$^6$He-CRES: How to interpret the cyclotron radiation of betas in the $^6$He-CRES waveguide.*

The $^6$He-CRES experiment at the University of Washington CENPA measures the $^6{\rm He}$ beta decay energy spectrum by measuring the cyclotron radiation of magnetically trapped betas in a waveguide. Radiation in the TE$_{11}$ mode propagates down the guide, coupling to low noise amplifiers. The output of the amplifiers is mixed down to frequencies below about a GHz and then a Fourier transform is performed and a spectrogram recorded. The resulting spectrogram contains high power bins forming tracks that increase in frequency over time. The slope of the tracks is determined by the total radiated power, which also includes coupling to higher harmonic modes outside of the observation bandwidth. In this talk I will discuss how an understanding of guide and cavity modes that betas can excite in our system allows for more accurate predictions of how slopes and observed power change with frequency, field, and position in the guide.