Terahertz and sub-terahertz science and technology are promising topics today. However, it is difficult to obtain high power source of terahertz wave. In this paper, the mode competition and beam-wave interaction in a gradually tapered cavity are studied to achieve high efficiency of a 0.4THz second harmonic gyrotron in practice. In order to attain high power and stable radiation, the TE32,5 mode is selected as the operating mode of the desired gyrotron to realize single mode oscillation. The issues of studying on the high-order mode gyrotrons are solved effectively by transforming the generalized telegraphist's equations. The efficiency and output power of the gyrotron under different conditions have been calculated by the code, which is based on the transformed equations. Consequently, the results show that single mode second harmonic radiation with power of over 150 kW at frequency of 0.4 THz could be achieved.

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