The radiation from a modulated electron beam, such as that produced in
a radio-frequency accelerator, passing through a magnetic undulator i
s analyzed. We show that in a waveguide FEL, this may lead to an emiss
ion of a significant amount of coherent radiation in the far infrared
to millimeter wave range. A simple and powerful method of calculating
the spectral distribution of the radiated power is presented along wit
h an analysis of the gain and the saturated power. The experimental re
sults of spontaneous emission measurements on an RF driven FEL are pre
sented and compared to theoretical predictions.