Analytic solution for the cyclotron radiation of an electron in a simple harmonic magnetic trap

The Project 8 collaboration is aiming to measure the neutrino mass with the tritium endpoint method using the CRES (Cyclotron Radiation Emission Spectroscopy) technique. In the tritium endpoint method for direct neutrino mass measurement, the neutrino mass is inferred from the distortion of the beta-electron energy spectrum near the endpoint. In CRES, the energy of a beta-electron is measured through the frequency of the cyclotron radiation emitted by the electron when it is magnetically confined in a bottle trap. For an ideal magnetic trap configuration where the field map follows a parabolic function (i.e. a harmonic trap), we found the system has analytic solutions. In this talk, we will present the solution and show that the cyclotron radiation of an electron in a simple harmonic magnetic trap is a nice example problem for a graduate electromagnetism course.