Harmonic operation is of special significance due to its low magnetic field operation, and the magnetic field of the sth harmonics gyrotron at a given frequency is reduced by a factor of s for operation. By using an interaction circuit with dielectric loaded, the operating parameters of the W band TE02 mode second harmonic gyrotron Traveling-Wave Tube(gyro-TWT) amplifier are determined by analysis of dielectric loaded, mode competition and interaction between electron beam and wave. Nonlinear analysis shows that the amplifier can generate a saturated peak power of 465 kW with a gain of 49 dB at 91 GHz when utilizing a 100 kV, 20 A, α=1.2 electron beam. Based on coupled mode theory, a TE02-TE01 mode converter within a tapered waveguide radius is discussed and a bandwidth about 4 GHz is obtained when the conversion efficiency exceeds 95%.