles, pioneered by the Project 8 experiment to measure the neutrino mass using the tritium end-point method. It was recently employed for the first time to measure the molecular tritium spectrum and place a limit on the neutrino mass using a cubic-centimeter-scale detector. Future direct neutrino mass experiments are developing the technique to overcome the systematic and statistical limitations of current detectors. This paper describes one such approach, namely the use of antenna arrays for CRES in free space. Phenomenology, detector design, simulation, and performance estimates are discussed, culminating with an example design with a projected sensitivity of ${m}_{\ensuremath{\beta}}<\phantom{\rule{4pt}{0ex}}0.04\phantom{\rule{0.28em}{0ex}}\mathrm{eV}/{c}^{2}$. Prototype antenna array measurements are also shown for a demonstrator-scale setup as a benchmark for the simulation. By consolidating these results, this paper serves as a comprehensive reference for the development and performance of antenna arrays for CRES.