Time-domain PIC-modeling of the multiple cavity klystron oscillator with delayed feedback

The results of time-domain numerical simulation of a four-cavity klystron oscillator with external delayed feedback using a 1.5D PIC-code are presented. Basic properties of oscillation regimes are studied. With the increase of the beam current self-modulation and transition to chaos via the sequence of period-doubling bifurcations are observed. The results are in good agreement with the theoretical predictions obtained previously for approximate model of the oscillator based on a system of time-delayed differential equations.