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A W-band gyrotron travelling wave amplifier (gyro-TWA) with a cusp electron gun and a helically corrugated waveguide is presented. The large orbit electron beam from the cusp gun interacts resonantly with an ideal eigenwave existing in the interaction region based on the cyclotron resonance maser instability. When driven by the 40 keV, 1.5 A electron beam the amplifier was simulated to output a maximum 10 kW (CW) with a 3 dB frequency bandwidth of 90-100 GHz and saturated gain of 40 dB. Linear analysis and numerical simulations of the performance characteristics of the amplifier as well as the input coupler and the output window are presented.