Electron radiated power in cyclotron radiation emission spectroscopy experiments

Abstract

The recently developed technique of Cyclotron Radiation Emission Spectroscopy (CRES) uses frequency information from the cyclotron motion of an electron in a magnetic bottle to infer its kinetic energy. Here we derive the expected radio frequency signal from an electron in a waveguide CRES apparatus from first principles. We demonstrate that the frequency-domain signal is rich in information about the electron's kinematic parameters, and extract a set of measurables that in a suitably designed system are sufficient for disentangling the electron's kinetic energy from the rest of its kinematic features. This lays the groundwork for high-resolution energy measurements in future CRES experiments, such as the Project 8 neutrino mass measurement.

Cyclotron radiation emission spectroscopy signal classification with machine learning in project 8

“…Indeed, in Project 8 Phase I the 32 keV tracks are well described by figure 3 and the three cases above; but the story is very different at 17 keV, where the mainband is almost completely suppressed and we detect only the n=1 sidebands. For further discussion of this effect where the n=1 sideband is visible we refer the reader to section VII of [4]. This exemplifies the powerful influence of the short, and the importance of understanding sideband effects.…”

“…Going forward, we will simply use θ to refer to this minimum pitch angle, rather than the time-varying instantaneous pitch angle θ(t). In fact, there is also a limit to the smallest pitch angle value due to conservation of energy which depends on the ratio of the trap depth and maximum magnetic field, for more on this see [4]. At a nominal 4 mT trap depth the lower bound is about 86°a nd may be higher depending on the chosen geometry.…”

“…At a nominal 4 mT trap depth the lower bound is about 86°a nd may be higher depending on the chosen geometry. A detailed mathematical discussion of trapped electron dynamics and the resultant CRES signal characteristics is outside the scope of this work but may be found in [4]; we refer to their nomenclature for the rest of the paper. There, a phenomenological model is developed using approximate Project 8 magnetic trap geometries to analytically describe the motion of electrons with θ<90°.…”

“…The power spectrum P(ω) is calculated from the Poynting vector in the axial direction, and decomposed as a sum of waveguide modes. For a single mode denoted by λ, we take advantage of the quasi-periodic motion of the electron in the trap to express the power averaged over the axial period with equation (45) in [4], reproduced here:…”

“…The pitch angle dependence of P λ (ω) comes from Ω 0 , Ω a , and in turn k λ ; in particular, the coefficients a n (k λ ) describe the relative strength of each peak in the comb structure. Considerable discussion about these coefficients and their calculation for some models is included in [4].…”