An exact small-signal analysis of the interaction of two electron streams in a finite longitudinal magnetic field

Using the mathematical field analysis of a companion paper in this issue, solutions are found for the wave interactions occurring in several different configurations of drifting electron beams in a longitudinal magnetic field. First, wave interactions are found for both single and double beams of infinite extent. Next, single and double beams completely filling a cylindrical waveguide are analyzed. Finally, examination is made of single and double beams which only partially fill the waveguide. The resulting wave interactions are described with ω-β (dispersion) diagrams. Since only the small-signal approximation is made, space-charge waves, cyclotron waves, and waveguide waves are all present in this analysis.