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Gyrotron devices are based on the principle of the relativistic electron cyclotron maser and capable of generating high-power coherent radiation in the millimeter-THz wave range, which are important in imaging, communication, biomedicine. However, traditional particle-in-cell software, simulating the beam-wave interaction of terahertz gyrotron devices, is of huge resource consumption due to massive particles and grid-size dependency of wavelength. Specialized theories need to be developed. In this paper, frequency-domain and time-domain nonlinear theories are introduced. Based on macro-particle assumption and 1-D analytic approximation, the resource consumption is dramatically reduced. The results of two theories coincide with each other. The accuracy of simulation result is demonstrated by comparison with particle-in-cell software. The investigation presented in this paper provides efficient and accurate method to analyze the terahertz gyrotron devices.