A comparison between a self-consistent nonlinear theory and particle simulation of current modulation in relativistic klystron amplifiers

This paper presents a self-consistent nolinear theory and gives the integrodifferential equations of the instantaneous current and the beam kinetic energy. For two groups of typical parameters, the coefficients of current modulation versus the propagation distance were calculated by the numerical method and 2D-PIC code. The kinetic energy of the beam and the mode strength Cn versus the propagation distance were also calculated and analyzed. The results of the simulation are consistent with the results of the nonlinear theory.