Damping of Waves in Electron Beams

Abstract

The damping of plasma oscillations in velocity-modulated electron beams with large-velocity spreads has been analyzed. It is shown that the observed spatial decay of rf current along the beam (a loss of the fundamental interference pattern) can be characterized by the exponential decay of one of the space-charge waves. The exponential-decay rates for this wave are extracted from the data of over 50 experiments which exhibited a spatial damping. The parameters of the measured ``near-Maxwellian'' distribution of velocities (cutoff with a slow ``tail'') associated with each decay lead to the characterization of an equivalent temperature for the beam condition of each experiment. This is used to calculate the damping-determining parameters (ratio of plasma wavenumber to Debye wavenumber, k/kD, or equivalent). The experimentally observed damping rates for a variety of beam conditions are found to vary with k/kD in a consistent fashion and are also comparable with rates extracted from electron-beam theories. This is interpreted as a demonstration of a damping mechanism without collisions, and leads to the ascription of the decay as Landau damping in electron beams. Further experiments, in which the decay is observed as a function of the driving amplitude of the electron-beam plasma oscillations, are studied as possible evidence of Landau damping in electron beams.