Exact treatment of spontaneous emission in helical and solenoidal magnetic field

In this paper we discuss the spectral properties of the radiation emitted by electrons moving in helical undulators and solenoids. The analysis is exact, in the sense that the electron beam is not assumed to be ultrarelativistic but the far-field condition is still retained. We also discuss the low-energy corrections, the limits of validity of the usual approximations and the relevance of our results to gyrotron-type devices