A time-dependent nonlinear theory for complex cavity gyrotron is presented in this paper. The theory includes generalized telegrapher's equations and electron motion equations, which are deduced in detail. A calculation code for the self-consistent nonlinear beam-wave interaction is developed based on the presented theory. Using the code, a 94 GHz complex cavity gyrotron operating in TE021-TE031 modes is thoroughly studied. Numerical results show that an output power of 180 kW, about 36% efficiency is achieved with a 50 kV, 10 A electron beam at a focused magnetic field of 1.78 T and a beam velocity ratio of 1.65. The results from MAGIC simulation are also given and an output power of 192 kW, 38.4% efficiency is obtained. This tells the agreement with these two simulation codes.
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