Three-wave parametric processes in electron beams

It was shown by Zadorozhnyi and Fedorchenko (1980) that there exist five different types of three-wave parametric processes, the one corresponding to the BWT process (type V) being the best understood. The present study shows that all five types of three-wave parametric interaction will occur when an electromagnetic wave interacts parametrically with a space charge wave in a relativistic electron beam. It is noted that some types, corresponding to the interaction of a fast space charge wave at the sum frequency omega(2) + omega(3) with an EM wave, can occur only when there is field retardation.