This study investigates the interaction between the relativistic electrons and the waves in cavities with fixed field profiles. Both the transverse electric (TE) and the transverse magnetic (TM) cavity modes are examined, including three first-axial modes, TE011, TM011, and TM111, and two zero-axial modes, TM010 and TM110. The first-axial modes have the same resonant frequency, so a direct comparison can be made. By sweeping the electron pitch factor (α) and the electron transit angle (Θ), the optimal converting efficiency of TM modes occurs at α = 1.5 and Θ = 1.5π, unlike the TE mode of α = 2.0 and Θ = 1.0π. The converting efficiencies of both the first-axial TM modes are much lower than that of TE011 mode. The starting currents of TM011 and TM111 modes are four times higher than that of TE011 mode, indicating that these two TM modes are very difficult to oscillate. This evidences that under the traditional operating conditions, the TM-mode gyrotrons are insignificant. However, the two unique, zero-axial TM modes have relatively high converting efficiency. The highest converting efficiency of TM110 is 27.4%, the same value as that of TE011 mode. The starting currents of TM110 mode and TE011 mode are at the same level. The results suggest that some TM-mode gyrotron oscillators are feasible and deserve further theoretical and experimental studies.

This study examines the transverse magnetic (TM) waveguide modes, which have long been considered as the unsuitable ones for the operation of the electron cyclotron maser. The beam-wave coupling strength of the TM modes, as expected, is found to be relatively weak as compared with that of the transverse electric (TE) waveguide modes. Unlike TE modes, surprisingly, the linear behavior of the TM modes depends on the sign of the wave number kz. The negative kz has a much stronger linear efficiency than that of the positive kz. The bunching mechanism analysis further exhibits that the azimuthal bunching and axial bunching do not compete but cooperate with each other for the backward-wave operation (negative kz). The current findings are encouraging and imply that TM modes might be advantageous to the gyrotron backward-wave oscillators.

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