Abstract-In this paper, we present the current status and both the ongoing investigation and the continuous improvements to the operational performance of a unique gyrotron, which is built using a 20 T superconducting magnet and holds a world record of 10 W THz wave generation at the highest frequency (1.08 THz) in continuous wave (CW) operation. Additionally, it has demonstrated highpurity single-mode generation on a sequence of modes that cover a wide range from sub-THz to THz frequencies at both fundamental and second-harmonic resonances of the electron cyclotron frequency. As an illustration, the measurements of the observed radiation patterns of eight output modes radiated from a currently used resonant cavity with a linear up-taper are presented and compared with the corresponding patterns simulated by scattering matrix calculations. A new design of an optimized cavity with a nonlinear up-taper, which improves further the mode purity of the generated output radiation has been proposed and is currently being implemented as a replacement of the existing resonator. The overall operational performance and the output characteristics of this gyrotron (called FU CW III in accordance with the nomenclature adopted at FIR UF Center) make it a versatile and appropriate source of coherent CW radiation for many novel applications in the fields of high-power THz science and technologies.