Gyrotron-type amplifiers are being developed for various applications requiring high power in the millimeter wavelength range. Calculations of the optimal designs of gyrotron traveling wave tubes (gyro-TWTs), presented in the article, were carried out using the Gyro-K computer program using a coordinate transformation technique, which made it possible to significantly reduce the calculation time of gyroresonance devices by reducing the three-dimensional problem of excitation of an irregular waveguide to a one-dimensional one. Two options for creating a gyro-TWT using the TE02 wave mode are considered: the first one is operating at the first harmonic of the gyrofrequency, the second is a frequency multiplier. The achievable characteristics of devices in the terahertz frequency range are presented, such as gain bands, efficiency, gain factors and distributions of high-frequency fields in longitudinal and transverse sections. The gyro-TWT frequency multiplier has a gain bandwidth of 7.2 %, an efficiency of 17 %, and a gain of 30 dB.