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Terahertz (THz) gyrotrons can operate with a lower applied magnetic field in harmonic operation, but the weakened harmonic interactions in harmonic gyrotrons can introduce serious challenges when mode competition occurs. The use of an axis-encircling electron beam can greatly alleviate mode competition in a harmonic gyrotron. In this paper, we study axial modes for third-harmonic ${\mathrm{\text{TE}}}_{3,7}$-mode large-orbit gyrotrons. Simulation results reveal that the minimum current for oscillation to begin in each axial mode in the gyrotron regime is associated with a specific range of applied magnetic field. To avoid mode competition, tapered applied magnetic fields and waveguide radii are employed to enhance the high-order axial modes and suppress the low-order axial modes. Furthermore, spurious transverse modes in a THz gyrotron are discussed below. A stable third-harmonic ${\mathrm{\text{TE}}}_{3,7}$-mode large-orbit gyrotron at the third-order axial mode is predicted to yield peak output power of 6.5 kW at 768.1 GHz with an efficiency of 10% for a 75-kV, 0.85-A electron beam with an axial velocity spread of 3%.

The central electron temperature of more than 15 keV is achieved in LHD as a result of increasing the injection power and the lowering the electron density. Such collision-less regime is important from the aspect of the neoclassical transport and also potential structure formation. The creation of the high energy electrons and the transport of them can trigger the potential structure formation. Evidences of the presence of high energy electrons are indicated from hard X-ray PHA, and the discrepancy between the stored energy and kinetic energy estimated from Thomson scattering. ECE spectrum in such low density regime under the presence of high energy electrons are discussed by comparing the calculated one that solves the radiation transfer equation. Such investigation might be used for the estimation of high energy electrons as an inverse process of the ECRH.