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A systematic theoretical and experimental study on a 35-GHz 45-kV third-harmonic gyrotron with a permanent magnet system is presented in this paper. A complex cavity with gradual transition and a diode magnetron injection gun (MIG) are employed in the gyrotron. A self-consistent field nonlinear theoretical investigation and numerical simulation for electron beam interaction with RF fields are given. The diode MIG is simulated numerically utilizing our code in detail. The permanent magnet system provided the maximum axial magnetic field of about 4.5 kG in the cavity region of the gyrotron. The Ka band third-harmonic complex cavity gyrotron with a permanent magnet system has been designed, constructed, and tested. A pulse output power of 147.3 kW was obtained at a beam voltage of 45 kV with beam current of 32.2 A, corresponding to an efficiency of 10.2%.