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Cyclotron radiation emission spectroscopy (CRES) is a modern technique for high-precision energy spectroscopy, in which the energy of a charged particle in a magnetic field is measured via the frequency of the emitted cyclotron radiation. The He6-CRES collaboration aims to use CRES to probe beyond the standard model physics at the TeV scale by performing high-resolution and low-background beta-decay spectroscopy of $ {} ^6\textrm{He}$ and $ {} ^{19}\textrm{Ne}$ . Having demonstrated the first observation of individual, high-energy (0.1–2.5 MeV) positrons and electrons via their cyclotron radiation, the experiment provides a novel window into the radiation of relativistic charged particles in a waveguide via the time-derivative (slope) of the cyclotron radiation frequency, $\mathrm{d}{f}_\textrm{c}/\mathrm{d}{t}$ . We show that analytic predictions for the total cyclotron radiation power emitted by a charged particle in circular and rectangular waveguides are approximately consistent with the Larmor formula, each scaling with the Lorentz factor of the underlying $e^\pm$ as γ ^4 . This hypothesis is corroborated with experimental CRES slope data.