He6-CRES: Cyclotron Radiation of Relativistic Particles in a Waveguide*

Cyclotron Radiation Emission Spectroscopy (CRES) is a modern technique for high-precision beta spectroscopy, in which the energy of an $e^pm$ in an external magnetic field is measured via the frequency of the emitted cyclotron radiation ($f_ extrm{c}$). The He6-CRES experiment aims to use CRES for discovery-level sensitivity to Fierz interference by high-resolution $e^pm$-decay measurements of ${}^{19} extrm{Ne}$ and ${}^6 extrm{He}$. 

In addition to its primary physics objective, the experiment provides a novel experimental window into the radiation of relativistic charged particles in a waveguide via the chirp-rate ($ extrm{d} f_ extrm{c}/ extrm{d}t$) of cyclotron radiation signals. Characterizing this phenomenon is critical for accurate energy measurements across high-endpoint beta spectra. We show numerical and experimental evidence that CRES chirp-rates for highly-relativistic betas are consistent with the free-space Larmor formula, scaling with the Lorentz factor of the underlying beta as $gamma^4$. We also briefly discuss the potential implications regarding detection efficiency and energy resolution given this more comprehensive model for CRES signals in a waveguide.