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A second-harmonic TE21 gyrotron traveling-wave tube (gyro-TWT) amplifier with an axis-encircling electron beam is being constructed at the University of California-Davis that is predicted to double the efficiency of our previous 200-kW 12%-efficient magnetron injection gun (MIG) TE21(2) gyro-TWT. Both devices employ a sliced mode-selective circuit to suppress the odd-order azimuthal modes. The new device will avoid the loss in efficiency that is due to off-axis electrons interacting with the resulting linearly polarized mode. The amplifier is predicted by our large signal code to produce 50 kW in Ka-band with 20% efficiency, 30 dB saturated gain, and 3% bandwidth. The 70-kV 3.5-A axis-encircling electron beam with υ⊥/υz = 1.2 and Δυz/υz = 7% will be produced by a Cusp electron gun delivered by Northrop Grumman. The amplifier has been designed using linear theory to provide a 30% safety margin from absolute instability. Distributed loss is added to the first 30.5 cm of the circuit to ensure the device is stable to harmonic gyro-BWO. The last 11.5 cm of the circuit is standard copper to avoid attenuating the wave at high power levels.