Larmor Power Limit for Cyclotron Radiation of Relativistic Particles in a Waveguide

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 \(\gamma^4\). This hypothesis is corroborated with experimental CRES slope data.