Fig. 1. （a） The conventional interaction unit with the E_z field across the λ_g0/2 length，（b） two such units connected along the x-direction to form an integrated-two-unit circuit，（c） the integrated-three-unit circuit formed by connecting three such units along the x-direction，and （d） the proposed integrated-two-unit circuit with specific coupling cavities for power extraction

Fig. 2. The schematic drawing of the integrated-two-unit circuit with two output ports located on both sides of the two symmetrical coupling cavities

Fig. 3. The effect of the beam perveance on g_e and Q_a

Fig. 4. （a） The E_z field along the axis of tunnel 1 and 2，and （b） the three-dimensional （3-D） model of the input cavity with the 3-D distribution of the E_zfield

Fig. 5. （a） The effect of M²R/Q on the beam voltage，and （b） the effect of the absorption efficiency η on the frequency of the input signal of the input cavity loaded by the two beams with the voltage of 45 kV and each current of 5.6 A

Fig. 6. （a） The group delay τ_g from two output ports，and （b） the absolute amplitude of the normalized E_z field along the axis of the y-direction of the output cavity

Fig. 7. （a） The shape of a bunch current by the Gaussian model，and （b） the effect of the ratio of the critical parameter σ to Δt，on the output power extracted from the output cavity and the electronic efficiency

Fig. 8. （a） The waveform of the bunch currents corresponding to the output power of 200 kW （Beam 1 and 2 represent specifically the pre-modulated beam 1 and beam 2），and （b） the output signal obtained from port 1 and 2

Fig. 9. FFT of the bunch currents in the gap centers beam 1 and beam 2 located （I₀ is the DC current of the beams and I₁ is the current of the fundamental harmonics of the two bunches）

Fig. 10. The overall interaction circuit of the designed klystron with the E_z field

Fig. 11. The effect of the input power on the output power and the gain of the klystron

Fig. 12. The effect of the frequency of the input signal on the output power and the electronic efficiency of the klystron

Fig. 13. （a） The output power versus time，（b） the FFT amplitude of the input signal，and output signals from port 2 and port 3 （Output signal 1 and 2 are extracted from port 2 and port 3）

Fig. 14. The beam trajectories

Fig. 15. The phase space of the electrons

Fig. 16. The effect of the height of the coupling cavity on the frequency and Q₀ value of the buncher cavity