Analytical theory of prepulsed electron beam propagating through a drift tube

Summary form only given, as follows. A self-consistent nonlinear theory of the current and energy modulation in a prepulsed electron-beam train propagating through a grounded drift tube is developed. The theory is based on the assumption that the beam current is highly modulated before it enters the tube. A closed integrodifferential equation for the beam current is obtained, assuming that the beam current is a function of time t and propagation distance z. Properties of the current and energy modulation are investigated from this integrodifferential equation for a broad range of system parameters. Magnitudes of the energy and current modulation are determined in terms of the strength and frequency of initial current modulation, geometric configuration, beam intensity and kinetic energy of the beam. Linearization of this integrodifferential equation gives a simple wave equation, which exhibits propagation of forward and backward space-charge waves. Spatial periodic length of the space-charge waves is proportional to the beam velocity and inversely proportional to the square-root of beam intensity. Simple analytical expression of current modulation is described in terms of a sum of the forward and backward space charge waves.