Propagation properties of a relativistic electron beam 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. It is shown that the initial energy modulation is a very effective means for downstream current modulation. The downstream energy modulation is also expressed by a linear combination of the forward and backward waves of the initial current and energy modulations. In general, the maximum current modulation occurs at the propagation distance where the energy modulation is minimum. Properties of the current and energy modulations are numerically investigated from the integrodifferential equation for a broad range of system parameters. Numerical data even for a large initial current and energy modulations agree reasonably well with analytical results predicted by the linear theory.