  The shape of the beta decay energy distribution is sensitive to the mass of
the electron neutrino. Attempts to measure the endpoint shape of tritium decay
have so far seen no distortion from the zero-mass form, thus placing an upper
limit of m_nu_beta < 2.3 eV. Here we show that a new type of electron energy
spectroscopy could improve future measurements of this spectrum and therefore
of the neutrino mass. We propose to detect the coherent cyclotron radiation
emitted by an energetic electron in a magnetic field. For mildly relativistic
electrons, like those in tritium decay, the relativistic shift of the cyclotron
frequency allows us to extract the electron energy from the emitted radiation.
We present calculations for the energy resolution, noise limits, high-rate
measurement capability, and systematic errors expected in such an experiment.
