Cyclotron Radiation Signal Characterization in Resonant Cavities for the Project 8 Neutrino Mass Experiment

TL;DR

This work develops a comprehensive analytic framework for modeling cyclotron radiation from electrons in resonant cylindrical cavities, focusing on how the particle’s three-dimensional motion couples to TE/TM/EI cavity modes and how this coupling shapes the emitted power and spectrum. By deriving explicit expressions for cavity mode amplitudes, power transfer, and the resulting spectral content—including sidebands from axial motion and parity effects in magnetic-box traps—the authors provide a detailed map from cavity design to observable CRES signals. The paper also constructs a complete noise model, integrating thermal cavity fluctuations with a realistic RF readout chain to quantify SNR and optimize detector performance. Taken together, the framework informs cavity design and readout strategies for Project 8 and general cavity-based charged-particle spectroscopy, with applicability to large-volume detectors and other precision physics experiments reliant on cavity-enhanced emission.

Abstract

Many experimental methods in physics require understanding radiation from single particles into non-trivial electromagnetic mode structures. Such characterization is critical for Cyclotron Radiation Emission Spectroscopy (CRES), an advancing new measurement technique that has the potential to greatly benefit fundamental physics measurements. In CRES, charged particles emit cyclotron radiation at frequencies that provide their energy measurement. As a notable example, the Project 8 experiment aims to kinematically infer the neutrino mass by measuring the energies of electrons emitted in tritium beta decay using CRES. In near-term realizations of Project 8, resonant cylindrical cavities will be used for CRES readout, in a configuration with a magnetic field oriented along the symmetry axis, and electrons following helical cyclotron trajectories confined to the cavity interior. The physics of electromagnetic radiation in these environments is complicated, since it involves both the motion of the emitting particle and the mode structure imposed by the cavity. In this work, we derive and validate an analytic model for how an oscillating, trapped electron radiates into cavity modes, and the power and frequency content of the radiation that can be read out from these events. These results can be used to guide the design of cavities for future CRES and other experiments.

Figures (10)

• Figure 1: A cartoon of a cavity CRES experiment, showing a cross-section of the cavity's cylindrical symmetry axis. The electron is emitted with pitch angle $\theta_p$ relative to the magnetic field at the trap center and undergoes axial motion (parallel to the cavity's symmetry axis). The electron is bound by the magnetic bottle field produced by the two pinch trapping coils near the ends of the cavity. The heat map is the electric field magnitude of a cylindrical TE$_{011}$ mode.
• Figure 2: Sketch of the cavity volume and port boundaries. $S_0$ is the surface of the cavity walls (black outline), and $S_{i>0}$ are the cavity readout ports (each white dashed line). Each labelled section of the cavity boundary has a distinct impedance and quality factor. The cavity volume is enclosed in the gray dotted line. The background electric field pattern is representative of a cylindrical TE$_{011}$-like mode that is strongly coupled to multiple readouts.
• Figure 3: Cylindrical cavity of radius $a$ and length $L$. The electron's cyclotron radius is denoted by $\rho_c$ and its guiding center position by $r_0$. The axial motion (along $\hat{z}$) and grad-B drift motion (along $\hat{\phi}$) are shown by the gray line. The depicted period of drift motion is for illustrative purposes and is much less than what is expected in Project 8 experiments.
• Figure 4: Illustration of the parameters used in the Graf Addition Theorem. Here, $O$ is the cavity-centered coordinate system, and $O_1$ is the electron's guiding center. The phase in the guiding center coordinate system is defined relative to the phase in the cavity-centered coordinate system.
• Figure 5: Power radiated into forward/backward propagating (a) TE modes and (b) TM modes in a cylindrical waveguide with radius $a=$ 5.3 mm, up to the sixth harmonic ($p$ in the previous section) of the cyclotron frequency. The convergence properties of the power emitted are further explored in buzinskyLarmorPowerLimit2024. The dashed lines represent the sum of the power lost to possible harmonics of the cyclotron frequency for the first eight TE/TM propagating modes. The solid lines represent the point dipole approximation of ashtariesfahaniElectronRadiatedPower2019, which accounts for the first cyclotron harmonic only.