Towards CRES-Based Non-destructive Electron Momentum Estimation for the PTOLEMY Relic Neutrino Detector

Abstract: The novel electron spectrometry method proposed by the PTOLEMY relic neutrino experiment requires a real-time, non-destructive estimate of the parallel and transverse momentum splits of tritium $\beta$-decay electrons. The collaboration has proposed to obtain this estimate using cyclotron-radiation emission spectroscopy (CRES), in which the kinetic energy of a charged particle is determined by measuring the relativistic frequency shift of the cyclotron radiation emitted by the particle in a magnetic field. However, no suitable approach to extract this information in a non-destructive manner has been developed to date. In this paper, we characterize the performance of a configuration that can be feasibly integrated directly into the existing design for the transverse drift filter proposed by the PTOLEMY collaboration. We study a geometry incorporating a cavity resonator to enhance a ${\sim}\mathcal{O}(1) \hspace{1mm}\mathrm{fW}$ cyclotron radiation signal and derive key features of the expected observed radiation specific to our radio-frequency (RF) tracking configuration. We estimate the performance of our design using electromagnetic simulations and propose a general signal reconstruction algorithm capable of matching an observed signal to electron kinematic parameters. The projected signal-to-noise ratio (SNR) of this technique suggests that a non-destructive RF tracking system based on an array of these components as building blocks is applicable for extracting the kinematic parameters of tritium endpoint electrons to the precision required for the PTOLEMY experiment.