Abstract The conditions of the steady operation of the amplifiers are analyzed based on the characteristics of beam-wave interactions of harmonic gyroklystron amplifiers in this paper. The optimized design parameters of the circuit of the beam-wave interactions are obtained by simulation and calculation of the beam-wave interactions of a Ka-band, second harmonic, three cavities gyroklystron amplifier. The results show that this gyroklystron amplifier can produce an output peak power of over 250kW with more than 21dB gain and 23% maximum efficiency at 35GHz with a 70kV, 15A electron beam, and a 3dB bandwidth of about 120 MHz. This work is beneficial to the actual engineering design of the Ka-band second harmonic gyroklystron amplifier.