Based the mathematic and physical mechanisms of the beam-wave synchronization and coupling in an extended interaction klystron,the coupling coefficient and the beam conductance were calculated.Numerical simulation was done for a Ka-band extended interaction klystron operating in 2π mode by CST-PIC code.The results show the output power of 3.75 kW can be reached with the gain of 34.77 dB and the efficiency of 26.79% at the input power of 1.25 W and the frequency of 35 GHz,under the beam voltage and beam curr...