Abstract
This paper presents a self-consistent nonlinear theory of the current and energy modulations when an electron beam propagates through an inductively-loaded wide gap cavity. The integro-differential equations are obtained to describe the modulation of the beam current and kinetic energy. A relativistic klystron amplifier (RKA) model is introduced, which uses an inductively-loaded wide gap cavity as an input cavity. And a numerical code is developed for the extended model based on the equations, from which some relations about the modulated current and modulated energy are numerically given.
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