Electron beam propagation with premodulated energy and current

This paper considers an electron beam whose energy and current are simultaneously premodulated at the injection point of a drift tube. A theoretical model is developed for the subsequent current and energy modulations which propagate downstream. A closed integrodifferential equation for the normalized beam current is obtained in terms of time and propagation distance. To make the nonlinear current modulation analytically tractable, a small signal theory is introduced into the modulation calculation. The current modulation in the linear regime is a linear combination of the forward and backward waves of the initial current and energy modulations. The downstream energy modulation is also expressed by a linear combination of the forward and backward waves of the initial current and energy modulations. It is shown that the initial energy modulation is a very effective means for downstream current modulation. Numerical data even for a large initial current and energy modulations agree reasonably well with analytical results predicted by the linear theory