Decay of Space‐Charge Waves on Electron Beams

摘要

The decay of space‐charge waves with distance is observed in an electron beam with a velocity spread. This effect has previously been attributed to spatial Landau damping. We extend Landau's theory to include finite diameter electron beams and calculate the steady‐state damping of the fast and slow space‐charge waves using measured axial velocity distributions. For a density modulated beam injected from a shielded cathode, it is found that the fast wave does not exhibit Landau damping, while the slow wave is damped of the order of 0.1 dB per plasma wavelength. It is concluded that the large initial damping observed by Mihran is due to a ballistic or free‐streaming process, and is not primarily due to Landau damping as calculated for the steady‐state regime.