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In this article, the design of a fourth-harmonic gyrotron with 1-kW-level output power at 1 terahertz (THz) is presented. A unique advantage of this design is that, with a well-optimized magnetic-cusp large-orbit electron gun, the designed gyrotron can operate from first-harmonic to fourth-harmonic in multiple discrete bands by varying the confining magnetic field strength. By carefully balancing the competing modes, the gyrotron can be tuned to operate at six candidate modes, including TE1,2 for fundamental harmonic, TE2,3 and TE2,4 for second-harmonic, TE3,5 and TE3,6 for third-harmonic, and TE4,8 for fourth-harmonic interactions. As the main operating mode, the TE4,8 can generate a peak output power of 1.68 kW, with an output efficiency of about 2.1%, and a magnetically controlled frequency tuning range of about 1.5 GHz around 1 THz. The impact of the longitudinal nonuniformity of the cavity at high-harmonic interaction was also studied. It shows that a radial tolerance of several micrometers will significantly elevate the start-oscillation current and deteriorate output performance. This design is to produce a THz source with ultra-wideband tuning capability ranging from the submillimeter-wave to 1-THz bands. [ABSTRACT FROM AUTHOR]

High-quality axis-encircling electron beam is essential to drive a high-harmonic gyrotron. A magnetic cusp gun that can generate a low-spread axis-encircling electron beam at an extremely high magnetic-compression ratio was developed for a 1-THz fourth-harmonic gyrotron toward continuous-wave operation. The optimized gun could generate an axis-encircling electron beam with 80-kV voltage, 1-A current, and a nearly constant pitch factor of about 1.5 in a wide range of magnetic field strength. The transverse velocity spread was less than 2.1% and the guiding center radius was $26.6 ~\mu \text{m}$. The design was verified by using MAGIC, EGUN, and CST simulations and good agreements were achieved. [ABSTRACT FROM AUTHOR]