Propagation in Periodic Electron Beams

Abstract

A small-signal analysis of smooth electron beams with periodic variations in their dc parameters reveals the existence of infinite sets of space harmonics of the fast and slow space-charge waves. For a finite beam coupling between the space-charge waves and field waves exists at an infinite number of frequencies. The periodicity of a beam has a very small effect on the space-charge wave propagation constants. Velocity-jump, rippled-stream, and rippled-wall amplification are shown to result from coupling between fast and slow space-charge waves of adjacent harmonics. The periodicity of an electron beam will have negligible effect on most conventional traveling-wave devices. Although the frequency dependence of the amplitudes of the beam harmonics may introduce difficulties in some devices, this dependency may also be made use of in a variety of ways. Beam harmonics make millimeter-wave interactions possible in smooth circuits, but practical devices at these frequencies will probably be limited to those employing positional periodicity of the beam.