Numerical analysis of one dimensional nonlinear theoryin relativistic klystron amplifier

The integrodifferential equation of instantaneous current and beam kinetic energy are presented. The relationship among the normalized beam current, the kinetic energy of the beam and the normalized distance are calculated using the Matlab-based numerical method including the progressive deduction method, the central difference method and the trapezoidal integration. The normalized factor based on conservation of charge is introduced as well. Finally, the mode strength versus the propagation distance is included.