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The gyrotron traveling-wave-tube (gyro-TWT) amplifier is a high-power broad-band millimeter-wave amplifier. Its operation at a high harmonic number is of practical importance because the required magnetic field strength can be reduced by a factor of the harmonic number. Although hollow circular waveguides have typically been used as the interaction structure in harmonic gyro-TWTs, spurious oscillations limit their performance. This study investigates the possibility of using coaxial waveguides as the interaction structure in a second-harmonic gyro-TWT. Stability is achieved by applying distributed losses on the outer and inner walls. Simulation results indicate that the distributed losses on the inner wall can suppress specific oscillating modes without deteriorating the performance of the amplifying mode. Under stable operating conditions, simulations indicate that the second-harmonic coaxial gyro-TWT generates a peak power of 293 kW in the Ka-band with 21% efficiency, a saturated gain of 42 dB, and a bandwidth of 1.31 GHz (≈ 4.1%) for a 70-kV 20-A electron beam with an α = 1.0 and an axial velocity spread of 5%.