[[abstract]]Summary form only given. The injection locking technique has been applied on the experiment of gyrotron backward wave oscillator (gyro-BWO) for phase control and spectral purity. The efficiency of the gyro-BWO was considerably enhanced when it was locked by an injected signal, which has never been thorough examined in the locked oscillator. Therefore, the physics underpinning is still unclear. A stationary model with modified boundary conditions was applied on studying the phenomena. The numerical results show that the injected power is absorbed by the electron beam when the oscillator is locked, then relative phases between the electrons and the wave are adjusted to increase the time the bunched electrons staying in the phase of losing energy, thus enhance the efficiency of the gyro-BWO. The various detuning determined by tuning the beam voltage or the external magnetic field is another critical factor to affect the efficiency enhancement of the locked oscillators, in addition to the power and frequency of the injected signal. The detailed results will be presented in the paper
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