In this paper, a coaxial gyrotron with a double electron beam is investigated on the ohmic loss, starting current, mode competition, and beam wave interaction. Its beam-wave interaction equation and dependence of the starting current on the static magnetic field and parameter K (the ratio of the current of an electron beam to the total current of a double electron beam) are given. On this basis, a 4 MW 170 GHz coaxial gyrotron with a double electron beam is studied. By the numerical calculation, the influence of K on the starting current is analyzed under a given static magnetic field and at different guiding center radii of the double electron beam. Studies show that the ability of the gyrotron to suppress the mode competition has a relation with the selection of the guiding center radii of the two electron beams. Then, the investigation of a time-dependent multi-mode competition of the gyrotron is performed, which shows that the gyrotron can stably operate in the TE38,18 mode. The results show that by considering the ohmic loss, the gyrotron can operate at 170.4 GHz with the output power of 4.04 MW and the beam-wave interaction efficiency of 35.47% when B = 6.82 T, U = 88 KV, I =129 A, and K = 0.4. Each of the two electron beams in the gyrotron has different beam-wave interaction efficiencies. Compared to the coaxial gyrotron with one electron beam, the beam-wave interaction efficiency of each electron beam in the coaxial gyrotron with a double electron beam has a different increase.

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