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

TL;DR

This paper investigates the power limits of cyclotron radiation emitted by relativistic particles in waveguides, combining theoretical predictions with experimental data to understand radiation behavior for high-energy particles.

Contribution

It provides an analytic model for cyclotron radiation power in waveguides and validates it with experimental measurements, advancing understanding of relativistic particle radiation in these structures.

Findings

Analytic predictions align with the Larmor formula for power scaling.

Cyclotron radiation power scales with the Lorentz factor as γ^4.

Experimental data supports the theoretical model.

Abstract

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.