Larmor power limit for cyclotron radiation of relativistic particles in a waveguide

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>6</mml:mn> </mml:msup> <mml:mtext>He</mml:mtext> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mn>19</mml:mn> </mml:mrow> </mml:msup> <mml:mtext>Ne</mml:mtext> </mml:mrow> </mml:math> . 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, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> <mml:mtext>c</mml:mtext> </mml:msub> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> </mml:mrow> </mml:math> . 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>±</mml:mo> </mml:msup> </mml:mrow> </mml:math> as γ 4 . This hypothesis is corroborated with experimental CRES slope data.